DEPARTMENT OF ELECTRONICS AND

COMMUNICATION ENGINEERING

EC T71 MICROWAVE AND OPTICAL

ENGINEERING NOTES

IV YEAR/ VII SEM

 UNIT 1

Introduction of Microwave devices:

 Microwaves are electromagnetic waves (E.M. waves) having wavelength in the

micron range.
 Though microwave frequencies refer to those from 1GHz to 106GHz but generally
used for those wavelengths measured in centimeters, roughly from 10cm to 1cm(3
to 30 GHz) and the waves having wavelengths less than 1cm corresponds to higher
frequencies(>30 GHz) are called millimeter waves (mm waves).

Microwave Frequencies
Relationship between the frequency and the wavelength of an E.M. wave is
λ f=c

Where,
c - Velocity of electromagnetic radiation, usually called the speed of light.
λ- Wavelength
f- Frequency
Microwave Frequency Band

Designation Frequency range in GHz

HF 0.003 to 0.03
VHF 0.03 to 0.3
UHF 0.3 to 1.0
L-Band 1.0 to 2.0
S-Band 2.0 to 4.0
C-Band 4.0 to 8.0
X-Band 8.0to 12.0
Ku-Band 12.0 to 27.0
K- Band 18.0 to 27.0
Ka-Band 27.0 to 40.0
Millimeter 40.0 to 300
Sub-millimeter 300 and above.
Microwave devices:

E-PLANE TEE
 Model 3061 E - plane tee are series type T - junction and consists of three section of
wave guide joined together in order to divide or compare power levels.
 The signal entering the first port of this T - junction will be equally dividing at second and
third ports of the same magnitude but in opposite phase.

H - PLANT TEE
 Model 3065 H - Plane Tee are shunt type T - junction for use in conjunction with VSWR
meters, frequency - meters and other detector devices.
 Like in E-plane tee, the signal fed through first port of H - plane Tee will be equally
divided in magnitude at second and third ports but in same phase.

MAGIC TEE
 Model 3045 E - H Tee consists of a section of wave guide in both series and shunt
wave guide arms, mounted at the exact midpoint of main arm. Both ends of the section
of wave guide and both arms are flanged on their ends.
 These Tees are employed in balanced mixers, AFC circuits and impedance
measurement circuits etc. This becomes a four terminal device where one terminal is
isolated from the input terminal.

DIRECTIONAL COUPLERS
 Model 6000 series Multi-hole directional couplers are useful for sampling a part of
Microwave energy for monitoring purposes and for measuring reflections and
impedance.

 These consist of a section of Wave guide with addition of a second parallel section of
wave guide thus making it a four port network. However the fourth port is terminated with
a matched load.
 These two parallel sections are coupled to each other through many holes, almost to
give uniform coupling; minimum frequency sensitivity and high directivity. These are
available in 3, 6, 10, 20 and 40dB coupling.

CIRCULATORS
 Model 6021 and 6022 are T and Y types of three port circulators respectively. These are
precisely machined and assembled to get the desired specifications.
 Circulators are matched three port devices and these are meant for allowing Microwave
energy to flow in clockwise direction with negligible loss but almost no transmission in
the anti-clockwise direction.

ISOLATORS
 The three port circulators Model 6021 may be converted into isolators by terminating one
of its port into matched load.
 These will work over the frequency range of circulators. These are well matched devices
offering low forward insertion loss and high reverse isolation.
Gunn diode and its modes of operation:

 A Gunn Diode is considered as a type of diode even though it does not contain any
typical PN diode junction like the other diodes, but it consists of two electrodes. This
diode is also called as a Transferred Electronic Device.
 This diode is a negative differential resistance device, which is frequently used as a low-
power oscillator to generate microwaves.
 It consists of only N-type semiconductor in which electrons are the majority charge
carriers. To generate short radio waves such as microwaves, it utilizes the Gunn Effect.

Fig: Structure of Gunn Diode

Construction of Gunn Diode:

 The central region shown in the figure is an active region, which is properly doped N-
type GaAs and epitaxial layer with a thickness of around 8 to 10 micrometers.
 The active region is sandwiched between the two regions having the Ohmic contacts.
 A heat sink is provided to avoid overheating and premature failure of the diode and to
maintain thermal limits.
 Only N-type material is used, which is due to the transferred electron effect applicable
only to N-type materials and is not applicable to the P-type materials. The frequency can
be varied by varying the thickness of the active layer while doping.

Fig: Gunn Diode

Gunn Effect:

 Gunn-Effect diodes are named after J.B.Gunn, who discovered periodic fluctuations of
current passing through the n-type Gallium Arsenide (GaAs) specimen when the applied
voltage exceeded a certain critical value.
  The Gunn Effect can be defined as generation of microwave power (power with
microwave frequencies of around a few GHz) whenever the voltage applied to a
semiconductor device exceeds the critical voltage value or threshold voltage value.

Fig: Structure of Gunn Diode

 Above some critical voltage, corresponding to an electric field of 2000 – 4000 Volts/Km.
the period of oscillations will be usually inversely proportional to the specimen length and
closely equal to the transit time of electrons between the electrodes.
 Gunn Effect can be explained on basis of two valley theory of Ridley-Watkins-Hilsum
(RWH) theory or the transferred electron mechanism.

Negative Resistance
 The carrier drift velocity is linearly increased from zero to a maximum when the electric
field is varied from zero to a threshold value.
 When the electric field is beyond the threshold value of 3000 V/cm for the n-type GaAs,
the drift velocity is decreased and the diode exhibits negative resistance. This shown in
figure below:

Fig; Drift Velocity of n-type Ga-As Vs Electric Field

 The current fluctuations of n-type GaAs diode is shown below: the current waveform was
produced by applying a voltage pulse of 16 V amplitude and 10 ns duration to a n-type
GaAs 2.5×10-3 cm in length. The oscillation was 4.5 GHz
 Fig: current waveform of n-type GaAs
 The electrical equivalent circuit of a Gunn diode is shown in figure below:

Fig: electrical equivalent circuit of a Gunn diode

Where, Cj diode capacitance
Rj Diode Resistance
Rs Total resistance of leads, ohmic contact
Lp Package Inductance
CpPackage Capacitance
 The negative resistance value that typically lies in the range -5 to -20 ohm.

Modes of operation:
 Depending on the material parameters and operating conditions, a Gunn Effect oscillator
can be made to oscillate in any of the four frequency modes.
1. Gunn Oscillation Mode
2. Stable Amplification Mode
3. Limited space charge Accumulator (LSA) Mode
4. Bias-Circuit Oscillation Mode
1. Gunn Oscillation Mode:
 This mode is defined in the region where the product of frequency multiplied by length is
about 107cm/s and the product of doping multiplied by length is greater than 1012 /cm2.

 In this region the device is unstable because of the cyclic formation of either the
accumulation layer or the high field domain.
 In a circuit with relatively low impedance the device operates in the high field domain
mode and the frequency of oscillation is near the intrinsic frequency.
  When the device is operated in a relatively high- Q cavity and coupled properly to the
load, the domain is quenched or delayed (or both) before nucleating.
 In this case, the oscillation frequency is almost entirely determined by the resonant
frequency of the cavity and has a value several times the intrinsic frequency.

Fig: Modes of Operation of Gunn Diode

 Here, Ɛ>Ɛth .The high field domain drifts along the specimen until it reaches the anode or
until the low - field value drops below the sustaining field is required to maintain Vs as
shown in the figure. Since the electron drift velocity v varies with E, there are 3 possible
modes

a)Transit time domain mode:

 In this mode the period of oscillation is equal to transit time, 𝜏𝑜 = 𝜏𝑡 as shown in
figure below(a)
 Drift velocity is, 𝒗𝒅 = 𝒗𝒔 = 𝒇𝑳 = 𝟏𝟎𝟕 𝐜𝐦/𝐬
 Efficiency is low, below10% because the domain arrives at the anode at a lower
current level.
 Operating frequency is lesser than 30 GHz.

b)Delayed or Inhibited Mode

 In this mode the oscillation period is greater than transit time 𝜏𝑜 > 𝜏𝑡 as shown in
figure below
  The transit time is chosen so that the domain is collected while the electric field E<
the threshold value (Eth). i.e E <Eth.
 This Delayed or Inhibited Mode has the efficiency of 20 % .Hence the operating
frequency can be equal or less than in Gunn diode.
 If the voltage or electric field is applied to GaAs diode (E), initially the current will
increase with a rise in the voltage when the diode voltage exceeds a certain
threshold value (Eth), a high electric field (3.2 KV / m for GaAs) is produced across
the active regions.

Fig: Mode the oscillation period

c)Quenched Domain Mode:

 When the bias field swings back above the threshold (Eth), a new domain will be
formed and the process repeats. Hence in this mode, the domain is quenched before
 it reaches the anode. Therefore the oscillation period is lesser than the transit time,
𝜏𝑜 < 𝜏𝑡.
 The efficiency is only about 13 %.
2. LSA Mode
 This mode is defined in the region where the product of frequency times length is about
107cm/s and the quotient of doping divided by frequency is between 2×104 and 2×105.
 The most important mode of operation in Gunn oscillator as this mode gives high power
up led with high efficiency.
 The frequency and RF voltage are so chosen that the domain do not have sufficient time
to form while the field is above threshold as shown n figure (d) as above. The LSA mode
yields high power and high efficiency. Operating frequency is 0.5 – 50 times more than
that for Gunn diode.
3. Stable Amplification Mode:
 This mode is defined in the region where the product of frequency times length is about
107cm/s and the product of doping times length is between 1018 and 1012 /cm2.
4. Bias-Circuit Oscillation Mode:
 This mode occurs only there is Gunn or LSA oscillator, and it is usually at the region
where the product of frequency times length is too small to appear in the figure.
 When a bulk diode is biased to threshold, the average current suddenly drops as Gunn
oscillation begins.
 The drop in current at the threshold can lead to oscillation in the bias circuit that are
typically 1 KHz to 100 MHz.
Applications
 In Radar transmitters, Industry telemetry systems, Broadband linear amplifier, Fast
combinational and Sequential logic Circuits, Low and medium power oscillator, etc.,

IMPATT and TRAPATT diodes:

 IMPATT diode consists of a high doping avalanching region and a drift region.
 All the above IMPATT diode types and their doping profile is shown in figure below.
 The field applied to the IMPATT diode is about 5KV/cm. The total field across the diode
is sum of a RF ac voltage superimposed on high dc voltage.
 When a p-n junction is reverse biased, in the depletion layer, avalanche breakdown
takes place. Avalanche current lags the applied field by π/2 radians.
 The distances travelled by various carriers are not equal but the additional phase shift
caused by the drift of carriers makes the carriers to create a negative resistance.
 Fig; Various structures of IMPATT diode
 A dc electric field distribution that exists when a large reverse bias is applied across the
diode is shown in figure below:

Fig: (a) IMPATT Diode (b) Field Distribution (c) Input Voltage (d) Output Pulse

 The diode is an n+-p-i-p+ structure, where the subscript plus sign denotes very high
doping and the ‘i’ refers to intrinsic material.
  The device consists essentially of two regions. one is the thin p region at which
avalanche multiplication occurs. This region is also called the high-field region or the
avalanche region. The other is the ‘i’ region through which the generated holes must drift
in moving to the p+ contact. This region is also called the intrinsic region or the drift
region.
 The p region is very thin. The space between the ‘n+-p’ junction and the ‘i-p’ junction is
called the space-charge region. Similar devices can be built in the p+-n-i-n+ structure,
in which electrons generated from avalanche multiplication drift through the i region.
 IMPATT diode exhibits negative resistance which can be obtained by a junction diode of
any doping profile, which in turn delivers power from the dc bias to the oscillation.

Working Principle
 When the reverse-biased voltage is well above the punch through or breakdown voltage,
the space-charge region always extends from the n+-p junction through the p and i
regions to the i-p junctions.
 The fixed charges in the various regions are shown fig.(b) above. A positive charge
gives a rising field in moving from left to right. The maximum field, which occurs at
then+-p junction is about several hundred kilovolts per centimeter.
 Carriers9holes) moving in the high field near n+-p junction acquire energy to knock
valence electrons into the conduction band, thus producing hole-electron pairs.
 The rate of pair production or avalanche multiplication is a sensitive nonlinear function of
the field. By proper doping, the field can be given a relatively sharp peak so that
avalanche multiplication is confined to a very narrow region at the n+-p junction.
 The electrons move into the n+ region and the holes drift through the space charge
region to the p+ region with a constant velocity e of about 10 3 cm/s for silicon.
 The field throughout the space charge region is above about 5 KV/cm.
𝑳
 The transit time of a hole across the drift i-region of length L is given by 𝝉 = 𝑽𝒅

Operating Frequency
Thus, the operating frequency around the π transit angle is
𝟏
𝒇=
𝟐𝝉
Where 𝜏 is the transit time
On substituting the value of 𝜏 ,then can be expressed as
𝑽𝒅
𝒇=
𝟐𝑳
Where,
τ- Transit time
Vd – Drift velocity (m/s)
L – Drift Length (m)
 When the holes generated at the n+-p junction drift throughthe space charge region,
they cause a reduction of the field in accordance with poison’s equation;
𝝏𝑬 𝝆
= −
𝝏𝒙 𝝐𝒔
 Where,
𝜌-Volume charge density
𝜀𝑠-semiconductor permitivity
𝑤ℎ𝑒𝑟𝑒, 𝜌 − 𝑣𝑜𝑙𝑢𝑚𝑒 𝑐ℎ𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑛𝑑 𝜀𝑠 − 𝑠𝑒𝑚𝑖𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑝𝑒𝑟𝑚𝑖𝑡𝑖𝑣𝑖𝑡𝑦.
 Since the drift velocity of the holes in the space charge region is constant, the induced
current Ie(t) in the external circuit is simply equal to
𝑸 𝒗𝒅𝑸
𝑰𝒆(𝒕) = =
𝝉 𝑳
Where,
vd- drift velocity,
Q-total charge of the moving holes,
L – drift Length
 When, the pulse of hole current Io(t) is suddenly generated at the n+-p junction, a
constant current Ie(t) starts flowing in the external circuit and continues to flow during the
time τ in which the holes are moving across the space-charge region.
 Thus, on the average, the external current Ie(t) because of the moving holes is delayed
by τ/2 or 90o relative to the ac voltage as shown in figure (d) above.
Output Power
 The external current approaches a square wave, being very small during the positive
half cycle of the ac voltage and almost constant during the negative half cycle.
 Since the direct current supplied by the dc bias is the average external current or
conductive current, it follows that the amplitude of variation of Ie(t) is approximately
equal to Id. If Vo is the amplitude of the ac voltage, the ac power delivered is found to be
𝑷 = 𝟎. 𝟕𝟎𝟕 𝑽𝒐 𝑰𝒅 𝑾/𝒖𝒏𝒊𝒕 𝒂𝒓𝒆𝒂

 The capacitance across the space-charge is given by,

𝝐𝒔 𝑨
𝑪=
𝑳
 The maximum output power is given by

𝑷𝒎 = 𝑰𝒎𝑽𝒎
𝑬𝒎𝟐 . 𝒗𝒅𝟐
𝒊. 𝒆. , 𝑷𝒎 =
𝟒𝝅𝟐 𝑿𝒄
Efficiency
The efficiency of the IMPATT diode is given by,
𝑃𝑎𝑐
𝜂=
𝑃𝑑𝑐
𝑽𝒂 𝑰𝒂
𝜼=
𝑽𝒅 𝑰𝒅
Advantages
 It is wideband
 Pulse power is high
 Suitable for high frequency
Disadvantages
 It is a noisy device
 Tuning range is not high
Application of IMPATT Diode
 As microwave oscillator
 As modulated oscillator
 As receiver local oscillator
 As parametric amplifier pump
 In radar reception
 In communication transmission
 As negative resistance

TRAPATT diodes:

Construction
 TRAPATT diode is derived from IMPATT diode.
 In TRAPATT diodes the doping level between the junction and anode changes
gradually. Silicon or Gallium Arsenide is used for fabricating TRAPATT diodes.
 Figure shows the construction of TRAPATT diode.
 Construction of avalanche p+ - n – n+ is shown but when better power dissipation is
required n+ - p – p+ structure is preferred.

Working Principle
 A square current pulse is used to excite TRAPATT diode.

 As soon as diode is excited the charge is accumulated in the depletion region at the
junction and the electric field across the junction increases linearly.
 When the sufficient carriers are generated it then depress throughout the depletion
region, causing the voltage to fall down.
 During the interval formation of plasma takes place. Voltage and current continue to
decrease to residual value and the plasma is extracted from the region.
 As the residual charge is removed, the voltage increase further and diode charges
again.
  At some point the diode is charged fully and maintains a constant voltage across it while
current drops down.
 When current comes back the cycle repeats.
VI Characteristics of TRAPATT diode
 The voltage and current waveforms for a avalanche TRAPATT diode is shown in figure
below.

Fig(a): voltage and current waveforms for a avalanche TRAPATT diode

Fig(b): voltage and current waveforms for a avalanche TRAPATT diode

 The current density is given by
𝒅𝑬
𝑱 = Є𝒔
𝒅𝒕
Where, Є𝑠 – permittivity of the diode
E – Applied Electric field
 The electric field is given by,
𝒒𝑵𝒂 𝑱
𝑬(𝒙, 𝒕) = 𝑬𝒎 𝒙+
Є𝒔 Є𝒔
 Where, Em – Maximum electric field
Q – Charge of an electron
Na – Dopingconcentration
Є𝒔 – Permittivity
x – Distance
J – Current density

 The avalanche zone velocity is given by,

𝑑𝑥
𝑉𝑧 =
𝑑𝑡
𝟏
𝑽𝒛 =
𝒒𝑵𝒂
Application of TRAPATT Diode

1. In pulsed radar as local oscillator

2. In radio altimeter
3. Air borne and marine radars

Limitations of TRAPATT Diode

 TRAPATT diodes are very sensitive to the harmonics, thus when operated in
fundamental mode precaution is to be taken that the second, third and fourth harmonics
cannot be maintained in the circuit.

Microwave bipolar transistor:

 The invention of the transistor (contraction for transfer resistor) by William Shock-ley.
and his coworkers at Bell Laboratory in 1948 had a revolutionary impact on electronic
technology in general and on solid-state devices in particular.
 Since then transistors and related semiconductor devices have replaced vacuum
tubes for lower-power sources. Microwave power transistor technology has advanced
significantly during the past three decades.
 The microwave transistor is a nonlinear device, and its principle of operation is similar to
that of the low-frequency device, but requirements for dimensions, process control, heat
sinking, and packaging are much more severe.
 For microwave applications, the silicon (Si) bipolar transistors dominate for
frequency range from UHF to about S band (about 3 GHz).
 As the technology improves, the upper frequency limit for these devices is
continuously being extended, and at the present time the devices are capable of
producing useful power up to 22 GHz.
Physical Structures
 All microwave transistors are now planar in form and almost all are of the silicon
N-p-n type. The geometry can be characterized as follows: (a) interdigitated, (b)
overlay, and (c) matrix (also called mesh or emitter grid) as shown in below Fig.
  The interdigitated type is for a small signal and power, but the overlay type and
Matrix type are for small power only.

 For high-frequency applications, the n-p-n structure is preferred because the electron
mobility (µ,n = 1500 cm2/V · s) is much higher than the hole mobility (µ,p = 450
cm2/V · s). The above figure shows an example of the densities for an n-p-n transistor.

 The density unit is in cm2/V · s. Although there are many ways of fabricating a transistor,
diffusion and ion implantation is generally used.

Fig: Geometry of all microwave transistors

 For example, the structure would typically start with a lightly doped n-type epitaxial layer
as the collector. The base region would be formed by counter-doping the base region p-
type by diffusion.

Principles of Operation:

The bipolar junction transistor (BJT) is an active three-terminal device which is commonly
used as an amplifier or switch. Its principles of operation are discussed in this section. Modes
of operation. A bipolar transistor can operate in four different modes depending on the
voltage polarities across the two junctions: normal (active) mode, saturation mode, cutoff
mode, and inverse (or inverted) mode.

1. Normal Mode. If the emitter junction of an n-p-n transistor is forward-biased and the
collector is reverse-biased, the transistor is operated in the normal mode The term
forward bias means that the positive polarity of the bias voltage is connected to the p
side and the negative polarity to the n side for a p-n junction; the opposite obtains for
reverse bias. Most transistor amplifiers are operated in normal mode, and its common-
 base current gain alpha is known as the normal alpha αN.

2. Saturation Mode. When both transistor junctions are forward-biased, the transistor is
in its saturation mode with very low resistance, and acts like a short circuit.

3. Cutoff Mode. If both transistor junctions are reverse-biased the transistor is operated
in its cutoff mode. As the current is cut off, the transistor acts like an open circuit. Both the
cutoff and saturation modes of a transistor are used as switching devices for the OFF
and ON states.

4. Inverse Mode. When the emitter is reverse-biased and the collector is forward-biased,
the transistor is operated in the inverse (or inverted) mode, and its current gain is
designated as the inverse alpha a1. If the transistor is symmetric, the normal alpha
αN is nearly equal to the inverse alpha a1. The two current gains, however, are not
actually equal because of their unequal doping. In practice, the inverse mode is not
commonly used except as a multiemitter transistor in TTL (transistor-transistor logic)
logic gate.

MESFET and Parametric amplifiers:

 If the field-effect transistor is constructed with a metal-semiconductor Schottky-
barrier diode, the device is called a metal-semiconductor field-effect transistor
(MESFET).
 The material may be either silicon or gallium arsenide (GaAs), and the channel
type may be either n channel or p channel.
 Since GaAs MEFSETs have the capability of amplifying small signals up to the
frequency range of X band with low-noise figure, they have lately replaced the
parametric amplifiers in airborne radar systems because the letters are
complicated to fabricate and expensive to produce.
 The GaAs MESFET has higher electron mobility, higher electric field, and higher
electron saturation drift velocity than silicon devices, so its output power is also
greater.
 Another special feature is its lower noise figure, accounted for by its higher
electron mobility.
 Therefore the GaAs MESFETs are very commonly used in microwave integrated
circuits for high-power, low-noise, and broadband amplifier applications.
Physical Structures
 In GaAs MESFETs the substrate is doped with chromium (Cr), which has an
energy level near the center of the GaAs bandgap. As Cr is the dominant impurity,
the Fermi level is pinned near the center of the bandgap.
 Thus, a very high-resistivity substrate (near 108 ohm-cm) generally results, and it
is commonly called the semi-insulator GaAs substrate.
 On this nonconducting substrate a thin layer of lightly doped n-type GaAs is
grown epitaxially to form the channel region of the field-effect transistor.
 Fig Schematic diagram of a GaAs MESFET.

 In many cases a high resistivity GaAs epitaxial layer, called the buffer layer, is
grown between the n-type GaAs layer and the substrate. The photolithographic
process may be used to define the patterns in the metal layers such as Au-Ge for
source and drain ohmic contacts and in the Al layer for the Schottky barrier-gate
contact.
 The reason for using GaAs instead of Si is that GaAs has higher electron mobility and
can operate at higher temperature and higher power.

Principles of Operation

Fig: Schematic diagram and circuit symbol of a GaAs MESFET.

 a voltage is applied in the direction to reverse-bias the p-n junction between the
source and the gate, while the source and the drain electrodes are forward-biased.

 Under this bias condition, the majority carriers (electrons) flow in then-type epitaxial
layer from the source electrode, through the channel beneath the gate, to the drain
 electrode. The current in the channel causes a voltage drop along its length so that
the Schottky barrier-gate electrode becomes progressively more reverse-biased toward
the drain electrode.

 As a result, a charge-depletion region is set up in the channel and gradually pinches

off the channel against the semi-insulating substrate toward the drain end. As the
reverse bias between the source and the gate increases,

 So does the height of the charge-depletion region. The decrease of the channel height in
the nonpinched-off region will increase the channel resistance.

 Consequently, the drain current Id will be modulated by the gate voltage VR.

 This phenomenon is analogous to the characteristics of the collector current le versus

the collector voltage Ve with the base current has a parameter in a bipolar transistor.

 In other words, a family of curves of the drain current Id versus the voltage Vd,
between the source and drain with the gate voltage VR as a parameter will be
generated in an unipolar GaAs MESFET,

The trans-conductance of a field-effect transistor (FET) is expressed as

Pinch-off voltage Vp. The pinch-off voltage is the gate reverse voltage that removes all the
free charge from the channel. Poisson's equation for the voltage in the n channel, in
terms of the volume charge density is given by

where p = volume charge density in coulombs per cubic meter

q = charge in coulombs
Nd = electron concentration in electrons per cubic meter
Es = permittivity of the material in farads per meter
E, = Er Ea, Er is the relative dielectric constant
Ea = 8.854 x 10-12 F/m is the permittivity of free space

Two cavity klystron amplifier:

The two cavity reflex klystron is a widely used microwave amplifier operated by the principle
of velocity modulation and current modulation
 Fig.: Schematic diagram of two cavity Reflex klystron oscillator

Mechanism of operation
1. All the electrons injected from the cathode arrive at the first cavity with uniform velocity.
These electrons passing at the cavity gap at zeros of the gap voltage(or) signal voltage
pass through unchanged velocity.
2. Those passing through the positive half cycles of the gap voltage undergo an increase in
the velocity.
3. Those passing through the negative swings of the gap voltage undergo a decrease in
velocity. As the result of these actions, the electrons gradually bunch together as they
travel down the drift space is known as velocity modulation.
4. The electron beam modulated to form bunches (or) undergoes density modulation in
accordance with the input RF cycle.
5. While passing through the catches cavity grid, this density modulated electron beam
induces RF current in the output cavity and thereby excite the RF field in the output
cavity at input signal cycle.
6. The phase of field in the output cavity is opposite to that of the input cavity so that the
bunched electrons are retarded by the output gap voltage. The loss of kinetic energy of
the electrons on retardation process transfers RF energy to the output cavity
continuously at signal.
  The electrons then emerge from the second cavity with reduced velocity and finally
terminate at the collector.
 The characteristics of a two cavity klystron amplifier are as follows:

Efficiency - about 40%

Power Output –
 The average power (CW power) is upto 500 KW at 10 GHz.
 The pulsed power is upto 30 MW at 10 GHz

Power Gain = about 30 dB.

Velocity Modulation
 When the electrons are first accelerated by the high DC voltage V0before entering
the buncher grids . Their velocity is uniform.
𝟐𝒆𝑽𝟎
𝒖𝟎 = √ 𝒎
= 5.93×105 √𝑽𝟎 ms-1 ------------ (1)
 Let the signal voltage across the gap be V1𝐬𝐢𝐧 𝝎𝒕.
 Let t1 = Time taken by the electron beam to enter the buncher cavity (or) the input
cavity with velocity V0.
t2 = Time taken by the electron beam to pass out from the buncher cavity.
 The transit time and transit angle through the transit gap is
𝒅
𝒕𝒈 = 𝒖 ----------- (2)
𝟎
Transit angle,
𝝎𝒕𝒈 = 𝜽𝒈 ---------(3)
  Due to input RF signal in the buncher cavity, the average RF voltage in the buncher
gap can be obtained as,
𝑡2
1
𝑉𝑎𝑣 = ∫ 𝑉1 sin 𝜔𝑡 𝑑𝑡
𝑡𝑔
𝑡1
𝑉1 − cos 𝜔𝑡 𝑡2
= 𝜃𝑔
[ 𝜔 ]
𝑡1
𝑉1 (− cos 𝜔𝑡2 + cos 𝜔𝑡1 )
=
𝜃𝑔
𝑉1 cos 𝜔𝑡1 −𝑉1 cos 𝜔𝑡2
∴ 𝑉𝑎𝑣 = ---------- (4)
𝜃𝑔
Let
𝜃𝑔
A = 𝜔𝑡1 + 2
𝜃𝑔
B= 2
Also, A+B = 𝜔𝑡1 + 𝜃𝑔
A-B = 𝜔𝑡1
We know that, 𝜔𝑡𝑔 = 𝜃𝑔
𝜔(𝑡2 − 𝑡1 ) = 𝜃𝑔
𝜔𝑡2 = 𝜃𝑔 + 𝜔𝑡1
𝑉1
𝑉𝑎𝑣 = [cos 𝜔 𝑡1 − cos 𝜔 𝑡2 ]
𝜃𝑔
𝑉
𝑉𝑎𝑣 = 𝜃1 [ cos 𝜔 𝑡1 − cos(𝜃𝑔 + 𝜔𝑡1 )]
𝑔

Obtained by (A-B) Obtained by (A+B)

𝑉1
𝑉𝑎𝑣 = [cos(A − B) − cos(A + B)]
𝜃𝑔
We know that,
cos(A − B ) − cos(A + B ) = 2 sin 𝐴sinB
Equation (4) can be rewritten as,
𝑉1 𝜃𝑔 𝜃𝑔
𝑉𝑎𝑣 = [2 sin (𝜔𝑡1 + ) sin ]
𝜃𝑔 2 2
𝜃𝑔
𝜃𝑔 sin 2
𝑉𝑎𝑣 = 𝑉1 sin (𝜔𝑡1 + )
2 𝜃𝑔
2
𝜃𝑔
𝑉𝑎𝑣 = 𝑉1 𝛽1 sin (𝜔𝑡1 + 2 ) ------------ (5)
𝜃𝑔
where𝛽1 = sin 2
= beam coupling co-efficient of buncher cavity gap
We know that, 𝜔𝑡2 = 𝜃𝑔 + 𝜔𝑡1
 𝜔𝑡1 = 𝜔𝑡2 - 𝜃𝑔
𝜃𝑔
From (5), 𝑉𝑎𝑣 = 𝑉1 𝛽1 sin (𝜔𝑡2 − 𝜃𝑔 + )
2
𝜃𝑔
𝑉𝑎𝑣 = 𝑉1 𝛽1 sin (𝜔𝑡2 − 2
) ---------- (6)
The exit velocity from buncher gap is given by,
2𝑒(𝑉0 +𝑉𝑎𝑣 )
𝑢(𝑡2 ) = √ 𝑚
------------ (7)

𝑉1 𝛽1 𝜃𝑔
2𝑒𝑉0 (1+ sin(𝜔𝑡2 − ))
=√
𝑉0 2
𝑚
𝑉1 𝛽1
The factor is known as depth of modulation.
𝑉0
If the modulation amplitude is very small (<<<1), then
𝑉1 𝛽1 𝜃𝑔
𝑢(𝑡2 ) ≅ 𝑢0 (1 + 2𝑉0
sin (𝜔𝑡2 − 2
)) ----------- (8)
𝑉1 𝛽1
The factor is represented as m.
𝑉0
𝑚 𝜃𝑔
𝑢(𝑡2 ) ≅ 𝑢0 (1 + sin (𝜔𝑡2 − )) ------- (9)
2 2

Transit Time in Drift Space

If t3 is the time when the bunched electrons are at the catcher grid after travelling through the
field free drift space.
𝐿
𝑡3 = 𝑡2 + 𝑢(𝑡 --------- (10)
2)
𝐿
= 𝑡2 +
𝑚 𝜃𝑔
𝑢0 (1 + 2 sin (𝜔𝑡2 − 2 ))
𝐿
Let 𝑡0 = 𝑢 be the transit time of the reference electron.
0
𝑚 𝜃𝑔 −1
𝑡3 = 𝑡2 + 𝑡0 (1 + sin (𝜔𝑡2 − ))
2 2
We know that,
(1+x)-1 = 1-x+x2-……………..
Neglecting the higher order terms we get,
𝑚 𝜃𝑔
𝑡3 = 𝑡2 + 𝑡0 (1 − 2
sin (𝜔𝑡2 − 2
)) ----- (11)
Density modulation

Because of the difference in velocities of electrons in the velocity modulated beam, the
electron will form bunches ie., becomes density modulated, in accordance with input cycle. A
maximum degree of bunching takes place when the buncher and catcher cavities are spaced to
satisfy the condition,
𝐿
𝑡𝑑 = 𝑡3 − 𝑡2 =
𝑢(𝑡2 )
From (11),
𝑚 𝜃𝑔
𝑡𝑑 = 𝑡3 − 𝑡2 = 𝑡0 (1 − 2
sin (𝜔𝑡2 − 2
)) ---- (12)
The corresponding transit angle in the drift space L is,
ω 𝑡𝑑 = ω(𝑡3 − 𝑡2 ) (From equation (12))
𝑚 𝜃
= 𝜔𝑡0 (1 − sin (𝜔𝑡2 − 𝑔 ))
2 2
𝑚𝜃0 𝜃𝑔
ω 𝑡𝑑 = 𝜃0 − 2 sin (𝜔𝑡2 − 2 ) ------------ (13)

where, 𝜃0 = 𝜔𝑡0 = DC transit angle

The transit time of reference electron in terms of N is given by,
𝐿
𝑡0 = = 𝑁𝑇
𝑢0
Where N = number of RF cycles that are elapsed during the transit time of reference
electron.
1
Now, 𝜔𝑡0 = 𝜔𝑁𝑇 = 2𝜋𝑓(𝑁) (𝑓)
𝜃0 = 𝜔𝑡0 = 2𝜋𝑁 ------------ (14)

Using equation (14), equation (11) can be rewritten as,

𝑚 𝜃𝑔
𝑡3 = 𝑡2 + 𝑡0 (1 − sin (𝜔𝑡2 − ))
2 2
2𝜋𝑁 𝑚 𝜃𝑔
𝑡3 = 𝑡2 + (1 − sin (𝜔𝑡2 − ))
𝜔 2 2
2𝜋𝑁 𝑉1 𝛽1 2𝜋𝑁 𝜃𝑔
𝑡3 = 𝑡2 + − sin (𝜔𝑡2 − )
𝜔 2𝑉0 𝜔 2
Let X bethe bunching parameter and it is given by,
𝜋𝑁𝑉1 𝛽1
𝑋=
𝑉0
2𝜋𝑁 𝑋 𝜃𝑔
∴ 𝑡3 = 𝑡2 + 𝜔
− 𝜔 sin (𝜔𝑡2 − 2
) ------------ (15)

Bunched Beam Current: (Ib)

The bunched beam current ib in the catcher cavity is given by,

𝐼0
𝑖𝑏 =
𝑑𝑡3
𝑑𝑡2
𝑑𝑡3 𝑋 𝜃𝑔
= 1 − . 𝜔 . cos (𝜔𝑡2 − )
𝑑𝑡2 𝜔 2
𝜃𝑔 −1
𝑖𝑏 = 𝐼0 (1 − 𝑋 cos (𝜔𝑡2 − ))
2
By Fourier expansion, the beam current of two cavity reflex klystron is,
∞
𝜃𝑔
𝑖𝑏 = 𝐼0 + 2𝐼0 ∑ 𝐽𝑛 (𝑛𝑋) cos n (𝜔𝑡2 − )
2
𝑛=1
Expanding the summation we get,
𝜃𝑔 𝜃𝑔
𝑖𝑏 = {𝐼0 } + {2𝐼0 𝐽1 (𝑋)cos (𝜔𝑡2 − 2
)} + {∑∞
𝑛=2 𝐽𝑛 (𝑛𝑋) cos n (𝜔𝑡2 − 2
)}

Dc component Fundamental Ac Component Harmonics

The klystron is generally tuned to the fundamental AC component of current and it is given by,
𝜃𝑔
𝑖𝑏 = 2𝐼0 𝐽1 (𝑋)cos (𝜔𝑡2 − ) ------------ (16)
2

Optimum Drift Space Length: Lopt

𝐿𝑜𝑝𝑡
𝑡0 =
𝑢0
𝐿𝑜𝑝𝑡 = 𝑢0 𝑡0 ------------ (17)
We know that,
𝜋𝑁𝑉1 𝛽1 2
𝑋= ×
𝑉0 2
𝜔𝑡0 𝑉1 𝛽1
𝑋=
2𝑉0
2𝑋𝑉
𝑡0 = 𝜔𝑉 𝛽0 ---------- (18)
1 1
Substituting eqn.(18) in (17),we get
2𝑢0 𝑋𝑉0
𝐿𝑜𝑝𝑡 =
𝜔𝑉1 𝛽1
From the Bessel function table,𝐽1 (𝑋) is maximum ie., 0.582 at X=1.841
2𝑢0 (1.841)𝑉0
𝐿𝑜𝑝𝑡 =
𝜔𝑉1 𝛽1
3.682𝑢0 𝑉0
𝐿𝑜𝑝𝑡 = 𝜔𝑉1 𝛽1
------------- (19)

Power and efficiency considerations:

Power Output:
The fundamental component of RF beam current passing through the output cavity gap
induces a current in the catcher cavity.
𝑖𝑐 = 𝛽2 |𝑖𝑏 |
Where 𝛽2 → beam coupling coefficient of catcher cavity.

𝑖𝑐 = 𝛽2 .[2𝐼0 𝐽1 (𝑋)]
 I2
Therefore,
𝑖𝑐 = 𝛽2 I2
If the buncher and catcher cavities are identical, then 𝛽0 = 𝛽1 = 𝛽2
∴ 𝑖𝑐 = 𝛽0 I2
The output power delivered to catcher cavity is,
(𝛽0 𝐼2 )2 𝑅𝑠ℎ
𝑃𝑜𝑢𝑡 =
2
(𝛽0 𝐼2 )[(𝛽0 𝐼2 )𝑅𝑠ℎ ]
𝑃𝑜𝑢𝑡 =
2
(𝛽0 𝐼2 ) 𝑉2
𝑃𝑜𝑢𝑡 =
2
Efficiency: 𝜼
The electronic efficiency of klystron amplifier is defined as the ratio of the output power to
the input power.
𝑃𝑜𝑢𝑡
𝜂=
𝑃𝑑𝑐 (𝑜𝑟)𝑃𝑖𝑛
(𝛽0 𝐼2 ) 𝑉2
𝜂=
2𝐼0 𝑉0
If the coupling co-efficient is perfect ie.,𝛽0 = 1 and 𝑉2 = 𝑉0, then there is maximum beam
current in the catcher cavity.
2𝐼0 𝐽1 (𝑋)
𝜂=
2𝐼0
𝜂 = 0.582 × 100
𝜂 = 58.2%
The maximum electronic efficiency of two cavity reflex klystron is 58.2 %

Reflex Klystron oscillators:

 A reflex Klystron is a low power, low efficiency, microwave oscillator.

Mechanism of Oscillation
1. Due to d.c. voltage in the cavity circuit, RF field is generated in the cavity. The electrons
passing through the cavity gap‘d’ experience this RF field and are velocity modulated in
the following manner.

2. Electrons as shown in fig. below which encountered the positive half cycle of the RF field
in the cavity gap ’d’ will be accelerated, the electrons at ‘b’ which encountered zero RF
field will pass with unchanged original velocity and the electrons at ‘c’ which
encountered the negative half cycle will be retarded on entering the repeller space.
 Fig.: Schematic diagram of Reflex klystron oscillator

3. All these velocity modulated electrons will be repelled back to the cavity by the repeller
due to its negative potential. Repeller distance L and the voltages can be adjusted to
receive all the velocity modulated electrons at the same time on the positive peak of the
cavity RF voltage cycle.
4. Thus the velocity modulated electrons are bunched together and lose their kinetic energy
when they encounter the positive cycle of the cavity RF field. This loss of energy is thus
transferred to the cavity to conserve the total power.
5. If the power delivered by the bunched electrons to the cavity is greater than the power
lose in the cavity, the electromagnetic field amplitude at the resonant frequency of the
cavity will increase to produce microwave oscillations.

Bunching of Electrons
 The reference electron is taken as one that passes the gap on its way to the repeller at
the time when the gap voltage is zero and going negative. This electron overshoots the
gap and return to it with some distance penetrated into the repeller.
 An electron passing the gap slightly earlier will have slightly positive voltage at the gap.
The resulting acceleration would have propelled this electron slightly farther into the
repeller space, and the electron would have taken slightly longer time than reference
electron to return to the gap.
 Similarly electron passing after reference electron will have slightly negative voltage.
Thus bunching of electrons takes place.
Applegate Diagram
Applegate diagram of Reflex Klystron is shown in figure below:

Fig.: Apple gate diagram of Reflex Klystron

 When the gap voltage is at positive peak, electron passing at this moment is called early
electron (ee). This electron is accelerated towards repeller and travels a distance, which
is longer comparatively. The electron at natural zero of gap voltage is called reference
electron(eR). When the gap voltage is at negative peak the corresponding electron is
called late electron (eL).
 The late electron is decelerated and travels less distance. Thus, ee, eR, eLof different
velocities cover different forms bunch at cavity gap. Thus oscillations build up.

M o d e s a n d e f f i c i e nc y considerations:

Modes of oscillations
 The condition for oscillation
to=(n+¾)T=NT
N=n+¾, n=0, 1, 2…
Where, N=n+3/4 and n=0,1,2,3,……

Relation between Repeller Voltage and Accelerating Voltage

𝑉𝑜 1 1 𝑒 𝜋 2
= . . . (2𝜋𝑛 − )
(𝑉𝑅 − 𝑉𝑜 )2 8 𝜔 2 𝐿2 𝑚 2
Where, V0 – anode voltage
VR – repellervoltage
L – Distance between cavity gap and repeller electrode.
Output Power
𝟐𝑽𝒐 𝑰𝒐 𝑋 ′ 𝐽1 (𝑋 ′ ) 𝒆
𝑷𝒐𝒖𝒕 = . (𝑉𝑅 − 𝑉𝑜 ). √
𝝎𝑳 𝟐𝒎𝑽𝒐
𝟎. 𝟑𝟗𝟖𝟔 𝑽𝒐 𝑰𝒐
𝑷𝒐𝒖𝒕 𝒐𝒓 𝑷𝑹𝑭 =
𝑵
Efficiency of Reflex Klystron
𝟐𝑿′ 𝑱𝟏 (𝑿′ ) 𝟎. 𝟑𝟗𝟖𝟔
𝜼= 𝝅 𝒐𝒓 𝜼 =
(𝟐𝝅𝒏 − 𝟐 ) 𝑵
Where, J1(X) is Bessel function of 1st order for argument X.
The factor 𝑋 ′ 𝐽1 (𝑋 ′ ) reaches maximum value of 1.252 at 𝑋 ′ = 2.408 and 𝐽1 (𝑋 ′ ) = 0.52.

Applications of Reflex Klystron

 Pump oscillator for parametric amplifiers.
 Frequency modulated oscillator portable microwave links
 Local oscillator in microwave receivers
 Signal source in microwave generators

Cylindrical Magnetrons and Helix TWT:

 A magnetron oscillator is used to generate high microwave power. Magnetrons are cross
field tubes in which the dc magnetic field and dc electric field are perpendicular to each
other.
 The cathode is a rod in the center of the tube and anode is a solid block. The anode
contains several resonant cavities. The space between cathode and anode is known as
interaction space.

Fig. Magnetron
 Radial electric field is established by dc voltage𝑽𝟎 in between cathode and anode and
dc magnetic flux denoted by 𝛽0 is maintained in positive Z-direction by means of a
permanent (or) electromagnet.
  There are three forces acting on an electron in the interaction region of the magnetron,
 force due to electric field (-eE)
 force due to magnetic field [-e (V× 𝑩)]
𝒎𝒗𝟐
 centrifugal force ( 𝒓
)
 The electrons emitted from the cathode try to travel towards anode.

At zero magnetic field, the electron takes the straight path a by the influence of electric
field only.
 For a given𝑽𝟎 , if the magnetic field is increased, the electrons take curved path b to
reach the anode.
 At a critical value of magnetic field Bc, the electrons just graze the anode surface and
return to the cathode for a given voltage 𝑽𝟎 .The value B c is called the cut-off magnetic
flux density.
 If the magnetic field is greater than Bc, all the electrons return to the cathode by a typical
path X without reaching the anode.
At the equilibrium condition,
𝑚𝑣 2
𝑟
+ 𝑒𝐸 = 𝑒𝑉𝐵 ------------- (1)

CENTRIFUGAL FORCE FORCE DUE TO FORCE DUE TOELECTRONS MAGNETIC FIELD

The electric field E is a function of radial direction only and is given by

𝑉0
𝐸(𝑟) = − 𝑏 ------------ (2)
𝑟 ln( )
𝑎
Where a andb are the anode and cathode radius respectively.
In the absence of electric field, the electrons move in a circular path and return to the cathode,
then
𝑚𝑣 2
= 𝑒𝑉𝐵
𝑟
𝑉 𝑒𝐵
𝑟
= 𝑚 =𝜔 ------------ (3)
Where 𝜔 is called the cyclotron angular frequency
The equation of motion for electrons in magnetic field in cylindrical co-ordinates is given by,
1 𝑑 𝑑∅ 𝑒𝐵 𝑑 𝑟
𝑟 𝑑𝑡
(𝑟 2 𝑑𝑡 ) = 𝑚 𝑑𝑡
------------ (4)
𝑑 2𝑑∅ 𝑒𝐵 𝑑𝑟
(𝑟 )= (𝑟)
𝑑𝑡 𝑑𝑡 𝑚 𝑑𝑡
We know that,
𝑑 2 𝑑𝑟
(𝑟 ) = 2𝑟
𝑑𝑡 𝑑𝑡
𝑑 𝑟 1 𝑑 𝑟2
∴𝑟 =
𝑑𝑡 2 𝑑𝑡
So,
𝑑 2𝑑∅ 1 𝑒𝐵 𝑑 𝑟 2
(𝑟 )=
𝑑𝑡 𝑑𝑡 2 𝑚 𝑑𝑡
𝑒𝐵
From equation (3) , 𝑚 = 𝜔. So we get,
𝑑 2𝑑∅ 𝜔 𝑑 𝑟2
(𝑟 )=
𝑑𝑡 𝑑𝑡 2 𝑑𝑡
Integrating on both sides we get,
𝑑∅ 𝜔𝑟 2
𝑟2 𝑑𝑡
= 2
+𝑘 ----------- (5)
Where k = integration constant.
Let a be the radius of the cathode cylinder .
𝑑∅
At r=a and 𝑑𝑡
= 0 , then the constant k is given by
1
𝑘 = − 2 𝜔𝑎2 ----------- (6)
Substitute (6) in (5),
𝑑 ∅ 𝜔𝑟 2 1 2
𝑟2 = − 𝜔𝑎
𝑑𝑡 2 2
2
𝑑 ∅ 𝜔𝑟 𝑎2
𝑟2 = (1 − 2 )
𝑑𝑡 2 𝑟
𝑑∅ 𝜔 𝑎2
𝑑𝑡
= 2
(1 − 𝑟2 ) ------------ (7)
This expression gives the angular velocity of electron.
The kinetic energy of electron is given by,
𝑚𝑣 2
= 𝑒𝑉
2
2𝑒𝑉
𝑣2 = 𝑚 ------------- (8)
However, the electron velocity has r and ∅ components such as,
𝑣 2 = 𝑣𝑟 2 + 𝑣∅ 2
𝑑𝑟 2 𝑑∅ 2
𝑣2 = ( ) + (𝑟 ) ------------- (9)
𝑑𝑡 𝑑𝑡

Let b be the radius from the centre of the cathode to the edge of the anode.
𝒅𝒓
At r=b, V= V0 , 𝒅𝒕 =0 , the electron just grazes the anode.
𝑑∅ 2
𝑣0 2 = 𝑏 2 ( 𝑑𝑡 ) ------------ (10)
From equation (8),
2𝑒𝑉0
𝑣0 2 = 𝑚
------------ (11)
Comparing (10) and (11),
2𝑒𝑉0 𝑑∅ 2
= 𝑏2 ( )
𝑚 𝑑𝑡
2
2𝑒𝑉0 2 𝜔 𝑎2
𝑚
=𝑏 ( 2 (1 − 𝑏2
)) ------------- (12)
𝑒𝐵
Substituting 𝑚
=𝜔,
 2
2𝑒𝑉0 𝑒𝐵 𝑎2
= 𝑏2 [ (1 − 2 )]
𝑚 2𝑚 𝑏
2
2𝑒𝑉0 (𝑒𝐵)2 𝑎2
= 𝑏2 (1 − )
𝑚 4𝑚2 𝑏2
2
8𝑚2 𝑒𝑉0 𝑎2
𝑚
= 𝑏 2 (𝑒𝐵)2 (1 − 𝑏2 )
8𝑚𝑒𝑉0
2 = 𝐵2
𝑎2
𝑒 2 𝑏2 (1− 2 )
𝑏
𝑚
8𝑉0 ( 𝑒 )
2
𝐵 = 2
𝑎2
𝑏 2 (1 − )
𝑏2
At the critical magnetic field, Bc= B
1
𝑚
(8𝑉0 )2
𝑒
𝐵𝑐 = 𝑎2
------------ (13)
𝑏(1− 2 )
𝑏

Thus if applied magnetic field B is greater than Bc for a given 𝑉0 , the electron will not reach the
anode.
For a given B0, the cut off voltage is given by,
2
𝑒 𝑎2
𝑉𝑐 2 = 8 𝑚𝑏 2 (1 − 𝑏2 ) 𝐵2 ------------ (14)
If V0< V c, for a given B, the electron will not reach the anode. Equations(3)and(14) for BcandVc
called Hull- cut off magnetic and voltage equation, respectively.

RF Structure of Magnetron:
 Magnetron structure supports varieties of modes depending upon the phase difference
between fields in two adjacent cavities.
 Boundary conditions are satisfied when total phase shift around the 8 cavities is a
multiple of 2π radians.
 The phase shift between the fields of adjacent cavities is π radians. This is known as π
mode. Magnetron oscillators operated in π mode. [∅𝑛 = π mode]
 Frequency of π –mode can be easily separated from adjacent modes by incorporating
conducting straps connected to alternate segment of anode block.
Mechanism of oscillations
 The electron beams a come across an electric field in the direction of its velocity. It is
retarded by the field, slow down and drifts towards the anode values of the static E and
H fields are so adjusted that the time the electron reaches near the second cavity.
 Last a time period elapses, The electron experiences a retarding field again and loses
energy to the RF field. This process continues the transfer of energy takes place again
near the third cavity.

Phase Focusing Effect:

 Π – Mode oscillations of cavity magnetron causes electron to bunch, and this effect is
 called as phase focusing effect.
 Without this effect electrons would fall behind the phase change of the electric field
across the gaps, since such electrons are retarded at each interaction with RF field.
 The bunches rotate counter clockwise with correct velocity to keep up with RF phase
changes between adjoining a mode poles. Thus continued interchange of energy takes
place, with RF field
Applications:
 RADAR transmitters
 Microwave owens
 Industrial heating
 In oscillators with great power and pulsed operation at 100 GHZ and greater.

Helix TWT:

 The travelling wave tube is an amplifier which makes use of a distributed interaction
between an electron beam and a travelling wave.
 The travelling wave tube (TWT) is an O-type parallel field, linear beam device, but it
differs from the Klystron in that the RF field and the electron beam interact with each
other over the entire length of the active region, instead of only at the cavity gaps.
 Although TWTs exists that use resonant cavities, most TWTs are non-resonant devices
and hence have wider bandwidths than Klystrons.

Construction
 The TWT contains an electron gun, which produces and then accelerates an electron
beam along the axis of the tube.
 The surrounding static magnet provides a magnetic field along the axis of the tube. The
focus the electrons into a tight beam.
 A longitudinal helix slow wave non-resonant guide is placed at the center of the tube.
 The RF input and output are coupled into and removed from the helix by directional
couplers that have no physical connection to the helix.
 The TWT is designed with helix delay structure to slow the travelling wave down to or
below the speed to the electrons in the beam.
 The electrons of the beam are accelerated to travel faster than the waves travelling on
the helix wire through the velocity modulation caused by the interaction between the
travelling wave fields and the electron beam.
 This effect results in bunching and the electrons give up energy to the travelling wave
when the fields of the correct polarity slow down the bunches.
 Fig; TWT Tube and Circuit

 The energy from the bunches increase the amplitude of the travelling wave in a
progressive action that takes place all along the length of the TWT.

 The RF signal injected at the input end of the helix travels down the helix wire at the
speed of light, but the coiled shape causes the wave to travel a much greater total
distance than the electron beam.

 Changing the number of turns in the helix wire, the speed at which the RF signal wave
travels in the form of axial E field down the tube, can be varied.

 DC beam voltage is adjusted so that beam velocity is slightly greater than that of the
axial field. The helical delay structure has the added advantage of causing a large
portion of electric fields that are parallel to the electron beam provides maximum
interaction between the fields and the electron beam to form bunching.

 As the electron bunches release energy to the signal on the helix, amplification begins.
 The initial amplified signal causes the denser electron bunch which in turn, amplifies the
signal even more. This process continues as the RF wave and the electron beam travel
down the length of the tube. When the loss in the system is compensated by this energy
transfer, a steady amplification of the microwave signal appears at the output end.

 An attenuator is placed over a part of the helix on midway to attenuate and reflected
waves generated due to impedance mismatch that could be fed back to the input to
cause oscillations.

 The attenuator is placed after sufficient length of the interaction region so that the
attenuation of the amplified signal is insignificant compared to the amplification.

 The internal attenuator reduces the gain of the tube. The TWT also produces heat which
must be dissipated by either air-conditioning or liquid-cooling systems.
Analysis of TWT

 If d dis the diameter of the helix and p is the pitch, the time taken by signal along the
wire must be equal to that taken by the axial wave, so that
𝒑 √𝒑𝟐 + (𝝅𝒅)𝟐
𝑻= =
𝒗𝒑 𝒄
𝒄𝒑 𝒄𝒑 𝝎
𝒗𝒑 = = =
√𝒑𝟐 + (𝝅𝒅)𝟐 𝝅𝒅 𝜷
Gain in TWT
 The gain in TWT is proportional to the length of the slow wave structure and is found
from
𝟒𝟕. 𝟑 𝑭𝑳 𝟑 𝟏𝑲
𝑮𝒂𝒊𝒏(𝒅𝑩) = [ √ ] − 𝟗. 𝟓𝟒
𝟐𝝅𝑽𝒐 𝟒𝑽
Where, F – RF frequency in hertz
Vo – Electron Velocity
K – Helix impedance in ohms
V – applied dc voltage
I - Dc current
Applications of TWT
 Low noise tubes are used in RF amplifiers in broadband microwave receivers.
 Medium and high power satellite transponder output.
 CW radar and radar jamming
 UNIT-II S Parameters:
Scattering parameters:

Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix)

describe the electrical behavior of linear electrical networks when undergoing various steady
state stimuli by electrical signals.

properties of S matrix:

1.) Zero diagonal element for perfect matched network

For an ideal N-port matched network with matched termination at all ports, Sii=0, since
there is no reflection from any port. Therefore, under perfect matched conditions, the
diagonal elements of [S] are zero.
2.) Symmetry of [S] For a Reciprocal Network
A reciprocal device has the same transmission characteristics in either direction of a pair
of ports and is characterized by a symmetric scattering matrix
Sij=Sji (i=j)
Which results [St] =[S]. This property is known as symmetry property of S-matrix.
Proof
The impedance Z of a network is given by
[V] = [Z][I] -----------(1)
The average power flowing in to the port n may be evaluated using the following relation
an = Vn+ / √𝑍0--------(2)
bn = Vn- / √𝑍0 --------(3)
Where, Vn+ = incident
Vn- = outgoing wave
Using above relation Vn and In can be written as
Vn = (Vn+) + (Vn-) = √𝑍0(an + bn) ------ (4)
In = {(Vn+) + (Vn-)} / Z0 = (an – bn)/ Z0 ------- (5)
Subs eqn (4) & (5) in eqn (1)
[V+] + [V-] = [Z] (⅟ Z0) ([V+] – [V-]) --------------- (6)
= [Z1] ([V+] – [V-]) ---------------- (7)
Where,Z1= [Z] / Z0
Equation (6) can be written as
{( [Z1] + [U] ) [V-] } = {( [Z1] – [U] ) [V+] }
 Since (Z1 + U)(V-) = (Z1 – U)(V+)
Where, [U] is the unity matrix.
[V-] = [V+] { ( [Z1] – [U] ) / ( [Z1] + [U]) }
[V-] = ( [Z1] – [U] ) { 1/ ([Z1] + [U]) } [V+]
[V-] = [S] [V+] ---------(8)
Where,
[S] = ( [ Z1] – [U] ) {1/ ( [Z1] + [U] )
Writing transpose of [S] ,
[St] = ( [Z1] – [U] )t {1/([Z1] + [U]) }t
As [Z1] and [U] are symmetrical matrixes,
{ 1/([Z1] + [U]) }t = 1/( [Z1]+ [U] )
( [Z1] – [U] )t = ( [Z1] – [U] )
Hence [S] = [St].
This indicates that scattering matrix [S] is SYMMETRICAL.
(3.) Unitary Property for a Lossless Junction
For any lossless network the sum of the products of each term of any one row or of any
column of the S matrix multiplied by its complex conjugate
For lossless n port device, the total power rating
N port must be equal to the total power input to these ports. The mathematical statement
for this power conservation condition is,
∑𝑁
𝑛=1|𝑏𝑛|
2
= ∑𝑁
𝑛=1|𝑎𝑛|
2
---------------------- (1)
The relationship between bn and an for two port network may be return as
[b] =[S] [a]
Using above relations bn =∑𝑛𝑖=1(𝑆𝑖 𝑎𝑖)--------------(2)
sub (2) in (1)
𝑁 𝑁 𝑁
2
∑ | ∑ 𝑆𝑛𝑖 . 𝑎𝑖| = ∑|𝑎𝑛|2
𝑖=1 𝑛=1 𝑛=1

If only I the port is executed and all other ports are matched terminated, all an=0 except
ai, so that,
∑𝑁 2
𝑛=1|𝑆𝑛𝑖. 𝑎𝑖| = ∑𝑁
𝑛=1|𝑎𝑛|
2

∑𝑁
𝑛=1|𝑆𝑛𝑖|
2
= 1

ie∑𝑁
𝑛=1 𝑆𝑛𝑖. 𝑆𝑛𝑖 ∗ = 1
 The above equation states that for a lossless network the product of any column of the
scattering matrix with the conjugate of this column equals UNITY.If all an=0 except ai&ak
∑𝑁
𝑛=1 𝑆𝑛𝑘. 𝑆𝑛𝑖 = 0 ; for i≠k
This equation states that the product of any column of the scattering matrix with the
complex conjugate of any other column is zero.In matrix notation, the relations are
expressed as
[S*] [S]t = [U]
[S*] = [𝑆𝑡]−1
[U]= Unit matrix. A matrix [S]for lossless network which satisfies the above three
conditions is called unitary matrix.
Shifting of reference planes in two port network

(a.) Phase shift property:-

Complex S-parameters of a network are defined with respect to the position of the port
(or) reference planes. For a two port network with unprimed reference planes 1 and 2
𝑏1 𝑆11 𝑆12 𝑎1
( ) = ( ) .( )
𝑎1 𝑆21 𝑆22 𝑎2
Where a1 a2 are incident waves & b1,b2 are out going waves
S-matrix for any network when the reference plane for one of its ports is shifted away
along the transmission line is given by (in fig, shifted reference is mentioned as
(12 𝑎𝑛𝑑 21 )

(
𝑏1 0
) = ( −𝑗𝛽2 𝑒 −𝑗𝛽1 𝑙1) . (𝑎1) (for lossless network)
𝑏2 𝑙2 𝑎2
𝑒 0

(
𝑏1
) 0
= ( −𝑗𝛷2 𝑒 −𝑗𝛷1 ) . (𝑎1 )
𝑏2 𝑒 0 𝑎2
Where, l1 l2 = path length.
β 1 β 2 =phase constant.

This property is valid for any number of ports and is called the phase shift property
applicable to shift of reference planes. The resultant 𝑆 1 MATRIX is
−𝑗𝛷1 −𝑗𝛷1
(𝑆 1 ) = ( 𝑒 0 ) . (S) . ( 𝑒 0 )
0 𝑒 −𝑗𝛷2 0 𝑒 −𝑗𝛷2
(4.) Zero property of S matrix
The sum of products of each term of any column (or row) multiplied by the complex
conjugate of the corresponding terms of any other column(or row) as zero and as
S11 𝑆12∗ + S21 𝑆22∗ = 0
b1 = S11 a1 + S12 a2
b2 = S21 a1 + S22 a2

Wave guide Tee:

The waveguide tees are 3 port components and are mainly of two types E-plane tee connected
in series and H-plane tee connected in shunt with section or branch of main waveguide
transmission line.
 Tees are junctions having three or more ports. Waveguide tees are used for the purpose
of connecting a branch section of waveguide in series or parallel with main waveguide.
 There are E or H- plane tees depending on whether they are in the plane of electric field
or magnetic field. Because of junctions waveguides tees are poorly matched device. For
matching reactance, tuning screws are used.
E-Plane Tee
 All the arms of E-plane tee lie in the plane of electric field which divide among the arms
as shown in figure below:

Fig: E- plane Tee

 The E-plane tee is a voltage or series junction. Each junction is symmetrical about the
central arm so that the signal to be split up is fed from it.
 The propagation of an E-field through tee junction when electromagnetic waves in TE10
mode.
 Due to the junction’s symmetry, the power delivered to port 1 and 2 are the same. Also
 the electric fields at the two outputs are 180o out of phase.
 When powers P1 and P2 are applied to port 1 and port 2 respectively and if magnitude
and phase of P1 and P2 are same then power at P3 is zero.

 Scattering matrix [S] of E-plane tee is 3x3 matrixes since there are 3 ports.
𝑆11 𝑆12 𝑆13
[𝑆] = [𝑆21 𝑆22 𝑆23]
𝑆31 𝑆32 𝑆33
 When port 3 is perfectly matched S33 = 0
𝑆13 = 𝑆31 = 1⁄√2and𝑆23 = 𝑆32 = − 1⁄√2

Therefore, S-matrix is given as

𝑆11 𝑆12 𝑆13 1 ⁄2 1⁄2 1⁄√2

[𝑆] = [𝑆21 𝑆22 𝑆23] = [ 1⁄2 1⁄2 −1⁄√2]
𝑆31 𝑆32 𝑆33 1⁄√2 −1⁄√2 0
H-Plane Tee
 H-Plane Tee is so called because the axis of the side arm is parallel to the planes of H-
field of the main transmission line. As all three arms of H-plane tee lie in the plane of
magnetic field the magnetic field divides itself into the arms, therefore it is a current
junction. Figure shows H-plane tee.

Fig: H-Plane Tee

 If the H-plane junction is completely symmetrical and the electromagnetic wave enters
through the side arm, the wave that comes out from main arms are equal in magnitude
and phase i.e the input power of port 3 is equally split into ports 1 and 2.
 When the same input powers are applied at ports 1 and 2 the output power at port 3 is
sum of input powers.
  Scattering matrix of H-plane Tee is

𝑆11 𝑆12 𝑆13 1⁄2 −1⁄2 1⁄√2

[𝑆] = [𝑆21 𝑆22 𝑆23] = [−1⁄2 1⁄2 1⁄√2]
𝑆31 𝑆32 𝑆33 1⁄√2 1⁄√2 0

Applications of E-plane and H-plane tee

 The E and H plane tees are used for impedance matching purposes. Also these are
employed for splitting the power and summing the power.

Hybrid or Magic Tee:

 A magic Tee is a combination of an E-plane and H-plane tee. It acts as a 4-port hybrid
circuit. It is also called as Hybrid Tee. Figure below shows magic tee.

Fig: Magi Tee

Characteristics of magic tee
 If two waves of equal magnitude and the same phase are fed into port-1 and port-2, the
output will be zero at port-3 and additive at port-4
 If a wave is fed into port-4, it will be divided equally between port-1 and port-2 of the
collinear arms and will not appear at port-3.
𝑺𝟏𝟒 = 𝑺𝟒𝟏 = 𝟏⁄√𝟐 𝑺𝟐𝟒 = 𝑺𝟒𝟐 = 𝟏⁄√𝟐and S34 = 0
 If a wave is fed into port-3, it will produce an output of equal magnitude and opposite
phase at port-1 and port-2. The output at port-4 is zero.
𝑺𝟏𝟑 = 𝑺𝟑𝟏 = 𝟏⁄√𝟐 𝑺𝟐𝟒 = 𝑺𝟒𝟐 = 𝟏⁄√𝟐and S34 = 0
 If a wave is fed into one of the collinear arms at port-1 or port-2, it will not appear in the
other collinear arm at port-2 or port-1 because the E-arm causes a phase delay while the
H-arm causes a phase lead.
𝑺𝟏𝟐 = 𝑺𝟐𝟏 = 𝟎
  Magic Tee is symmetrical about an imaginary plane bisecting arms port-3 and port-4.
 If port-1 and 2 are terminated in matched loads and no reflections take place inside the
junction, entrance of power through either port 3 or 4 results in equal power delivery to
arm 1 and 2. Reflections may take place due to severe discontinuities in the junction.

Effects of reflections
1. Only a portion of the power that approaches the junction through port-3 or 4 is delivered to
port-1 and 2.
2. Power is not divided equally between port-1 and 2, when power enters through port-3 or 4
3. Balance does not exist between port-1 and 2 i.e some power transmits directly from port-1
to port-2.

𝑆11 𝑆12 𝑆13 𝑆14

[𝑆] = [ 𝑆21 𝑆22 𝑆23 𝑆24
]
𝑆31 𝑆32 𝑆33 𝑆34
𝑆41 𝑆42 𝑆43 𝑆44
But S21 = 0,S12 = 0, S43 = 0, S34 = 0
S11 = 0, S22 =0, S33 = 0, S44 = 0
And S14 = S24, S13 = -S23
For port-3 and port 4 matched
Therefore S-matrix becomes
0 0 𝑆13 𝑆14 0 0 1 1
0 0 − 𝑆13 𝑆14 1 0 0 −1 1
[𝑆] = [ ]= [ ]
𝑆31 𝑆32 0 0 0 √2 1 − 1 0 0
𝑆41 𝑆42 0 0 1 1 0 0
Applications of magic Tee
1. As an isolator
2. As a matching device
3. As a phase shifter
4. As duplexer
5. As mixer
Hybrid rings (Rat-Race Circuits)
A rat-race coupler (also known as a hybrid ring coupler) is a type of coupler used in RF and
Microwave systems. In its simplest form it is a 3dB coupler and is thus an alternative to a magic
tee.
A hybrid ring consists of an annular line of proper electrical length to sustain standing waves,
to which four arms are connected at proper intervals by means of series or parallel
junctions. The below figure shows a hybrid ring with series junctions.

Fig hybrid ring with series junctions.

The hybrid ring has characteristics similar to those of the hybrid tee. When a wave is fed
into port 1, it will not appear at port 3 because the difference of phase shifts for the
waves traveling in the clockwise and counterclockwise directions is 180°. Thus the waves
are canceled at port 3. For the same reason, the waves fed into port 2 will not emerge at port 4
and so on.
The S matrix for an ideal hybrid ring can be expressed as

0 𝑆12 0 𝑆14
𝑆21 0 𝑆23 0
[𝑆] = [ ]
0 𝑆32 0 𝑆34
𝑆41 0 𝑆43 0

It should be noted that the phase cancellation occurs only at a designated frequency
for an ideal hybrid ring. In actual hybrid rings there are small leakage couplings, and
therefore the zero elements in the matrix of Eq. are not quite equal to zero.

waveguide corners, bends and twists :

These waveguide components are normally used to change the direction of the guide
through an arbitrary angle. In order to minimize reflections from the discontinuities, it is
desirable to have the mean length L between continuities equal to an odd number of
quarter-wave-lengths.

Fig Waveguide corner, bend, and twist. (a) E-plane corner. (b) H-plane corner. (c) Bend.
(d) Continuous twist.

λg.
That is, 𝐿 = (2𝑛 + 1) )
4

where n = 0, 1, 2, 3, ... , and A 8 is the wavelength in the waveguide. If the mean

length L is an odd number of quarter wavelengths, the reflected waves from both ends of
the waveguide section are completely canceled. For the waveguide bend, the minimum radius
of curvature for a small reflection is given by South worth.
as R = l.5b for an E bend
R = I.5a for an H bend
Directional couplers :

A directional coupler is a four-port waveguide junction as shown in Fig. It consists of a

primary waveguide 1-2 and a secondary waveguide 3-4. When all ports are terminated in
their characteristic impedances, there is free transmission of power, without reflection,
between port 1 and port 2, and there is no transmission of power between port 1 and port 3
or between port 2 and port 4 because no coupling exists between these two pairs of ports.
The degree of coupling between port 1 and port 4 and between port 2 and port 3 depends on
the structure of the coupler.

Fig Directional coupler.

The characteristics of a directional coupler can be expressed in terms of its coupling

factor and its directivity. Assuming that the wave is propagating from port 1 to port 2 in
the primary line, the coupling factor and the directivity are defined, respectively,
by
𝑃1
Coupling factor (dB) = 10 log10 𝑃4
𝑃4
Directivity (dB) = 10 log10𝑃3
 It should be noted that port 2, port 3, and port 4 are terminated in their characteristic
impedances. The coupling factor is a measure of the ratio of power levels in the primary and
secondary lines. Hence if the coupling factor is known, a fraction of power measured at port 4
may be used to determine the power input at port 1. This significance is desirable for
microwave power measurements because no disturbance, which may be caused by the
power measurements, occurs in the primary line. The directivity is a measure of how well
the forward traveling wave in the primary waveguide couples only to a specific port of
the secondary waveguide. An ideal directional coupler should have infinite directivity. In other
words, the power at port 3 must be zero because port 2 and port 4 are perfectly
matched. Actually, well-designed directional couplers have a directivity of only 30 to 35 dB.

S Matrix of a Directional Coupler

In a directional coupler all four ports are completely matched. Thus the diagonal elements
of the S matrix are zeros and
S11=S22=S33=S44=0
As noted, there is no coupling between port 1 and port 3 and between port 2 and port
4. Thus
S13=S31=S24=S42=0
Consequently, the S matrix of a directional coupler becomes

0 𝑆12 0 𝑆14
[𝑆] = [ 𝑆21 0 𝑆23 0
]
0 𝑆32 0 𝑆34
𝑆41 0 𝑆43 0

Equation can be further reduced by means of the zero property of the S-matrix , so we have
S12 S14*  S32 S34*  0
S 21S 23*  S41S43*  0

Also from the unity property of S matrix, we can write

S12 S12*  S14 S14*  1

Equation .......... and........... can also be written as

S12 S14  S32 S34

 S21 S23  S41 S43

Since, S12  S 21 , S14  S 41 , S 23  S32 and S34  S 43 , then

S12  S34
S14  S23
Let

S12  S34  p

Where p is positive and real, then from equation

p  S23
*
 S41   0
Let
S23  S41  jq

Where q is positive and real, then from equation

p2  q2  1

The S matrix of a directional coupler is reduced to

0 p 0 jq 
p 0 jq 0 
S
0 jq 0 p
 
 jq 0 p 0

Circulators:

 A microwave circulator is a multiport device n which power is circulated from nth port to
(n+1)th port only in one direction.
 A four port circulator is most commonly used. Figure shows a four port circulator
 Fig; Circulator
Circulator is a non-reciprocal component. All the four ports are matched and transmission
of power takes place in cyclic order only. An ideal circulator is perfectly lossless.

Principle of Operation

 Working of circulator is based on principle of Faraday rotation.

 All the ports 1, 2, 3 and 4 are oriented such that the E-field of transmitted signal couples
to these ports successively after going through a rotation of 45o in clockwise direction.

Three Port Circulator

 A three port circulator is symmetrical Y type junction of three identical waveguides with
an axially magnetized ferrite post placed at the center. Figure shows a typical three port
circulator.

Fig: Three port circulator

 The ferrite post is magnetized by static Bo field along the axis. It provides the necessary
non reciprocal property. The junction can be matched by placing suitable tuning element
in each arm.
 It is an essential component used to isolate the input and output in negative resistance
amplifier. Three port circulators are also used to couple a transmitter to various
receivers.

Four Port Circulator

 A four port Faraday rotation circulator is shown in figure below:

 Fig: Four Port Circulator

 Power entering port-1 travels along the magnetized ferrite. The direction of the field
vector gets rotated by 45o.Therefore power entered at port-1 appears at port-2.
 The power cannot be coupled to port-4 because ports-2 and 4 are 90o out of phase.
Similarly, port-3 is coupled to port-4 and port-4 to port-1.

S-matrix of Circulator:

It matrix is given by
S11 S12 S13
[S]= S21 S22 S23 ---------(1)
S31 S32 S33
As its properly matched function,

S11 = S22 = S33 = 0

The circulator is a non-reciprocal device and hence it is not symmetrical. It means

Sij ≠ Sji
But [S] is unitary

[ S ] [ S*]=1

0 𝑆12 𝑆13 0 𝑆12 ∗ 𝑆13 ∗

[𝑆] = [𝑆21 0 𝑆23] [𝑆 ∗] = [𝑆21 ∗ 0 𝑆23 ∗]
𝑆31 𝑆32 0 𝑆31 ∗ 𝑆32 ∗ 0
This gives
IS12 I^2 + I S13 I^2 = 1 --→ I S13 I^2 = 1- IS12 I^2 -------(2)
IS21 I^2 + I S23 I^2 = 1 --→ I S23 I^2 = 1- IS21 I^2 -------(3)
IS31 I^2 + I S32 I^2 = 1 --→ I S32 I^2 = 1- IS31 I^2 -------(4)
Using zero property of S matrix,
S13 S23* = 0 , S12 S32* = 0, S21 S31* = 0 and using zero property,
S23= 0 S12 = 0 S31 = 0
IS12 I=1. `. S23= 0
 I S32 I=1. `. S31 = 0
I S13 I=1. `. S12 = 0
0 0 𝑆13
[𝑆] = [𝑆21 0 0 ]
0 𝑆32 0

Thus,
0 0 1
[𝑆] = [1 0 0]
0 1 0

Applications of Circulator

 Isolation of transmitters and receivers connected to same antenna e.g. in radar system.
 Isolation of input and output in two terminal amplifying devices e.g. parametric amplifiers.

Isolators:
 Isolator is a non-reciprocal ferrite transmission device. Isolators are generally used to
improve the frequency stability of microwave generators.
 Isolators transmits electromagnetic wave only in one direction, the reflected wave is
attenuated (absorbed). Thus microwave generating active devices are isolated.
 An ideal isolator completely absorbs power of propagation in one direction and provides
loss less transmission in the opposite direction.
 The Faraday rotation provides 1 dB insertion loss in forward transmission and about 20
to 30 db isolation in reverse direction.

Fig Isolators
  Let the incident wave has E in x-direction when it propagates through ferrite rod, it is
rotated by 45o. It is launched into waveguide which is at 45o.
 Reflected wave from load travels in reverse direction and is again rotated by 45o by
ferrite rod. Reflected E appearing at resistive vane-1 is in Y-direction and it is completely
attenuated.
 The performance of an isolator is measured in terms of two basic parameters.

Insertion Loss (IL)

Insertion loss is defined as the ratio of power at the input power to the power received at the
output port. It is expressed as,
𝑃1
𝐼𝐿 (𝑑𝐵) = 10 log
𝑃2
Where, P1 Power launched at input port
P2 Power received at output port
Isolation loss(Is)
Isolation is defined as the ratio of power reflected from the output port to the power at the
input port. It is expressed as
𝑃2 ′
𝐼𝑆 (𝑑𝐵) = 10 log
𝑃1′
Where, P1’ Power at input port
P2’ Power launched from output port

For an ideal lossless matched isolator

I S21 I=1, IS12 I = IS11 I= I S22 I=0

[S] = [0 0]
1 0
Application of Isolator
 In Klystrons and Magnetrons to improve the frequency stability.
Microwave Measurements: VSWR

VSWR stands for Voltage Standing Wave Ratio, and is also referred to as Standing Wave
Ratio (SWR). VSWR is a function of the reflection coefficient, which describes the power
reflected from the antenna.
 Two commonly method used methods for measuring VSWR are:
1. Slotted Line Technique – for Low VSWR(S < 20)
2. Double Minimum Method – for High VSWR(S > 20)
 When load impedance is not equal to source impedance, standing waves are produced.
By inserting a slotted line section in the transmission line, standing waves can be traced
by moving the carriage with a tunable probe detector along the line.
 VSWR can be measured by detecting Vmax and Vmin in the VSWR meter:
S=Vmax / Vmin
 The setup for measuring VSWR using slotted line technique is shown in the figure
below:

VSWR Tunable Probe

Meter detector

AM Microwave Frequency Slotted Line

Isolator Variable
Source Meter Section
Attenuator

Matched
Termination
Fig: Slotted Line Method of VSWR Measurement - Basic Experimental Setup
 The variable attenuator is adjusted to 10dB. The microwave source is set to required
frequency. The 1 KHz modulation is adjusted for maximum reading on the VSWR meter
in a 30dB scale. The probe carriage stub is tuned for maximum detected signal in VSWR
meter.
 The probe carriage is slided along the non-radiating slot from the load end until a peak
reading is obtained in VSWR meter. The meter’s gain control is adjusted to get the meter
reading at 1.0 or 0dB corresponding to the position of voltage maximum.
 The probe is moved towards the generator to an adjacent voltage minimum. The
 corresponding reading in VSWR meter directly gives the VSWR = Vmax / Vmin on the
top of SWR normal scale for 1≤S≤4 or on the Expanded scale for 1≤S≤1.33.
 The experiment is repeated for other frequencies as required to obtain a set values of S
Vs f.
 For VSWR between 3.2 and 10, a 10dB lower range should be selected and reading
corresponding to Vmin position should be taken from the second VSWR normal scale
from the top.

Power for VSWR:

 Power is defined as the quantity of energy dissipated or stored per unit time. The range
of microwave power is divided into three categories – low power(less than 10mW),
medium power (from 10mW to 10W) and high power (greater than10W).
 The average power is measured while propagation in a transmission medium and is
defined by,
1 nT
Pav = ∫ v(t)i(t)dt
nT 0
Where, T is the time period of the lowest frequency involved in the signal and n cycles
are considered. For pulsed signal
1 τ
Ppeak = ∫ v(t)i(t)dt
τ 0
Pav = Ppeak ∗ Duty Cycle
Duty cycle = pulse width ∗ p. r. f. d = τfr = τT < 1
Where τ is the pulse width, T is the period and fr is the pulse repetition frequency. The
most convenient unit of power at microwaves is dBm.
P(mW)
P(dBm) = 10 log
1mW
viz. , 30 dBm = 1W and − 30 dBm = 1μW.
 The sensors are used for power measurements are the schottky barrier diode, bolometer
and the thermocouple.
Impedance scattering parameters:
Impedance can be measured by the following two methods:
i. Slotted Line Method
ii. Impedance measurement
Slotted Line Method:
 For high frequencies, the impedance will be complex. The complex impedance ZL
of the load can be measured by measuring the phase angle фL of the complex
reflection co-efficient ГL from the distance of first voltage standing wave minimum
(dmin) and the magnitude of the same from the VSWR,S.
 The equation below gives the relation between the load impedance and the
reflection co-efficient for the computation of ZL.
1 + ГL
𝑍𝐿 = 𝑍𝑜
1 − ГL
1−𝑆
Where,ГL = ρ𝐿𝑒 𝑗фL and 𝑆 = (1 + ρ𝐿 )(1 − ρ𝐿 ) 𝑜𝑟 ρ𝐿 = 1+𝑆

Tunable Probe
Detector VSWR Meter

Unknown
Slotted line
load or short

Fig: Determination of load impedance using slotted line

 The method of using slotted line to determine an unknown impedance is

explained as follows:
1. Adjust the probe depth of the slide screw tuner to an approximate level.

2. Move the probe position of the SWR, to a minimum and note down the Verne
reading (d1).

3. Also note down the corresponding SWR value (S) on the SWR meter.

4. Remove the load and connect only the tunable detector or movable short.

5. Move the probe position of SWD carefully in any one direction and note down
the Vernier reading (d2) for two successive minima d1 and d2.
 6. Calculate the guide wavelength, λg as, λg= 2×distance between successive
minima i.eλg = 2(d1-d2)and 𝛽 = 2𝜋⁄λg

7. Now the phase angle can be calculated by the formula, φL = 2βdmin − π

8. The unknown impedance of the load is the calculated from the above said
relation,
1 + ГL
𝑍𝐿 = 𝑍𝑜
1 − ГL

Fig: Determination of dmin

 To ease the calculation, smith chart ZL from the measurements of S and dmin as
following:

1. Draw a circle on the Smith chart corresponding to the SWR values

(S).
2. Locate the point X on the chart.
NOTE: (a) d1-d2 >0 (corresponding to wavelength towards load)
(b) dL-dS1<0 (corresponding to wavelength towards generator).
3. Draw the line from the point (1+j0) to X.
4. Identify the ZL as the impedance at the point of intersection of S circle and the
line joining (1+j0) and X. Therefore,
ZL = (impedance obtained from Smith chart)*(characteristics impedance ).
 For Example. Let us consider VSWR(S) = 2 and (dmin /λg) = 0.2 say,
 Draw the VSWR circle centered at 0 (r=1) with radius cutting the r-axis at
S=2.
 Move from the short circuit load point A on the chart along the wavelengths
toward load scale by distance (dmin /λg) B. join OB.
 The point of intersection between the line OB and the VSWR circle gives the
 normalized load 𝑧𝐿 = 𝑍𝐿⁄𝑍𝑜 and hence the complex load
ZL = Zo × (1.0 +j 0.7)

Dielectric constant measurements:

 The dielectric constant εr is defined by the permittivity ε of the material with respect to
that εo of air or free space
10−9 𝑓𝑎𝑟𝑎𝑑
εr = ε⁄εo , εo = ( )
36𝜋 𝑚
 Due to presence of non-zero conductivity, dielectric material exhibits loss resulting in
complex value represented by,
εr = ε′ r + jε′′ r

 The loss tangent, 𝑡𝑎𝑛 𝜕 = ε′′r⁄

ε′r
 The measurement of the complex dielectric constant is required not only in scientific
application but also for industrial applications such as microwave heating or ovens and
to study the biological effects of microwaves.
 The dielectric constant is not independent of frequency hand for most common
microwave applications. On the other hand, the percent variation in ε’’r is almost always
greater than that of ε’r so that ε’’r should be measured near the frequency or frequencies
of interest.
 There are several methods available for dielectric constant measurement. The following
sections describe two commonly used two methods: the waveguide method and cavity
perturbation method.

Waveguide Method
 In this method it is assumed that the material is lossless. A dielectric sample AB
completely fills a length of the waveguide and the end is terminated in a short as shown
in figure:
 A voltage standing wave minimum is observed in the slotted line at C (say)
Let, le = AB = the dielectric sample length
lo = BC
 Then the distance of Vmin from short circuit = le+lo = AC. For a dielectric filled guide
 of characteristics impedance Ze, input impedance at β is purely reactive,
Zin′ = jZe tan βele, where βe is propagation constant
 Using this Zin’ as termination at β, input impedance at C for the empty guide is
Zin′ + j Zo tan βolo
Zinc = = 0, at Vmin point
Zo + j Zin′ tan βolo
Therefore,Zin′ + j Zo tan βolo = 0 orjZe tan βele + j Zo tan βolo = 0
Or, Zo tan βolo = − Ze tan βele
Assuming nonmagnetic dielectric in the waveguide,
Zo βe
=
Ze βo
βe
Or, Zo = βo . Ze

Substituting this value, we get,

βe
. Ze. tan βolo = −Ze tan βele
βo
lo tan βolo le tan βele
or, = −
βolo βele

lo. tan Y tan X

or, = − ; where X = βele; Y = βolo
le. Y X
For dominant mode,βo = 2π⁄λgo and λgo = 2 ∗ distance between two successive Vmin

Which can be measured by the slotted line, lo and le are also measured in the
slotted line. Therefore, the left hand side of the above transcendental is known and it
tan X
can be written as X
= −α

The above equation can be solved for determiningX = βele, now

2π 2π λo 2
βe = = √[εr − ( ) ] , λc = 2a, where a − waveguide broadwall dimension.
λge λo λc

Since βe is known, εr. Hence two different lengths of sample are taken for two sets
of solutions.
For length le: X = X1, X2… εr = εr1, εr2, …
For length l’e:X = X1’,X2’,……; ε′r = εr′1, εr′2, …
Antenna radiation pattern and gain measurement:

 The radiation pattern is a representation of the radiation characteristics of the

antenna as a function of elevation angle θ and azimuthal angle φ for a constant
radial distance and frequency.
 The three-dimensional pattern is decomposed into two orthogonal two–dimensional
patterns in E and H field’s planes where the Z-axis is the line joining the transmitting
and receiving antennas and perpendicular to the radiating apertures.
 Due to the reciprocal characteristics of antennas, the measurements are performed
with the test antenna placed in the receiving mode.
 The source antenna is fed by a stable source and the received signal is measured
using a receiver.
 Or capacitive causes error in measurement. The output of the receiver is fed to Y-
axis input of an XY receiver.
 The receiving antenna positioner controller plane and the angle information is fed to
X-axis input of the XY recorder.
 Thus the amplitude Vs angle plot is obtained from the receiver output.
 Initially two antennas are aligned in the line of their maximum radiation direction by
adjusting the angle and height by the controller and the antenna mast. Effects of all
surrounding are removed or suppressed through increased directivity and low side
lobes of the source antenna, clearance of LOS, and absorption of energy reaching
the range surface.
 The following precautions are taken for better accuracy in the measurements:
1. Effects of coupling between antennas-inductive or capacitive causes error
measurements. The former exists at lower microwave frequencies and negligible
if range R ≥ 10 λ. Mutual coupling due to scattering and retardation of energy by
test and source antenna causes error in measurement.
2. Effect of curvature of the incident phase front produces variation over the
aperture of test antenna and this restricts the range R. for a phase deviation at
the edge ≤ π/8 radians, R ≤ 2D2 λ, where D is the maximum size of the aperture.
 3. Effect of amplitude taper over the test aperture will give deviation of the
measured pattern from the actual. This occurs if the illuminating field is not
constant over the region of the test aperture. Tolerable limit of amplitude taper is
0.25 dB, for which decrease in gain is 0.1 dB,
4. Interference from spurious radiating sources should be avoided.
Phase measurement of antenna:
 The phase of the radiated field is a relative quantity and is measured with respect to
a reference as shown in figure below:

Fig: Phase pattern Measurement

 This reference is provided either by coupling a fraction of the transmitted signal to
the reference channel of the receiver or by receiving the transmitted signal with a
fixed antenna placed near the test antenna. The fixed antenna output is fed to the
reference channel of the receiver and the phase pattern is recorded as the antenna
under the test is rotated in the horizontal plane.

Gain of the antenna:

There are three basic methods that can be used to measure the gain:
1. Standard Antenna Method
2. Two antenna method
3. Three antenna method
1. Standard Antenna Method
 This method uses two sets of measurements with the test and standard gain antennas.
Using the test antenna of gain Gr in receiving mode, the received power, Pr is recorded
in a matched recorder.
  The test antenna is then replaced by a standard gain antenna of gain Gs and the
received power, Ps is again recorded without changing the transmitted power and
geometrical configuration. Then,
Pr⁄ = Gr⁄
Ps Gs
Pr
Or, Gr(dB) = Gs(dB) + 10 log (Ps)

 Thus by measuring the received power with test and standard gain antennas and
knowing gain Gs of the standard gain antenna, the gain of the test antenna can be
found.
2. Two Antenna Method
 In this method, the signal is transmitted from a transmitting antenna of gain Gt, and the
signal is received by the test antenna of gain Gr placed at far-field distance R. The
received power is expressed by,
PtGtGrλ2
Pr =
(4πR)2
4πR Pr
or, Gr(dB) + Gt(dB) = 20 log ( λ
)+ 10 log ( Pt) ;

Where, Pr is the received power and Pt is the transmitted power. When the two antennas are
selected identical, Gr = Gt so that
4πR Pr
Gr(dB) = Gt(dB) = 10 log ( ) + 5 log ( )
λ Pt
 By measuring R, λ and Pr / Pt, the gain Gr can be determined.

AM
Variable Directional
Microwave Tuner Tuner
Attenuator Coupler
Source
Tx Rx
Attenuato
r
Power Meter
Power
Meter

Fig: Block Diagram of Antenna Gain Measurements

3. Three Antenna Method
 In two antenna method if the measuring systems are not exactly identical,error will be
introduced. Hence three antenna method is the most general method to find gain of all
the three antennas. Any two antennas are used at a time i.e 1 and 2, 2 and 3, and 3 and
1, respectively.
 The following equations can be developed for the received and transmitted powers.
4πR Pr2
G1(dB) + G2(dB) = 20 log ( ) + 10 log ( );
λ Pt1
4πR Pr3
G2(dB) + G3(dB) = 20 log ( ) + 10 log ( );
λ Pt2
4πR Pr1
G3(dB) + G1(dB) = 20 log ( ) + 10 log ( ).
λ Pt3
 Since R and λ are known and (Pr/Pt)’s measured, the right hand side of the above
equations are known. The three unknown quantities G1, G2 and G3 can be determined
from the above three equations.
 For accuracy of the measurements, care must be taken so that
1. All antennas meet the far field criteria: R ≥ 2D2 /λ
2. The antennas are aligned for bore=sight radiation face – to face.
3. The measuring system is frequency stable.
4. Impedance mismatched in the system components is minimum.
5. Polarization mismatch is minimum.
6. Reflection from various background and support structure is minimum.
 UNIT – III Optical Fibers

Element of an Optical Fiber Transmission link :

A fiber optic data link sends input data through fiber optic components and provides this data
as output information. It has the following three basic functions:
 To convert an electrical input signal to an optical signal
 To send the optical signal over an optical fiber
 To convert the optical signal back to an electrical signal
A fiber optic data link consists of three parts – transmitter, optical fiber and receiver. Figure
below shows the fiber optic connection. The transmitter, optical fiber and receiver perform the
basic functions of the fiber optic data link.

Fig: Major Elements of a Optical Fiber Transmission Link

 The transmitter, consisting of a light source can effectively convert an electrical input
signal to an optical signal and lunch the data containing light down the optical fiber.
 A receiver consisting of a photodetector plus amplification and signal-restoring
circuitry, can effectively detects the optical signal and transform this optical signal
back into its original form.
 Additional components include optical connectors, splices, couplers or beam splitters
and repeaters.

Transmitter
  The transmitter is used to launch optical power into the fiber.
 The two types of optical sources are: light-emitting diode(LEDs) and Laser diodes.
 The electric input signals to the transmitter circuitry converts these electric signals to
an optical signal by varying the current flow through the light source.

 An optical source is a square-law device, which means that a linear variation in drive
current results in a corresponding linear change in the optical output power.
 In the 800-900 nm region the light sources are generally alloys of GaAlAs. At the
longer wavelengths (1100 tp 1600 nm), an InGaAsP alloy is the principal optical
source material.
 After an optical signal has been launched into the fiber, it will become progressively
attenuated and distorted with increasing distance because of scattering, absorption
and dispersion mechanisms in the waveguide.
 When an optical signal has travelled a certain distance along the fiber, the signal has
become attenuated and distorted to such a degree that a repeater is needed in the
transmission line to amplify and reshape the signal.
 An optical repeater consists of a receiver and a transmitter placed back to back. The
receiver section detects the optical signal and converts it to an electric signal, which is
amplified, reshaped and sent to the electric input of the transmitter section.
 The transmitters section converts this electric signal back to an optical signal and
sends it on down the optical fiber waveguide.
 Finally, The coupler must efficiently transfer themodulated light beam from the source
to the optic fiber.

Information Channel

 The information channel is the path between the transmitter and receiver.
 The cabled optical fiber is one of the most important elements in an optical fiber link.
In addition to protecting the glass fibers during installation and service, the cable may
contain copper wires for powering repeaters which are needed for periodicity
amplifying and reshaping the signal when the link spans long distances.
 The cable generally contains several cylindrical hair-thin glass fibers, each of which is
an independent communication channel. Analogous to copper cables, the installation
of optical fiber cables can be aerial in ducts, undersea or buried directly in the ground.
 Individual cable lengths will range from several hundred meters to several kilometers
for long- distance applications. The shorter lengths tend to be used when the cables
are pulled through ducts. Longer cable lengths are used in aerial or direct-burial
applications.
 The complete long distance transmission line is formed by splicing or connecting
together these cable sections.
Receiver
 The design of the receiver is inherently more complex than that of the transmitter,
since it has to both amplify and reshape the degraded signal received by the
photodetector.
 The ability of a receiver to achieve a certain performance level depends on the
photodetector type, the effects of noise in the system, and the characteristics of the
successive amplification stages in the receiver.
 At the receiver the attenuated and distorted modulated optical power emerging from
the fiber end will be detected by a photodiode.
 Analogous to the light source, the photodetector is also a square-law device since it
converts the received optical power directly into an electric current
output(photocurrent).
 Semiconductor pin and avalanche photodiodes (APDs) are the two principal
photodetectors used in a fiber optical link.
 For low power application optical signal is received an avalanche photodiode is
normally used, since it has greater sensitivity.
 Silicon photodetectors are used in the 800-900 nm regions. A variety of optical
detectors are available at the longer wavelengths. The prime material candidate in the
1100 to 1600 nm region is an InGaAs alloy.


Advantages Of Optical Communication System:

1. Enormous Potential Bandwidth:

The optical carrier frequency in the range of 10¹³ to 10¹⁶ Hz (10¹⁴Tera hertzange) gives a
greater potential transmission bandwidth than metallic cable system.
2. Small Size and Weight:

Optical fiber has a very small diameter (diameter of a human hair) .Hence, even such fibers
are converted with protective coatings they are far smaller and lighter than copper cables.
3. Electrical Isolation:

Optical fiber which are fabricated from glass or plastic polymer are electrical insulators unlike
their metallic counter parts, they do not exhibit earth loop and interface problem. Therefore,
Optical fiber transmission is ideally suited for electrical hazardous environment as the fiber
creates no arcing (or) spark hazard at abrasion (or) short circuits.
4. Immunity to Interference and Crosstalk:
 Optical fiber forms a dielectric wave guide and free from electromagnetic interference
(EMI), radio frequency interference (RFI) (or) switching transient giving
electromagnetic pulses (EMP).
 Optical fiber transmission requires no shielding from EMI when it is used in electrically
noisy environment.
  Fiber cable also not suitable to lightning strikes if used over head rather underground.
5. Signal Security:
 The light from optical fiber doesn’t radiate significantly and therefore likely provide a
high degree of signal security.
 Transmitted optical signal cannot be trapped by third person. This feature is attractive
for military, banking and general data transmission applications.
6. Low Transmission Loss:
 Optical fiber exhibit low attenuation (or) transmission loss in comparison with the best
copper conductors. Fibers have been fabricated with losses as low as 0.2 dB/km.
7. Ruggedness and Flexibility:
 Fibers are manufactured with high tensile strengths. The fibers may also be bent to
quite small radii (or) twisted without damage.
 Because of the small sized, weight and flexibility optical fibers are generally superior in
terms of storage, transportation, handling and installation to corresponding copper
cables.
8. System Reliability And Ease Of Maintenance:

repeaters (or) line amplifiers to boost the transmitted signal strength with fewer
repeaters reliability is enhanced in comparison to conventional electrical system.
 Life time of optical fibers is 20 to 30 years. It reduces maintenance time and cost.

Propagation of light :

 Until the early seventeenth century it was generally believed that the light consisted of
a stream of minute particles that were emitted by luminous sources.
 These particles were pictured as travelling in straightlines, and it was assumed that
they could penetrate transparent materials but were reflected from opaque ones.
 This theory adequately described certain large scale optical effects such as reflection
and refraction, but failed to explain finer-scale such as interference and diffraction.
 Later the work of Maxwell in 1864 theorized that light waves must be electromagnetic
in nature.
 Furthermore observation of polarization effects indicated that light waves are
transverse (that is, the wave motion is perpendicular to the direction in which the wave
travels.)
 The electromagnetic wave radiated by a small optical source can be represented by a
train of spherical wave fronts with the source at the center as shown in figure.
Fig; Representation of Spherical and Plane Wave front

 A wave front is defined as the locus of all points in the wave train which have the
same phase.
 The speed of electromagnetic wave (c) in free space is approximately 3 x 108 m/sec.
 The distance travelled during eachcycle is called as wavelength (λ)

λ f=c

Where,
c - Velocity of electromagnetic radiation, usually called the speed of light.
λ- Wavelength
f- Frequency

 In fiber optics, it is more convenient to use the wavelength of light instead of the
frequency with light frequencies; wavelength is often stated in microns or nanometers.

1 micron (μ) = 1 Micrometre (1 x 10-6)

1 nano (n) = 10-9metre
 Fiber optics uses visible and infrared light. Infrared light covers a fairly wide range
ofwavelengths and is generally used for all fiber optic communications. Visible light is
normally used for very short range transmission using a plastic fiber.
 The photon energy is found to depend only on the frequency. This frequency inturn,
must be measured by observing a wave property of light.
 The relationship between the energy E and the frequency v of a photon is given by,

Where, h= 6.625×10-34 J is Planck’s constant.

 When light is incident on an atom, a photon can transfer its energy to an electron
within this atom, thereby exciting it to a higher energy level.
 The energy absorbed by the electron must be exactly equal to that required to excite
state can drop to a lower state separated from it by an energy hv by emitting a photon
of exactly this energy.
 Before studying how the light actually propagates through the fiber, laws governing the
 nature of light must be studied. This is called as laws of optics (Ray theory).

Fig: Electromagnetic Spectrum

 The speed of light depends upon the material or medium through which it is moving. In
free space light travels at its maximum possible speed i.e. 3 x 108 m/s or 186 x 103
miles/sec.
 When light travels through a material it exhibits certain behavior explained by laws of
reflection, refraction.
Reflection
 The law of reflection states that, when a light ray is incident upon a reflective surface
at some incident angle from imaginary perpendicular normal, the ray will be reflected
from the surface at some angle from normal which is equal to the angle of incidence.

Fig: Reflection
Refraction
 Refraction occurs when light ray passes from one medium to another i.e. the light ray
changes its direction at interface. Refraction occurs whenever density of medium
changes. E.g. refraction occurs at air and water interface, the straw in a glass of water
will appear as it is bent.
 The refraction can also observed at air and glass interface.
 When wave passes through less dense medium to denser medium, the wave is
refracted (bent) towards the normal. Fig. below shows the refraction phenomena.

Fig: Refraction
 The refraction (bending) takes place because light travels at different speed in
different mediums. The speed of light in free space is higher than in water or glass.
Refractive Index
 The amount of refraction or bending that occurs at the interface of two materials of
different densities is usually expressed as refractive index of two materials. Refractive
index is also known as index of refraction and is denoted by n.
 Based on material density, the refractive index is expressed as the ratio of the velocity
oflight in free space to the velocity of light of the dielectric material (substance).

 The refractive index for vacuum and air is 1.0. For water it is 1.3 and for glass
refractive index is 1.5.
Snell’s Law
 Snell‘s law states how light ray reacts when it meets the interface of two media having
different indexes of refraction.
 Let the two medias have refractive indexes n1 and n2 where n1 >n2. Let n1 and n2 be
the angles of incidence and angle of refraction respectively. Then according to Snell‘s
law, a relationship exists between the refractive index of both materials given by,

 A refractive index model for Snell’s law is shown in figure below:

 The refracted wave will be towards the normal when n1 < n2 and will away from it
when n1 > n2. And, the equation below shows that the ratio of refractive index of two
mediums is inversely proportional to the refractive and incident angles.
Critical Angle
 When the angle of incidence (θ1) is progressively increased, there will be progressive
increase of refractive angle (θ2). At some condition, the refractive angle (θ2) becomes
90o to the normal. When this happens the refracted light ray travels along the
interface. The angle of incidence (θ1) at the point at which the refractive angle (θ1)
becomes 90o is called the critical angle. It is denoted by θc.
 The critical angle is defined as the minimum angle of incidence (θ1) at which the ray
strikes the interface of two media and causes an angle of refraction (θ2) equal 90oto
90o. Figshows critical angle refraction.

Fig: Critical Angle

Total Internal Reflection

 “When the light travels from a medium of higher refractive index to a medium of lower
refractive index and it strikes the boundary at more than the critical angle, all the light
will be reflected back to the incident medium, which means it will not penetrate the
second medium”. The phenomenon is called “Total Internal Reflection”.
 Conditions for the total internal reflection are:
(1) Light should travel from high refractive index material to lower refractive index material.
(2) Incident angle should be greater than the critical angle.
.
 Total Internal Reflection can be observed only in materials in which the velocity of light
is less than in air.
 The two conditions necessary for Total Internal Reflection to occur are :
 The refractive index of first medium must be greater than the refractive index of
second one.
 The angle of incidence must be greater than (or equal to) the critical angle.

Fig: Representation of critical angle and total internal reflection at the glass-air
interface

 If the angle if incidence θ1 is decreased, a point will eventually be reached where the
light ray in air is parallel to the glass surface.
 This point is known as the critical angle of incidence θc. When the incident angle θ1 is
less than the critical angle, the condition for internal reflection is satisfied; that is, the
light is totally reflected back into the glass with no light escaping from the glass
surface.
Numerical Aperture

 The numerical aperture (NA) of a fiber is a figure of merit which represents its light
gathering capability. Larger the numerical aperture, the greater the amount of light
accepted by fiber.
 The acceptance angle also determines how much light is able to be enter the fiber and
hence there is relation between the numerical aperture and the cone of acceptance.
 The rays striking the core-cladding interface at angles less than θmin will refract out of
the core and be lost in the cladding.
Fig: Meridional Ray optic representation of the propagation mechanism
 By the formula of NA note that the numerical aperture is effectively dependent only on
refractive indices of core and cladding material. NA is not a function of fiber
dimension.
 The numerical aperture is a dimensionless quantity whichis less than unity, with
values normally ranging from 0.14 to 0.50.
 Also, the acceptance angle can be calculated by using the formula,

 The Cone of acceptance is the angle within which the light is accepted into the core
and is able to travel along the fiber. The launching of light wave becomes easier for
large acceptance come.

Fig: Acceptance Cone of Optic Fiber

 The angle is measured from the axis of the positive cone so the total angle of
convergence is actually twice the stated value

Types of Rays

 If the rays are launched within core of acceptance can be successfully propagated
along the fiber. But the exact path of the ray is determined by the position and angle of
ray at which it strikes the core.
 There exist three different types of rays.
i) Skew ray
ii) Meridional rays
iii) Axial rays.

 The skew ray does not pass through the center, as show in Fig.(a) shown below. The
skew rays reflects off from the core cladding boundaries and again bounces around
the outside of the core. It takes somewhat similar shape of spiral of helical path.
Fig: Different Ray Propagation
 The meridional ray enters the core and passes through its axis. When the core
surface is parallel, it will always be reflected to pass through the fiber. The meridional
ray is shown in fig. (b).
 The axial ray travels along the axis of the fiber and stays at the axis all the time. It is
shown in fig. (c).

Optical fiber structures with neat sketch:

 The basic structure of an optical fiber consists of three parts; the core, the cladding
and the coating or buffer. The basic structure of an optical fiber is shown on figure
below.

Fig: Structure of a single Fiber

 The core is a cylindrical rod of dielectric material.Dielectric material conducts no
electricity. Light propagates mainly along the core of the fiber. The core is generally
made of glass. The core is described as having a radius of ‘a’ and an index of
refraction ‘n1’.
 The core is surrounded by a layer of material called the cladding. Even though light
will propagate along the fiber core without the layer of cladding material, the cladding
does perform some necessary functions.
 The cladding layer is made of a dielectric material with an index of refraction ‘n2’. The
refractive index of the cladding material is less than that of the core material.
 The cladding is generally made of glass or plastic. The cladding performs the following
functions:
  Reduces loss of light from the core into the surrounding air
 Reduces scattering loss at the surface of the core.
 Protects the fiber from absorbing surface contaminants
 Adds mechanical strength.
 For extra protection, the cladding is enclosed in an additional layer called the coating
or buffer. The coating or buffer is a layer of material used to protect an optical fiber
from physical damage. The material used for a buffer is a type of plastic.
 The buffer is elastic in nature and prevents abrasions. The buffer also prevents the
optical fiber from scattering losses caused by microbends. Microbends occur when an
optical fiber is placed on a rough and distorted surface.
 The basic fiber building blocks are used to form large cable. These units are bound on
a buffer material which acts as strength element along with insulated copper
conductor. The fiber building blocks are surrounded by paper tape, PVC jacket, yarn
and outer sheath.

Fig: Six Fiber cable

Fiber Optic Cable Ducts

Number of cores is bundled in plastic ducts. To ease identification, individual fibers are color
coded Table below shows an example of the color coding used by manufacturers.

Fiber number Color

Optical Fiber types
 Variations in the material composition of the core give rise to the two commonly used
fibertypes shown in figure below: In the first case the refractive index of the core is
uniform throughout and undergoes an abrupt change (or step) at the cladding
boundary. This is called step-index fiber.
 The core typically has diameter of 50-80 μm and the cladding has a diameter of 125
μm.
 The refractive index profile of the step-index fiber is defined as,

 Second case the core refractive index is made to vary as a function of the radial
distance from the center of the fiber. This type is a graded-index fiber.

Fig: Index Profile

 The refractive index profile across the core takes the parabolic nature as shown in
figure above.
 A graded index fiber has lower coupling efficiency and higher bandwidth than the step
index fiber. It is available in 50/125 and 62.5/125 sizes. The 50/125 fiber has been
optimized for long haul applications and has a smaller NA and higher bandwidth.
62.5/125 fiber is optimized for LAN applications which is costing 25% more than the
50/125 fiber cable.
 The refractive index variation in the core is giver by relationship

Where, r- Radial distance from fiber axis

a- Core radius
n1- Refractive index of core
n2- Refractive index of core
α- Shape of index profile
 Profile parameter αdetermines the characteristic refractive index profile of fiber core.
 The range of refractive index as variation of αis shown in Figure below.
Fig: Possible fiber refractive index profiles for different values of α
 Both Step and graded-index fibers can be further divided into single mode and
multimode classes. Single Mode fiber sustains only one mode of propagation,
whereas multimode fibers contain many hundreds of modes.
Name of the subject: MICROWAVE AND OPTICAL ENGINEERING Sub Code: EC T-71
Name of the Faculty: N.SASIKALA Yr/Sem/Sec:IV/VII/
Date: Day: Hour:5

Single Mode Fibers

 Single mode fiber allows propagation to light ray by only one path.
 The core size of single mode fibers is small. The core size (diameter) is typically
around 8 to 12 micrometers.
 A fiber core of this size allows only the fundamental or lowest order mode to
propagate only one mode, because the core size approaches the operational
wavelength. The value of the normalized frequency parameter relates core size with
mode propagation.
 In single mode fibers, the frequency is less than or equal to 2.405. When the
frequency and wavelength 2.405, single mode fibers propagate the fundamental mode
down the fiber core, while high-order mode are lost in the cladding.
 For low frequency values, most of the power is propagated in the cladding material.
Power transmitted by the cladding is easily lost at the fiber ends. The value of
frequency should remain near the 2.405level.
 Single mode fibers have a lowersignal loss and a higher information capacity(
bandwidth) than multimode fibers. Single mode fibers are capable of transferring
higher amounts of data to low fiber dispersion.
 In single mode fibers, the wavelength can increase or decrease the losses caused by
fiber bending.
 They lose power because light radiates into cladding, which is lost at fiber bends. In
general, single mode fibers are considered to be low-loss fibers which increase
 system bandwidth and length.
 Some disadvantages of single mode fiber are smaller core diameter makes coupling
light into the core more difficult.

Fig: Single Mode Propogation

Multimode Fibers
 The term multimode simply refers to the fact that numerous modes (light rays) are
carried simultaneously through the waveguide. Multimode fiber has a much larger
diameter, compared to single mode fiber; this allows large number of modes.
 Another advantage is that multimode fibers permit the use of light emitting diodes
(LEDs). Single mode fibers typically must use laser diodes. LEDs are cheaper, less
complex and last longer. LEDs are preferred for most applications.
 The disadvantage is that multimode fibers suffers from intermodal dispersion

Optic Fiber Configurations

Depending on the refractive index profile of fiber and modes of fiber there exist three types of
optical fiber configurations. These optic-fiber configurations are -

i) Single mode step index fiber.

ii) Multimode step index fiber.
iii) Multimode graded index fiber

Single mode Step index Fiber

 Single mode step index fiber has a central core that is sufficiently small so that there is
essentially only one path for light ray through the cable. The light ray is propagated in
the fiber through reflection.
 Typical core sizes are 8 to 12μm.
 Single mode fiber is also known as fundamental or monomode fiber.
 Single mode fiber will permit only one mode to propagate and does not suffer from
mode delay differences. These are primarily developed for the 1300 nm window but
they can be also be used effectively with time division multiplex (TDM) and
wavelength division multiplex (WDM) systems operating in 1550 nm wavelength
region.
  The core fiber of a single mode fiber is very narrow compared to the wavelength of
light being used. Therefore, only a single path exists through the cable core through
which light can travel.
 The disadvantage of this type of cable is that because of extremely small size
interconnection of cables and interfacing with source is difficult.

 Another disadvantage of single mode fibers is that as the refractive index of glass
decreases with optical wavelength, the light velocity will also be wavelength
dependent. Thus the light from an optical transmitter will have definite spectral width.

Multimode step Index Fiber

 diameter is 50 to 1000 μm i.e. large aperture and allows more light to enter the cable.
The light rays are propagated down the core in zig-zag manner.
 There are many paths that a light ray may follow during the propagation.
 The light ray is propagated using the principle of total internal reflection. Since the
core index of refraction is higher than the cladding index of refraction, the light
entersat less than critical angle is guided along the fiber.
 Light rays passing through the fiber are continuously reflected off the glass cladding
towards the center of the core at different angles and lengths, limiting overall
bandwidth.
 The disadvantage of multimode step index fibers is that the different optical length
scaused by various angles at which light is propagated relative to the core, causes the
transmission bandwidth to be fairly small. Because of these limitations, multimode
step index fiber is typically only used in applications requiring distances of less than 1
km. Multimode step index fiber is more widely used type. It is easy to manufacture.
Its core

Multimode Graded Index Fiber

 The core size of multimode graded index fiber cable is varying from 50 to 100 μm
range.
 The light ray is propagated through the refraction. The light ray enters the fiber at
many different angles.
 As the light propagates across the core toward the center it is intersecting a less
dense to more dense medium.
 Therefore the light rays are being constantly being refracted and ray is bending
continuously. This cable is mostly used for long distance communication.
Fig (a) Single mode step index Fiber(b) Multimode Step-index Fiber(c) Multimode
graded-index Fiber
 The light rays no longer follow straight lines; they follow a serpentine path being
gradually bent back towards the center by the continuously declining refractive index.
 The modes travelling in a straight line are in a higher refractive index so they travel
slower than the serpentine modes. This reduces the arrival time disparity because all
modes arrive at about the same time.
 Figure below shows the light trajectory in detail. It is seen that light rays running close
to the fiber axis with shorter path length, will have a lower velocity because they pass
through a region with a high refractive index.

 Rays on core edges offers reduced refractive index, hence travel more faster than
axial rays and cause the light components to take same amount of time to travel the
length of fiber, thus minimizing dispersion losses.
 Each path at a different angle is termed as ‘transmission mode‘ and the NA of
graded index fiber is defined as the maximum value of acceptance angle at the fiber
axis.
 Typical attenuation coefficients of graded index fibers at 850 nm are 2.5 to 3 dB/km,
while at 1300 nm they are 1.0 to 1.5 dB/km.
 The main advantages of graded index fiber are:
Reduced refractive index at the center of core.
Comparatively cheap to produce.

Optical losses and brief square losses:

Introduction

The signal attenuation of fiber determines the maximum distance between transmitter and
receiver. The attenuation also determines the number of repeaters required, maintaining
repeater is a costly affair.
Attenuation
 Attenuation of a light as it propagates along a fiber is an important consideration in the
design of an optical communication system in determining the maximum transmission
distance between a transmitter and a receiver.
 Attenuation in an optical fiber is caused by absorption, scattering and bending losses.
 Absorption is related to the fiber material, whereas scattering is associated both with
the fiber material and with structural imperfections in the optical waveguide.
 Scattering due to structuralism perfection within the fiber. Nearly 90 % of total
attenuation is caused by Rayleigh scattering only.
 The Rayleigh scattering is wavelength dependent and reduces rapidly as the
wavelength of the incident radiation increases.
 Micro bending of optical fiber also contributes to the attenuation of signal.

Attenuation Units
 Signal attenuation (or fiber loss) is defined as the ratio of the optical output power Pout
from a fiber of length L to the optical input power Pin .
 This power ratio is a function of wavelength. The symbol α is commonly used to
express attenuation in decibels per kilometer (dB/Km).

Absorption
 Absorption is caused by three different mechanisms:
 Absorption by atomic defects in the glass composition
 Extrinsic absorption by impurity atoms in the glass material
 Intrinsic absorption by the basic constituent atoms of the fiber material.
 Atomic defects are imperfections of the atomic structure of the fiber material such as
missing molecules, high-density clusters of atom groups or oxygen defects in the
glass structure.
 Usually absorption losses arising from these defects are negligible compared to
intrinsic and impurity absorption effects.
 The absorption effect is most significant when fiber is exposed to ionizing radiation in
nuclear reactor, medical therapies, space missions etc. The radiation dames the
internal structure of fiber. The damages are proportional to the intensity of ionizing
particles. This results in increasing attenuation due to atomic defects and absorbing
optical energy.
 The total dose a material receives is expressed in rad (Si), this is the unit for
measuring radiation absorbed in bulk silicon.

1 rad (Si) = 0.01 J.kg

  The higher the radiation intensity more the attenuation as shown in Fig shown below:

Fig: Ionizing Radiation intensity Vs Fiber Attenuation

Intrinsic Absorption
 Intrinsic absorption is associated with the basic fiber material and is the principal
physical factor that defines the transparency window of a material over a specified
spectral region.
 It occurs when the material is in a perfect state with no density variations, impurities,
material in homogeneities, etc.,

 Intrinsic absorption thus sets the fundamental lower limit on absorption for any
particular material.

Fig: Optical Fiber Attenuation Characteristics

 Intrinsic absorption results from electronic absorption bands in the ultraviolet region
 and from atomic vibration bands in the near infrared region. The electronic absorption
bands are associated with the band gaps of the amorphous glass materials.
 Absorption occurs when a photon interacts with an electron in the valence band and
excites it to a higher energy level.
 The magnitude and characteristic exponential decay of the ultraviolet absorption is
shown in figure:
 The ultraviolet loss is small compared to scattering loss in the near infrared region.
Extrinsic Absorption
 Extrinsic absorption occurs due to electronic transitions between the energy level and
because of charge transitions from one ion to another.
 A major source of attenuation is from transition of metal impurity ions such as iron,
chromium, cobalt and copper. These losses can be upto 1 to 10 dB/km. The effect of
metallic impurities can be reduced by glass refining techniques.
 Another major extrinsic loss is caused by absorption due to OH (Hydroxil) ions
impurities dissolved in glass. Vibrations occur at wavelengths between 2.7 and 4.2
μm.
 The absorption peaks occurs at 1400, 950 and 750 nm. These are first, second and
third overtones respectively.
 Figure below shows absorption spectrum for OH group in silica. Between these
absorption peaks there are regions of low attenuation.

Fig: Absorption Spectra for OH group

 These absorption peaks define three regions or windows of preferred operation. The
first window is centered at 850 nm. The second window is centered at 1300 nm. The
third window iscentered at 1550 nm. Fiber optic systems operate at wavelengths
defined by one of these windows.
 The amount of water(OH-) impurities present in a fiber should be less than a few parts
per billion. Fiber attenuation caused by extrinsic absorption is affected by the level of
impurities(OH-) present in the fiber. If the amount of impurities in a fiber is reduced,
then fiber attenuation is reduced.
 Hydrolysis method is one of the fabrication processes of optical fiber. The streaming
materials used in this method are SiCl₄, GeCl₄, &PoCl₃. During hydrolysis process ie.,
when these materials used in hydrolysis process, gives OH ions.
 SiCl₄ + 2H₂O ――――――>SiO₂ + 4HCl + OH⁻ ions
Flame hydrolysis

Scattering Losses
 A beam propagating at the critical angle will change direction after it meet obstacle.
Therefore, the light will be scattered. The scattering effects prevent the attainment of
TIR at the core cladding boundary resulting in power loss. This loss is known as
SCATTERING LOSS.

 Non-linear scattering losses
 Scattering losses arise from microscopic variations in the material density, from
compositional fluctuations, and from structural in homogeneities or defects, occurring
during fiber manufacture.
 Scattering losses exists in optical fibers because of microscopic variations in the
material density and composition. As glass is composed by randomly connected
network of molecules and several oxides (e.g. SiO2, GeO2 and P2O5), these are the
major cause of compositional structure fluctuation.
Linear scattering losses:

Linear scattering mechanism causes transfer of optical power from one mode to different
mode. This process tend to result on attenuation of the transmitted light as the transfer may
be to a leaky mode (or) radiation mode which does not continue to propagate within the fiber .
There are two types of linear scattering losses.
1. Rayleigh Scattering
2. Mie Scattering

Rayleigh Scattering
 Rayleigh scattering in glass is the same phenomenon that scatters light from the sun
in the atmosphere, thereby giving rise to a blue sky.
 Rayleigh scatteringof light is due to small localized changes in the refractive index of
the core and cladding material. There are twocauses during the manufacturing of
fiber.
 The first is due to slight fluctuation in mixing of ingredients. The random changes
because of this are impossible to eliminate completely.
 The other cause is slight change in density as the silica cools and solidifies. When
light ray strikes such zones it gets scattered in all directions. The amount of scatter
depends on the size of the discontinuity compared with the wavelength of the light so
the shortest wavelength (highest frequency) suffers most scattering.
 The expressions for scattering induced attenuation are fairly complex owing to the
random molecular nature and the various oxide constituents of glass.
 For single component glass the scattering loss at a wavelength λ resulting from
 density fluctuations can be approximated by,

Where, p is the photo-elastic coefficient

For Multicomponent glasses the scattering is given by,

Figure below shows graphically the relationship between wavelength and Rayleigh scattering
loss.

Fig: Scattering Loss

Mie Scattering
Linear scattering also occurs at inhomogenities and these arise from imperfections in the
fiber‘s geometry, irregularities in the refractive index and the presence of bubbles etc. caused
during manufacture. Careful control of manufacturing process can reduce mie scattering to
insignificant levels.

Bending Loss
 Radiative losses occur whenever an optical fiber undergoes a bend of finite radius of
curvature.
 Fibers can subject to two types of bends: (a) microscopic bends having radii that are
large compared to the fiber diameter for example, such as occur when a fiber cable
 turns a corner and (b) random microscopic bends of the fiber axis that can arise when
the fibers are incorporated into cables.
 The sharp bend of a fiber causes significant radiative losses and there is also
possibility of mechanical failure. This is shown in Figure below:

Figure: Bending Loss

 As the core bends the normal will follow it and the ray will now find itself on the wrong
side of critical angle and will escape. The sharp bends are therefore avoided.
 The radiation loss from a bent fiber depends on –
 Field strength of certain critical distance xc from fiber axis where power is lostthrough
radiation.
 The radius of curvature R.
 The higher order modes are less tightly bound to the fiber core, the higher order
modesradiate out of fiber firstly.
 For multimode fiber, the effective number of modes that can be guided by curved fiber
is given expression :

Micro bend Loss

 Micro bends are due to small-scale fluctuations in the radius of curvature of the fiber
axis, as shown in figure.
 They are caused either by non-uniformities in the manufacturing of the fiber or by non-
uniform lateral pressures created during the cable of the fiber.
 An increase in attenuation results from micro bending because the fiber curvature
causes repetitive coupling of energy between the guided mode and the leaky or non-
guided modes in the fiber.

 One method of minimizing micro bending losses is by extruding a compressible jacket

 over the fiber. When the external forces will tend to stay relatively straight, as shown in
figure below.

 For multimode graded-index fiber having a core radius a, outer radius b(excluding the
jacket), and index difference , the micro bendingloss of a jacket is reduced from that of
an unjacketed fiber by a factor

 Here, and are the Young’s moduli of the fiber and jacket respectively. The Young’s
modulus of common jacket materials ranges from 20 to 500 MP and the Young’s
modulus of fused silica glass is about 65 GPa.

Macro Bending Loss

 The change in spectral attenuation caused by macro bending is different to micro
bending. Usually there are no peaks and troughs because in a macro bending no light
is coupled back into the core from the cladding as can happen in the case of
microbends.
 Figure: MacroBending Loss

Dispersion in optical fiber :

 An optical signal becomes increasingly distorted as it travels along a fiber. This
distortion is due to the effects of intramodal dispersion and intermodal delay effects.
These distortion effects can be explained by examining the behavior of the group
velocities of the guided modes, where the group velocity is the speed at which energy
in a particular mode travels along the fiber.
 Intramodal Dispersion
 Intramodal Dispersion is pulse spreading that occurs within a single mode. It is a result
of the group velocity being a function of the wavelength λ.
 It depends on the wavelength, its effect on signal distortion increases with the spectral
width of the optical source.This spectral width is the band of wavelengths over which
the source emits light.
 For LEDs the rms spectral width is approximately 5 % of a central wavelength. Laser
diode optical sources have much narrower spectral widths, typical values being 1 to 2
nm.
 The two main causes of intramodal dispersion are:
1. Material Dispersion:

 Material Dispersion, which arises from the variation of the refractive index of the core
material as a function of wavelength. It is also referred to as chromatic P. Arunagiri,
Assistant Professor, Department of ECE, Sri Manakula Vinayagar Engineering
College

 dispersion or spectral dispersion. This causes a wavelength dependence of the group

velocity of any given mode; that is pulse spreading occurs even when different
wavelengths follow the same path.
2. Wavelength Dispersion:
 Wavelength dispersion, occurs because a single-mode fiber only confines about 80 %
of the optical power to the core.
 Dispersion thus arises, since the 20 % of the light propagating in the cladding travels
 faster than the light confined to the core.
 The amount of waveguide dispersion depends on the fiber design, since the modal
propagation constant β is a function of a/λ, (where λ is the wavelength and a is the
core radius.)
 Dispersion and attenuation of pulse travelling along the fiber is shown in figure below.

Figure: Broadening and spreading of two adjacent pulses as they travel along fiber
 Figure above shows, after travelling some distance, pulse starts broadening and
overlap withthe neighboring pulses. At certain distance the pulses are not even
distinguishable anderror will occur at receiver. Therefore the information capacity is
specified by bandwidthdistanceproduct (MHz * km). For step index bandwidth
distance product is 20 MHz*kmand for graded index it is 2.5 MHz*km.
 The information carrying capacity can be determined by examining the deformation of
short light pulses propagating along the fiber.

Group Delay

 Consider a fiber cable carrying optical signal equally with various modes and each
modecontains all the spectral components in the wavelength band.
 All the spectral componentstravel independently and they observe different time delay
and group delay in thedirection of propagation. The group delay per unit length in the
direction of propagation is given by,

 The velocity at which the energy in a pulse travels along thefiber is known as group
velocity. Group velocity is given by,
  The group delay depends on the wavelength, each spectral component of any
particular mode takes a different amount of time to travel a certain distance. As a
result of this difference in time delays, the optical signal pulse spreads out with time as
it is transmitted over the fiber. Thus it also depends on pulse spreading.
 Thus, the dispersion is defines as the pulse spread as a function of wavelength. It is
measuredin picoseconds per kilometer per nanometer. It is expressed as,

Material Dispersion
 Material dispersion is also called as chromatic dispersion. Material dispersion exists
due to change in index of refraction for different wavelengths.The group velocity Vg of
a mode is a function of the index of refraction, the various spectral components of a
given mode will travel at different speeds, depending on the wavelength.
 Material dispersion is an intramodal dispersion effect, and is of particular importance
for single-mode waveguides and for LED systems.
 By considering a plane wave propagating in an infinity extended medium that has a
refractive indexn(λ) equal to that of the fiber core.
The propagation constant is thus given by,

The group delay can be written by substituting the value of β

The material dispersion for unit length (L = 1) is given by,

Figure below shows index of refraction as a function of optical wavelength

Fig: Index of refraction as a function of wavelength

Figure below shows the variation of material dispersion as a function of wavelength

Fig: Material Dispersion as a function of wavelength

 From the figure we understand that the amount of material dispersion depends upon
the chemical composition of glass.
Waveguide Dispersion

 Waveguide dispersion is caused by the difference in the index of refraction between

the core and cladding, resulting in a ‘drag‘ effect between the core and cladding
portions ofthe power.
 Waveguide dispersion is significant only in fibers carrying fewer than 5-10 modes.
Sincemultimode optical fibers carry hundreds of modes, they will not have
observablewaveguide dispersion.
The group delay (τwg) arising due to waveguide dispersion.

For small values of Vinstead of k in group delay yields,

The first term is constant and the second term is group delay arising from waveguide
dispersion.

 The mechanism of intermodal dispersion in multimode step index fiber:

 Single-mode fibers waveguide dispersion is of importance and can be of the same
order of magnitude as material dispersion.
 The pulse spread occurring over a distribution of wavelengths is obtained from the
derivative of the group delay with respect to wavelength,
Fig: Group Delay of waveguide dispersion as function of V number of step-index fiber

This factor reaches a maximum at V=1.2 but runs between 0.2 and 0.1 for a practical single-
mode operating range of V = 2.0 to 2.4. thus for values ofΔ = 0.01 and n2= 1.5, The figure
above shows that fused –silica –core single mode fiber having V=2.4

Intermodal Dispersion in single-mode fiber

 The final factor giving rise to signal degradation is intermodal distortion, which is a
result of different values of the group delay for each individual mode at a single
frequency.
 The variation in the group velocities of the different modes results in a group delay
spread or intermodal distortion. This distortion mechanism is eliminated by single-
mode operation, but is important in multimode fibers.
 The pulse broadening arising from intermodal distortion is the difference between the
travel time of the longest ray congruence paths ( the highest-order mode) and the
travel time of the shortest ray congruence paths ( the fundamental mode). This is
simply obtained from ray tracing and is given by,

Mode Coupling
 After certain initial length, the pulse distortion increases less rapidly because of mode
coupling. The energy from one mode is coupled to other mods because of:
- Structural imperfections.
- Fiber diameter variations.
- Refractive index variations.
- Microbends in cable.
  Due to the mode coupling, average propagation delay become less and intermodal
distortion reduces.
 Suppose certain initial coupling length = Lc, mode coupling length, over Lc = Z.
Additional loss associated with mode coupling = h (dB/ km). Therefore the excess
attenuation resulting from mode coupling = hZ. The improvement in pulse spreading
by mode coupling is given as :

where, C is a constant, is the pulse width increase in the absence of mode coupling, σ 0 is the
pulse broadening in the presence of strong mode coupling, and hZ is the excess attenuation
resulting from mode coupling.

 For long fiber length‘s the effect of mode coupling on pulse distortion is significant. For
a graded index fiber, the effect of distance on pulse broading for various coupling
losses is shown in Figure below.

Fig: Mode coupling effects on pulse distortion in long fibers for various coupling
losses
Design Optimization

Features of single mode fibers are :

- Longer life.
- Low attenuation.
- Signal transfer quality is good.
- Modal noise is absent.
- Largest BW-distance product.

Basic design – optimization includes the following :

- Cut-off wavelength.
- Dispersion.
- Mode field diameter.
- Bending loss.
- Refractive index profile.

Refractive Index Profile

 Dispersion of single mode silica fiber is lowest at 1300 nm while its attenuation
isminimum at 1550 nm. For archiving maximum transmission distance the dispersion
null should be at the wavelength of minimum attenuation.
 The waveguide dispersion is easier to control than the material dispersion. Therefore
a variety of core-cladding refractive index configuration fivers. Such as 1300 nm –
optimized fibers, dispersion shifted fibers, dispersion – flattened fibers and large
effective core area fibers.

1300 nm – Optimized Fibers

These are most popularly used fibers. The two configurations of 1300 nm – optimized single
mode fibers are :
- Matched cladding fibers.
- Dressed cladding fibers.
 Matched cladding fibers have uniform refractive index throughout its cladding. Typical
diameter is 9.0 μm and Δ = 0.35 %.
 Dressed cladding fibers have the innermost cladding portion has low refractive index
than outercladding region. Typical diameter is 8.4 μm and Δ1 = 0.25 %, Δ2 = 0.12 %.

Fig: (a) 1300 nm – Optimized (b) dispersion-shifted

The addition of wavelength and material dispersion can shift the zero dispersion point of
longer wavelength. Two configurations of dispersion shifted fibers are :
 Step index dispersion shifted fiber.
 

Dispersion Flattened
Dispersion flattened fibers are more complex to design. It offers much broader span of
wavelengths to suit desirable characteristics. Two configurations are :

Fig; Dispersion Flattened in single mode fibers

Figure below shows total resultant dispersion.

Fig: Total Resultant Dispersion

Dispersion Calculations
The total dispersion consists of material and waveguide dispersions. The resultant intermodal
dispersion is given as,

The broadening of an optical pulse is given as,

As the dispersion varies with wavelength and fiber type. Different formulae are used to
calculate dispersions for variety of fiber at different wavelength.
For a non –dispersion shifted fiber between 1270 nm to 1340 nm wavelength, the expression
for the dispersion is given as,

Figure below shows dispersion performance curve for non-dispersion shifted fibers in 1270 –
1340 nm region.

Maximum dispersion specified as 3.5 ps/(nm . km) marked as dotted line.

Cut-off Frequency of an Optical Fiber
The cut-off frequency of an optical fiber is determined not only by the fiber itself (modal
dispersion in case of multimode fibers and waveguide dispersion in case of single mode
fibers) but also by the amount of material dispersion caused by the spectral width of
transmitter.

Bending Loss Limitations

 The macro-bending and microbending losses are significant in single mode fibers at
1550 nm region, the lower cut-off wavelengths affects more. Figure below shows
macrobending losses.

Fig:Fiber attenuation due to microbending and Macro bending Loss

 The bending losses are function of mode-filed diameter, smaller the mode-field
diameter, the smaller the bending loss. Fig. 2.9.7 shows loss due to mode-field
diameter.
 The bending losses are also function of bend-radius of curvature. If the bend radius is
less, the losses are more and when the radius is more, the bending losses are less.
Fig; Loss due to mode field variation
 From figure we understand that the smaller the mode field diameter, smaller the
bending loss.
 UNIT – IV OPTICAL SOURCES, DETECTORS AND AMPLIFIERS

Fiber Optic Communications System

 A fiber optic data link sends input data through fiber optic components and provides this data
as output information. It has the following three basic functions:
 To convert an electrical input signal to an optical signal
 To send the optical signal over an optical fiber
 To convert the optical signal back to an electrical signal
 A fiber optic data link consists of three parts – transmitter, optical fiber and receiver. Figure
below shows the fiber optic connection. The transmitter, optical fiber and receiver perform the
basic functions of the fiber optic data link.

Fig: Major Elements of a Optical Fiber Transmission Link

 The transmitter, consisting of a light source can effectively convert an electrical input signal to
an optical signal and lunch the data containing light down the optical fiber.
 A receiver consisting of a photo detector plus amplification and signal-restoring circuitry, can
effectively detects the optical signal and transform this optical signal back into its original form.
 Additional components include optical connectors, splices, couplers or beam splitters and
repeaters.
Transmitter
 The transmitter is used to launch optical power into the fiber.
 The two types of optical sources are: light-emitting diode(LEDs) and Laser diodes.
 The electric input signals to the transmitter circuitry converts these electric signals to an optical
signal by varying the current flow through the light source.
 An optical source is a square-law device, which means that a linear variation in drive current
 results in a corresponding linear change in the optical output power.
 In the 800-900 nm region the light sources are generally alloys of GaAlAs. At the longer
wavelengths (1100 tp 1600 nm), an InGaAsP alloy is the principal optical source material.
 After an optical signal has been launched into the fiber, it will become progressively attenuated
and distorted with increasing distance because of scattering, absorption and dispersion
mechanisms in the waveguide.
 When an optical signal has travelled a certain distance along the fiber, the signal has become
attenuated and distorted to such a degree that a repeater is needed in the transmission line to
amplify and reshape the signal.
 An optical repeater consists of a receiver and a transmitter placed back to back. The receiver
section detects the optical signal and converts it to an electric signal, which is amplified,
reshaped and sent to the electric input of the transmitter section.
 The transmitters section converts this electric signal back to an optical signal and sends it on
down the optical fiber waveguide.
 Finally, The coupler must efficiently transfer the modulated light beam from the source to the optic
fiber.
Information Channel
 The information channel is the path between the transmitter and receiver.
 The cabled optical fiber is one of the most important elements in an optical fiber link. In addition
to protecting the glass fibers during installation and service, the cable may contain copper
wires for powering repeaters which are needed for periodicity amplifying and reshaping the
signal when the link spans long distances.
 The cable generally contains several cylindrical hair-thin glass fibers, each of which is an
independent communication channel. Analogous to copper cables, the installation of optical
fiber cables can be aerial in ducts, undersea or buried directly in the ground.
 Individual cable lengths will range from several hundred meters to several kilometers for long-
distance applications. The shorter lengths tend to be used when the cables are pulled through
ducts. Longer cable lengths are used in aerial or direct-burial applications.
 The complete long distance transmission line is formed by splicing or connecting together
these cable sections.
Receiver
 The design of the receiver is inherently more complex than that of the transmitter, since it has
to both amplify and reshape the degraded signal received by the photo detector.
 The ability of a receiver to achieve a certain performance level depends on the photo detector
type, the effects of noise in the system, and the characteristics of the successive amplification
stages in the receiver.
 At the receiver the attenuated and distorted modulated optical power emerging from the fiber
end will be detected by a photodiode.
 Analogous to the light source, the photo detector is also a square-law device since it converts
the received optical power directly into an electric current output(photocurrent).
 Semiconductor pin and avalanche photodiodes (APDs) are the two principal photo detectors
 used in a fiber optical link.
 For low power application optical signal is received an avalanche photodiode is normally used,
since it has greater sensitivity.
 Silicon photodetectors are used in the 800-900 nm regions. A variety of optical detectors are
available at the longer wavelengths. The prime material candidate in the 1100 to 1600 nm
region is an InGaAs alloy.
Advantages Of Optical Communication System:
1. Enormous Potential Bandwidth:
The optical carrier frequency in the range of 10¹³ to 10¹ ⁶ Hz (10¹ ⁴ Tera
hertzange) gives a greater potential transmission bandwidth than metallic cable
system.
2. Small Size and Weight:
Optical fiber has a very small diameter (diameter of a human hair) .Hence, even
such fibers are converted with protect ive coatings they are far smaller and lighter
than copper cables.
3. Electrical Isolation:
Optical fiber which are fabricated from glass or plastic polymer are electrical insulators unlike their
metallic counter parts, they do not exhibit earth loop and interface problem. Therefore, Optical fiber
transmission is ideally suited for electrical hazardous environment as the fiber creates no arcing (or)
spark hazard at abrasion (or) short circuits.
4. Immunity to Interference and Crosstalk :
 Optical fiber forms a dielectric wave guide and free from electromagnetic interference (EMI),
radio frequency interference (RFI) (or) switching transient giving electromagnetic pulses (EMP).
 Optical fiber transmission requires no shielding from EMI when it is used in electrically noisy
environment.
 Fiber cable also not suitable to lightning strikes if used over head rather underground.
5. Signal Security:
 The light from optical fiber doesn’t radiate significantly and therefore likely provide a high
degree of signal security.
 Transmitted optical signal cannot be trapped by third person. This feature is attractive for
military, banking and general data transmission applications.
6. Low Transmission Loss:
 Optical fiber exhibit low attenuation (or) transmission loss in comparison with the best copper
conductors. Fibers have been fabricated with losses as low as 0.2 dB/km.
7. Ruggedness and Flexibility:
 Fibers are manufactured with high tensile strengths. The fibers may also be bent to quite small
radii (or) twisted without damage.
 Because of the small sized, weight and flexibility optical fibers are generally superior in terms of
storage, transportation, handling and installation to corresponding copper cables.
8. System Reliability And Ease Of Maintenance :
 Low loss property of optical fiber cables reduces the requirements for intermediate repeaters (or)
line amplifiers to boost the transmitted signal strength with fewer repeaters reliability is
 enhanced in comparison to conventional electrical system.
 Life time of optical fibers is 20 to 30 years. It reduces maintenance time and cost.
PROPAGATION OF LIGHT.
 Until the early seventeenth century it was generally believed that the light consisted of a stream of
minute particles that were emitted by luminous sources. These particles were pictured as travelling
in straight lines, and it was assumed that they could penetrate transparent materials but were
reflected from opaque ones.
 This theory adequately described certain large scale optical effects such as reflection and refraction,
but failed to explain finer-scale such as interference and diffraction.
 Later the work of Maxwell in 1864 theorized that light waves must be electromagnetic in nature.
Furthermore observation of polarization effects indicated that light waves are transverse (that is, the
wave motion is perpendicular to the direction in which the wave travels.)
 The electromagnetic wave radiated by a small optical source can be represented by a train of
spherical wave fronts with the source at the center as shown in figure.

Fig; Representation of Spherical and Plane Wave front

 A wave front is defined as the locus of all points in the wave train which have the same phase.
 The speed of electromagnetic wave (c) in free space is approximately 3 x 108 m/sec.
 The distance travelled during eachcycle is called as wavelength (λ)
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒄
𝑾𝒂𝒗𝒆𝒍𝒆𝒏𝒈𝒕𝒉 = =
𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒇
 In fiber optics, it is more convenient to use the wavelength of light instead of the frequency with
light frequencies; wavelength is often stated in microns or nanometers.
1 micron (μ) = 1 Micrometre (1 x 10-6)
1 nano (n) = 10-9metre
 Fig: Electromagnetic Spectrum
 Fiber optics uses visible and infrared light. Infrared light covers a fairly wide range ofwavelengths
and is generally used for all fiber optic communications. Visible light is normally used for very
short range transmission using a plastic fiber.
 The photon energy is found to depend only on the frequency. This frequency inturn must be
measured by observing a wave property of light.
 The relationship between the energy E and the frequency v of a photon is given by,
𝑬 = 𝒉𝒗
-34
Where, h= 6.625×10 J is Planck’s constant.
 When light is incident on an atom, a photon can transfer its energy to an electron within this atom,
thereby exciting it to a higher energy level.
 The energy absorbed by the electron must be exactly equal to that required to excite state can drop
to a lower state separated from it by an energy hv by emitting a photon of exactly this energy.
 Before studying how the light actually propagates through the fiber, laws governing the
nature of light must be studied. This is called as laws of optics (Ray theory).
 The speed of light depends upon the material or medium through which it is moving. In free space
light travels at its maximum possible speed i.e. 3 x 108 m/s or 186 x 103 miles/sec.
 When light travels through a material it exhibits certain behavior explained by laws of reflection,
refraction.
Reflection
 The law of reflection states that, when a light ray is incident upon a reflective surface at some
incident angle 𝜃1 from imaginary perpendicular normal, the ray will be reflected from the surface at
some angle 𝜃2 from normal which is equal to the angle of incidence.
 Fig: Reflection
Refraction
 Refraction occurs when light ray passes from one medium to another i.e. the light ray changes its
direction at interface. Refraction occurs whenever density of medium changes. E.g. refraction occurs
at air and water interface, the straw in a glass of water will appear as it is bent. The refraction can
also observed at air and glass interface.
 When wave passes through less dense medium to denser medium, the wave is refracted (bent)
towards the normal. Fig. below shows the refraction phenomena.

Fig: Refraction
 The refraction (bending) takes place because light travels at different speed in different mediums.
The speed of light in free space is higher than in water or glass.

Refractive Index
 The amount of refraction or bending that occurs at the interface of two materials of different
densities is usually expressed as refractive index of two materials. Refractive index is also known as
index of refraction and is denoted by n.
 Based on material density, the refractive index is expressed as the ratio of the velocity oflight in free
space to the velocity of light of the dielectric material (substance).
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒕𝒉 𝒊𝒏 𝒂𝒊𝒓 𝒄
𝑹𝒆𝒇𝒓𝒂𝒄𝒕𝒊𝒗𝒆 𝒊𝒏𝒅𝒆𝒙, 𝒏 = =
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝒎𝒆𝒅𝒊𝒖𝒎 𝑽
 The refractive index for vacuum and air is 1.0. For water it is 1.3 and for glass refractive index is
1.5.
Snell’s Law

 Snell‘s law states how light ray reacts when it meets the interface of two media having different
indexes of refraction.
 Let the two medias have refractive indexes n1 and n2 where n1 >n2. Let n1 and n2 be the angles of
incidence and angle of refraction respectively. Then according to Snell‘s law, a relationship exists
 between the refractive index of both materials given by,
n1 sin θ1 = n2 sin θ2
Where, n1 is the refractive index of the core
n2 is the refractive index of the cladding
 A refractive index model for Snell’s law is shown in figure below:

Fig: Refractive Model for Snell’s law

 The refracted wave will be towards the normal when n1 < n2 and will away from it when n1 > n2.
And, the equation below shows that the ratio of refractive index of two mediums is inversely
proportional to the refractive and incident angles.
𝒏𝟏 𝐬𝐢𝐧 𝜽𝟐
=
𝒏𝟐 𝐬𝐢𝐧 𝜽𝟏

CONCEPT OF OPTICAL FIBER STRUCTURES

 The basic structure of an optical fiber consists of three parts; the core, the cladding and the coating
or buffer. The basic structure of an optical fiber is shown on figure below.
 Fig: Structure of a single Fiber
 The core is a cylindrical rod of dielectric material. Dielectric material conducts no electricity. Light
propagates mainly along the core of the fiber. The core is generally made of glass. The core is
described as having a radius of ‘a’ and an index of refraction ‘n1’.
 The core is surrounded by a layer of material called the cladding. Even though light will propagate
along the fiber core without the layer of cladding material, the cladding does perform some
necessary functions.
 The cladding layer is made of a dielectric material with an index of refraction ‘n2’. The refractive
index of the cladding material is less than that of the core material.
 The cladding is generally made of glass or plastic. The cladding performs the following functions:
 Reduces loss of light from the core into the surrounding air
 Reduces scattering loss at the surface of the core.
 Protects the fiber from absorbing surface contaminants
 Adds mechanical strength.
 For extra protection, the cladding is enclosed in an additional layer called the coating or buffer. The
coating or buffer is a layer of material used to protect an optical fiber from physical damage. The
material used for a buffer is a type of plastic.
 The buffer is elastic in nature and prevents abrasions. The buffer also prevents the optical fiber from
scattering losses caused by microbends. Microbends occur when an optical fiber is placed on a
rough and distorted surface.
 The basic fiber building blocks are used to form large cable. These units are bound on a buffer
material which acts as strength element along with insulated copper conductor. The fiber building
blocks are surrounded by paper tape, PVC jacket, yarn and outer sheath.

Fig: Six Fiber cable

Fiber Optic Cable Ducts
 Number of cores is bundled in plastic ducts. To ease identification, individual fibers are color coded
Table below shows an example of the color coding used by manufacturers.
Fiber number Color
 Fiber Number Color
1 Blue
2 Orange
3 Green
4 Brown
5 Grey
6 White
7 Red
8 Black
9 Yellow
10 Violet
11 Pink or Light blue
12 Tur quoise or Neutral
Optical Fiber types
 Variations in the material composition of the core give rise to the two commonly used fibertypes
shown in figure below: In the first case the refractive index of the core is uniform throughout and
undergoes an abrupt change (or step) at the cladding boundary. This is called step-index fiber.
 The core typically has diameter of 50-80 μm and the cladding has a diameter of 125 μm.
 The refractive index profile of the step-index fiber is defined as,
𝒏𝟏 𝒘𝒉𝒆𝒓𝒆 𝒓 < 𝑎(𝒄𝒐𝒓𝒆)
𝒏(𝒓) = { }
𝒏𝟐 𝒘𝒉𝒆𝒓𝒆 𝒓 ≥ 𝒂( 𝒄𝒍𝒂𝒅𝒅𝒊𝒏𝒈)

 Second case the core refractive index is made to vary as a function of the radial distance from the
center of the fiber. This type is a graded-index fiber.

Fig: Index Profile

 The refractive index profile across the core takes the parabolic nature as shown in figure above.
 A graded index fiber has lower coupling efficiency and higher bandwidth than the step index fiber.
It is available in 50/125 and 62.5/125 sizes. The 50/125 fiber has been optimized for long haul
applications and has a smaller NA and higher bandwidth. 62.5/125 fiber is optimized for LAN
applications which is costing 25% more than the 50/125 fiber cable.
 The refractive index variation in the core is giver by relationship
𝒓 𝜶
𝒏𝟏(𝟏 − 𝟐∆ ( ) 𝒘𝒉𝒆𝒏 𝒓 < 𝑎(𝑐𝑜𝑟𝑒)
𝒏(𝒓) = { 𝒂 }
𝟏/𝟐
𝒏𝟐(𝟏 − 𝟐∆) ≈ 𝒏𝟐 𝒘𝒉𝒆𝒏 𝒓 ≥ 𝒂(𝒄𝒍𝒂𝒅𝒅𝒊𝒏𝒈)
Where, r- Radial distance from fiber axis
 a- Core radius
n1- Refractive index of core
n2- Refractive index of core
α- Shape of index profile
 Profile parameter αdetermines the characteristic refractive index profile of fiber core.

 The range of refractive index as variation of αis shown in Figurebelow.

Fig: Possible fiber refractive index profiles for different values of α

 Both Step and graded-index fibers can be further divided into singlemode and multimode classes.
Single Mode fiber sustains only one mode of propagation, whereas multimode fibers contain many
hundreds of modes.
Single Mode Fibers
 Single mode fiber allows propagation to light ray by only one path.
 The core size of single mode fibers is small. The core size (diameter) is typically around 8 to 12
micrometers. A fiber core of this size allows only the fundamental or lowest order mode to
propagate only one mode, because the core size approaches the operational wavelength. The value
of the normalized frequency parameter relates core size with mode propagation.
 In single mode fibers, the frequency is less than or equal to 2.405. When the frequency and
wavelength 2.405, single mode fibers propagate the fundamental mode down the fiber core, while
high-order mode are lost in the cladding. For low frequency values, most of the power is propagated
in the cladding material. Power transmitted by the cladding is easily lost at the fiber ends. The value
of frequency should remain near the 2.405level.
 Single mode fibers have a lowersignal loss and a higher information capacity( bandwidth) than
multimode fibers. Single mode fibers are capable of transferring higher amounts of data to low fiber
dispersion.
 In single mode fibers, the wavelength can increase or decrease the losses caused by fiber bending.
They lose power because light radiates into cladding, which is lost at fiber bends. In general, single
mode fibers are considered to be low-loss fibers which increase system bandwidth and length.
 Some disadvantages of single mode fiber are smaller core diameter makes coupling light into the
core more difficult.
 Fig: Single Mode Propogation
Multimode Fibers
 The term multimode simply refers to the fact that numerous modes (light rays) are carried
simultaneously through the waveguide. Multimode fiber has a much larger diameter, compared to
single mode fiber; this allows large number of modes.
 Another advantage is that multimode fibers permit the use of light emitting diodes (LEDs). Single
mode fibers typically must use laser diodes. LEDs are cheaper, less complex and last longer. LEDs
are preferred for most applications.
 The disadvantage is that multimode fibers suffers from intermodal dispersion
Optic Fiber Configurations
 Depending on the refractive index profile of fiber and modes of fiber there exist three types of
optical fiber configurations. These optic-fiber configurations are -
i) Single mode step index fiber.
ii) Multimode step index fiber.

iii) Multimode graded index fiber

Single mode Step index Fiber
 Single mode step index fiber has a central core that is sufficiently small so that there is essentially
only one path for light ray through the cable. The light ray is propagated in the fiber through
reflection.
 Typical core sizes are 8 to 12μm.
 Single mode fiber is also known as fundamental or monomode fiber.
 Single mode fiber will permit only one mode to propagate and does not suffer from mode delay
differences. These are primarily developed for the 1300 nm window but they can be also be used
effectively with time division multiplex (TDM) and wavelength division multiplex (WDM) systems
operating in 1550 nm wavelength region.
 The core fiber of a single mode fiber is very narrow compared to the wavelength of light being used.
Therefore, only a single path exists through the cable core through which light can travel.
 The disadvantage of this type of cable is that because of extremely small size interconnection of
cables and interfacing with source is difficult.
 Another disadvantage of single mode fibers is that as the refractive index of glass decreases with
optical wavelength, the light velocity will also be wavelength dependent. Thus the light from an
optical transmitter will have definite spectral width.
Multimode step Index Fiber
 Multimode step index fiber is more widely used type. It is easy to manufacture. Its core diameter is
 50 to 1000 μm i.e. large aperture and allows more light to enter the cable. The light rays are
propagated down the core in zig-zag manner.
 There are many paths that a light ray may follow during the propagation.
 The light ray is propagated using the principle of total internal reflection. Since the core index of
refraction is higher than the cladding index of refraction, the light entersat less than critical angle is
guided along the fiber.
 Light rays passing through the fiber are continuously reflected off the glass claddingtowards the
center of the core at different angles and lengths, limiting overall bandwidth.
 The disadvantage of multimode step index fibers is that the different optical lengthscaused by
various angles at which light is propagated relative to the core, causes thetransmission bandwidth to
be fairly small. Because of these limitations, multimode stepindex fiber is typically only used in
applications requiring distances of less than 1 km.
Multimode Graded Index Fiber
The core size of multimode graded index fiber cable is varying from 50 to 100 μm range.
 The light ray is propagated through the refraction. The light ray enters the fiber at many different
angles.
 As the light propagates across the core toward the center it is intersecting a less dense to more dense
medium.
 Therefore the light rays are being constantly being refracted and ray is bending continuously. This
cable is mostly used for long distance communication.

Fig (a) Single mode step index Fiber(b) Multimode Step-index Fiber
(c) Multimode graded-index Fiber
 The light rays no longer follow straight lines; they follow a serpentine path being gradually bent
back towards the center by the continuously declining refractive index.
 The modes travelling in a straight line are in a higher refractive index so they travel slower than the
serpentine modes. This reduces the arrival time disparity because all modes arrive at about the same
time.
 Figure below shows the light trajectory in detail. It is seen that light rays running close to the fiber
 axis with shorter path length, will have a lower velocity because they pass through a region with a
high refractive index.

 Rays on core edges offers reduced refractive index, hence travel more faster than axial rays and
cause the light components to take same amount of time to travel the length of fiber, thus
minimizing dispersion losses.
 Each path at a different angle is termed as ‘transmission mode‘and the NA of graded index fiber is
defined as the maximum valueof acceptance angle at the fiber axis.
 Typical attenuation coefficients of graded index fibers at 850 nm are 2.5 to 3 dB/km,while at 1300
nm they are 1.0 to 1.5 dB/km.The main advantages of graded index fiber are:
 Reduced refractive index at the center of core.
 Comparatively cheap to produce.
Numerical Aperture
 The numerical aperture (NA) of a fiber is a figure of merit which represents its light gathering
capability. Larger the numerical aperture, the greater the amount of light accepted by fiber. The
acceptance angle also determines how much light is able to be enter the fiber and hence there is
relation between the numerical aperture and the cone of acceptance.
 The rays striking the core-cladding interface at angles less than θmin will refract out of the core and
be lost in the cladding.
𝒏𝟐
𝐬𝐢𝐧 𝜽 𝐦𝐢𝐧 =
𝒏𝟏
 The condition of the above equation can be related to the maximum entrance angle 𝜃𝑜𝑚𝑎𝑥 through
the relationship
𝒏𝟎 𝑺𝒊𝒏 𝜽𝒐𝒎𝒂𝒙 = 𝒏𝟏 𝐬𝐢𝐧 𝜽𝒄 = (𝒏𝟏 𝟐 − 𝒏𝟐 𝟐 )𝟏/𝟐

Fig: Meridional Ray optic representation of the propagation mechanism

𝟏/𝟐
(𝒏𝟏 𝟐 − 𝒏𝟐 𝟐 )
 Thus, Numerical Aperture, 𝑵𝑨 = 𝐬𝐢𝐧−𝟏 𝜽𝒐𝒎𝒂𝒙 = = 𝒏𝟏 √𝟐∆
𝒏𝟎
Where, ∆ s much less than 1.For air ∆ = 1.Thus,
𝑵𝑨 = (𝒏𝟏 𝟐 − 𝒏𝟐 𝟐 )𝟏/𝟐 =
Where, 𝑛1 - refractive index of the core; 𝑛1 - refractive index of the cladding.
 By the formula of NA note that the numerical aperture is effectively dependent only on
 refractive indices of core and cladding material. NA is not a function of fiber dimension.
 The numerical aperture is a dimensionless quantity whichis less than unity, with values normally
ranging from 0.14 to 0.50.
Also, the acceptance angle can be calculated by using the formula,
𝑨𝒄𝒄𝒆𝒑𝒕𝒂𝒏𝒄𝒆 𝒂𝒏𝒈𝒍𝒆 𝜽𝒐 = 𝐬𝐢𝐧−𝟏 (𝑵𝒖𝒎𝒆𝒓𝒊𝒄𝒂𝒍 𝑨𝒑𝒆𝒓𝒕𝒖𝒓𝒆)
 The Cone of acceptance is the angle within which the light is accepted into the core and is able to
travel along the fiber. The launching of light wave becomes easier for large acceptance come.

Fig: Acceptance Cone of Optic Fiber

 The angle is measured from the axis of the positive cone so the total angle of convergence is
actually twice the stated value

Introduction
 The signal attenuation of fiber determines the maximum distance between transmitter and receiver.
The attenuation also determines the number of repeaters required, maintaining repeater is a costly
affair.
Attenuation
 Attenuation of a light as it propagates along a fiber is an important consideration in the design of an
optical communication system in determining the maximum transmission distance between a
transmitter and a receiver.
 Attenuation in an optical fiber is caused by absorption, scattering and bending losses.
 Absorption is related to the fiber material, whereas scattering is associated both with the fiber
material and with structural imperfections in the optical waveguide.
 Scattering due to structuralimperfection within the fiber. Nearly 90 % of total attenuation is caused
by Rayleigh scattering only.
 The Rayleigh scattering is wavelength dependent and reduces rapidly as the wavelength of the
incident radiation increases.
 Microbending of optical fiber also contributes to the attenuation of signal.
Attenuation Units
 Signal attenuation (or fiber loss) is defined as the ratio of the optical output power P out from a fiber
of length L to the optical input power Pin . This power ratio is a function of wavelength. The symbol
α is commonly used to express attenuation in decibels per kilometer (dB/Km).
𝟏𝟎 𝑷𝒊𝒏
𝜶= 𝒍𝒐𝒈 ( )
𝑳 𝑷𝒐𝒖𝒕
Absorption
 Absorption is caused by three different mechanisms:
1. Absorption by atomic defects in the glass composition
2. Extrinsic absorption by impurity atoms in the glass material
3. Intrinsic absorption by the basic constituent atoms of the fiber material.
 Atomic defects are imperfections of the atomic structure of the fiber material such as missing
molecules, high-density clusters of atom groups or oxygen defects in the glass structure.
 Usually absorption losses arising from these defects are negligible compared to intrinsic and
impurity absorption effects.
 The absorption effect is most significant when fiber is exposed to ionizing radiation in nuclear
reactor, medical therapies, space missions etc. The radiation dames the internal structure of fiber.
The damages are proportional to the intensity of ionizing particles. This results in increasing
attenuation due to atomic defects and absorbing optical energy.
 The total dose a material receives is expressed in rad (Si), this is the unit for measuring radiation
absorbed in bulk silicon.
1 rad (Si) = 0.01 J.kg
 The higher the radiation intensity more the attenuation as shown in Fig shown below:

Fig: Ionizing Radiation intensity Vs Fiber Attenuation

Intrinsic Absorption
 Intrinsic absorption is associated with the basic fiber material and is the principal physical factor that
defines the transparency window of a material over a specified spectral region.
 It occurs when the material is in a perfect state with no density variations, impurities, material in
homogeneities, etc.,
 Intrinsic absorption thus sets the fundamental lower limit on absorption for any particular material.
 Fig: Optical Fiber Attenuation Characteristics
 Intrinsic absorption results from electronic absorption bands in the ultraviolet region and from
atomic vibration bands in the near infrared region. The electronic absorption bands are associated
with the band gaps of the amorphous glass materials.
 Absorption occurs when a photon interacts with an electron in the valence band and excites it to a
higher energy level.
 The magnitude and characteristic exponential decay of the ultraviolet absorption is shown in figure:
 The ultraviolet loss is small compared to scattering loss in the near infrared region.

Extrinsic Absorption
 Extrinsic absorption occurs due to electronic transitions between the energy level and because of
charge transitions from one ion to another. A major source of attenuation is from transition of metal
impurity ions such as iron, chromium, cobalt and copper. These losses can be upto 1 to 10 dB/km.
The effect of metallic impurities can be reduced by glass refining techniques.
 Another major extrinsic loss is caused by absorption due to OH (Hydroxil) ions impurities
dissolved in glass. Vibrations occur at wavelengths between 2.7 and 4.2 μm.
 The absorption peaks occurs at 1400, 950 and 750 nm. These are first, second and third overtones
respectively.
 Figure below shows absorption spectrum for OH group in silica. Between these absorption peaks
there are regions of low attenuation.
 Fig: Absorption Spectra for OH group
 These absorption peaks define three regions or windows of preferred operation. The first window is
centered at 850 nm. The second window is centered at 1300 nm. The third window iscentered at
1550 nm. Fiber optic systems operate at wavelengths defined by one of these windows.
 The amount of water(OH-) impurities present in a fiber should be less than a few parts per billion.
Fiber attenuation caused by extrinsic absorption is affected by the level of impurities(OH-) present
in the fiber. If the amount of impurities in a fiber is reduced, then fiber attenuation is reduced.
 Hydrolysis method is one of the fabrication processes of optical fiber. The streaming materials
used in this method are SiCl₄, GeCl₄, &PoCl₃. During hydrolysis process ie., when these
materials used in hydrolysis process, gives OH ions.
SiCl₄ + 2H₂O ――――――>SiO₂ + 4HCl + OH⁻ ions
Flame hydrolysis
Scattering Losses
A beam propagating at the critical angle will change direction after it meet obstacle. Therefore, the
light will be scattered. The scattering effects prevent the attainment of TIR at the core cladding
boundary resulting in power loss. This loss is known as SCATTERING LOSS.
 Linear scattering losses
 Non-linear scattering losses
 Scattering losses arise from microscopic variations in the material density, from compositional
fluctuations, and from structural in homogeneities or defects, occurring during fiber manufacture.
 Scattering losses exists in optical fibers because of microscopic variations in the material density
and composition. As glass is composed by randomly connected network of molecules and several
oxides (e.g. SiO2, GeO2 and P2O5), these are the major cause of compositional structure fluctuation.
 Linear scattering losses:
Linear scattering mechanism causes transfer of optical power from one mode to different mode.
This process tend to result on attenuation of the transmitted light as the transfer may be to a
leaky mode (or) radiation mode which does not continue to propagate within the fiber . There
are two types of linear scattering losses.
1. Rayleigh Scattering
2. Mie Scattering
Rayleigh Scattering
 Rayleigh scattering in glass is the same phenomenon that scatters light from the sun in the
atmosphere, thereby giving rise to a blue sky.
 Rayleigh scatteringof light is due to small localized changes in the refractive index of the core and
cladding material. There are twocauses during the manufacturing of fiber.
 The first is due to slight fluctuation in mixing of ingredients. The random changes because of this
are impossible to eliminate completely.
 The other cause is slight change in density as the silica cools and solidifies. When light ray strikes
such zones it gets scattered in all directions. The amount of scatter depends on the size of the
discontinuity compared with the wavelength of the light so the shortest wavelength (highest
frequency) suffers most scattering.
 The expressions for scattering induced attenuation are fairly complex owing to the random
 molecular nature and the various oxide constituents of glass.
 For single component glass the scattering loss at a wavelength λ resulting from density fluctuations
can be approximated by,
𝟖𝝅𝟑 𝟐
𝜶𝒔𝒄𝒂𝒕 = (𝒏 − 𝟏)𝟐 𝒌𝑩 𝑻𝒇 𝜷𝑻
𝟑𝝀𝟒
Where, n is the refractive index,
𝒌𝑩 is Boltzmann’s constant,
𝜷𝑻 is the isothermal compressibility of the material and the fictive temperature
𝑻𝒇 is the temperature at which the density fluctuations are frozen into the glass as it solidifies.
𝟖𝝅𝟑 𝟖 𝟐
𝜶𝒔𝒄𝒂𝒕 = 𝒏 𝒑 𝒌𝑩 𝑻𝒇 𝜷𝑻
𝟑𝝀𝟒
Where, p is the photo-elastic coefficient
 For Multicomponent glasses the scattering is given by,

𝟖𝝅𝟑
𝜶= (𝜹𝒏𝟐 )𝟐 𝜹𝑽
𝟑𝝀𝟒
Where, (𝜹𝒏𝟐 ) – mean square of refractive index over a volume 𝛿𝑉
 Figure below shows graphically the relationship between wavelength and Rayleigh scattering loss.

Fig: Scattering Loss

Mie Scattering
 Linear scattering also occurs at inhomogenities and these arise from imperfections in the fiber‘s
geometry, irregularities in the refractive index and the presence of bubbles etc. caused during
manufacture. Careful control of manufacturing process can reduce mie scattering to insignificant
levels.
Bending Loss
 Radiative losses occur whenever an optical fiber undergoes a bend of finite radius of curvature.
 Fibers can subject to two types of bends: (a) microscopic bends having radii that are large compared
to the fiber diameter for example, such as occur when a fiber cable turns a corner and (b) random
microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables.
 The sharp bend of a fiber causes significant radiative losses and there is also possibility of
mechanical failure. This is shown in Figure below:
 (a) (b)
Figure: Bending Loss
 As the core bends the normal will follow it and the ray will now find itself on the wrong side of
critical angle and will escape. The sharp bends are therefore avoided.
 The radiation loss from a bent fiber depends on –
 Field strength of certain critical distance xc from fiber axis where power is lostthrough radiation.
 The radius of curvature R.
 The higher order modes are less tightly bound to the fiber core, the higher order modesradiate out of
fiber firstly.
 For multimode fiber, the effective number of modes that can be guided by curved fiber is given
expression :
𝟐/𝟑
𝜶 + 𝟐 𝟐𝒂 𝟑
𝑵𝒆𝒇𝒇 = 𝑵∞ {𝟏 − [ +( ) ]}
𝟐𝜶∆ 𝑹 𝟐𝒏𝟐 𝒌𝑹
Where,𝜶 – defines the gradex-index profiles
∆ - Core-cladding index difference
𝒏𝟐 – Refractive index of cladding
𝟐𝝅
𝒌= – Wave propagation constant
𝝀
𝛼
𝑁∞ = (𝑛1 𝑘𝑎)2 ∆- The total number of modes in straight fiber
𝛼+2
Micro bend Loss
 Microbends are due to small-scale fluctuations in the radius of curvature of the fiber axis, as shown
in figure.
 They are caused either by non-uniformities in the manufacturing of the fiber or by non-uniform
lateral pressures created during the cable of the fiber.
 An increase in attenuation results from microbending because the fiber curvature causes repetitive
coupling of energy between the guided mode and the leaky or non-guided modes in the fiber.
 One method of minimizing micro bending losses is by extruding a compressible jacket over the
fiber. When the external forces will tend to stay relatively straight, as shown in figure below.
 Figure: Micro bending Losses
 For multimode graded-index fiber having a core radius a, outer radius b(excluding the jacket),
and index difference ∆, the microbendingloss𝜶𝑴 of a jacket is reduced from that of an
unjacketed fiber by a factor
−𝟐
𝒃 𝟒 𝑬𝒇
𝟐
)
𝑭(𝜶𝑴 = [𝟏 + 𝝅∆ ( ) ]
𝒂 𝑪

Here,𝑬𝒇 and𝑬𝒇 are the Young’s moduli of the fiber and jacket respectively. The Young’s modulus
of common jacket materials ranges from 20 to 500 MP and the Young’s modulus of fused silica
glass is about 65 GPa.
Macro Bending Loss
 The change in spectral attenuation caused by macro bending is different to micro bending. Usually
there are no peaks and troughs because in a macro bending no light is coupled back into the core
from the cladding as can happen in the case of microbends.
 The macrobending losses are cause by large scale bending of fiber. The losses are eliminated when
the bends are straightened. The losses can be minimized by not exceeding the long term bend radii.
Figure below illustrates macrobending.
Core-Cladding Losss
 Since the core and cladding have different indices of refraction hence they have different attenuation
coefficients α1 and α2 respectively. For step index fiber, the loss for a mode order (v, m) is given by,
 Figure: MacroBending Loss
𝑷𝒄𝒐𝒓𝒆 𝑷𝒄𝒍𝒂𝒅
𝜶𝒗𝒎 = 𝜶𝟏 + 𝜶𝟐
𝑷 𝑷
𝑷𝒄𝒐𝒓𝒆 𝑷𝒄𝒍𝒂𝒅
Where 𝑷 and 𝑷 are the fractional powers
 For low-order modes, the expression reduced to
𝑷𝒄𝒍𝒂𝒅
𝜶𝒗𝒎 = 𝜶𝟏 + (𝜶𝟐 − 𝜶𝟏 )
𝑷
DISPERSION
An optical signal becomes increasingly distorted as it travels along a fiber. This distortion is due to the
effects of intramodal dispersion and intermodal delay effects. These distortion effects can be
explained by examining the behavior of the group velocities of the guided modes, where the group
velocity is the speed at which energy in a particular mode travels along the fiber.
Intramodal Dispersion
 Intramodal Dispersion is pulse spreading that occurs within a single mode. It is a result of the group
velocity being a function of the wavelength λ.
 It depends on the wavelength, its effect on signal distortion increases with the spectral width of the
optical source.This spectral width is the band of wavelengths over which the source emits light.
 For LEDs the rms spectral width is approximately 5 % of a central wavelength. Laser diode optical
sources have much narrower spectral widths, typical values being 1 to 2 nm.
 The two main causes of intramodal dispersion are:
1. Material Dispersion:
Material Dispersion, which arises from the variation of the refractive index of the core
material as a function of wavelength. It is also referred to as chromatic dispersion or spectral
dispersion. This causes a wavelength dependence of the group velocity of any given mode;
that is pulse spreading occurs even when different wavelengths follow the same path.
2. Wavelength Dispersion:
 Wavelength dispersion, occurs because a single-mode fiber only confines about 80 % of
the optical power to the core.
 Dispersion thus arises, since the 20 % of the light propagating in the cladding travels
faster than the light confined to the core.
 The amount of waveguide dispersion depends on the fiber design, since the modal
propagation constant β is a function of a/λ, (where λ is the wavelength and a is the core
radius.)
 Dispersion and attenuation of pulse travelling along the fiber is shown in figure below.
 Figure: Broadening and spreading of two adjacent pulses as they travel along fiber
 Figure above shows, after travelling some distance, pulse starts broadening and overlap withthe
neighboring pulses. At certain distance the pulses are not even distinguishable anderror will occur at
receiver. Therefore the information capacity is specified by bandwidthdistanceproduct (MHz *
km). For step index bandwidth distance product is 20 MHz*kmand for graded index it is 2.5
MHz*km.
 The information carrying capacity can be determined by examining the deformation of short light
pulses propagating along the fiber.
Group Delay
 Consider a fiber cable carrying optical signal equally with various modes and each modecontains all
the spectral components in the wavelength band.
 All the spectral componentstravel independently and they observe different time delay and group
delay in thedirection of propagation. The group delay per unit length in the direction of propagation
is given by,
𝝉𝒈 𝟏 𝟏 𝒅𝜷 𝝀𝟐 𝒅𝜷
= = = −
𝑳 𝑽𝒈 𝒄 𝒅𝒌 𝟐𝝅𝒄 𝒅𝝀
Here, L is the distance travelled by the pulse, 𝜷 – propagation constant along the fiber axis, 𝑘 =
1⁄2𝜋𝜆
 The velocity at which the energy in a pulse travels along thefiber is known as group velocity. Group
velocity is given by,
𝒅𝜷 −𝟏
𝑽𝒈 = 𝒄. ( )
𝒅𝒌
 The group delay depends on the wavelength, each spectral component of any particular mode takes
a different amount of time to travel a certain distance. As a result of this difference in time delays,
the optical signal pulse spreads out with time as it is transmitted over the fiber. Thus it also depends
on pulse spreading.

Thus, the dispersion is defines as the pulse spread as a function of wavelength. It is measured in
picoseconds per kilometer per nanometer. It is expressed as,
𝟏 𝒅𝝉𝒈
𝑫=
𝑳 𝒅𝝀
WAVEGUIDE DISPERSION AND MATERIAL DISPERSION
Material Dispersion
 Material dispersion is also called as chromatic dispersion. Material dispersion exists due to change
in index of refraction for different wavelengths.The group velocity Vg of a mode is a function of the
index of refraction, the various spectral components of a given mode will travel at different speeds,
depending on the wavelength.
 Material dispersion is an intramodal dispersion effect, and is of particular importance for single-
mode waveguides and for LED systems.
 By considering a plane wave propagating in an infinity extended medium that has a refractive
indexn(λ) equal to that of the fiber core.
 The propagation constant is thus given by,
𝟐𝝅𝒏(𝛌)
𝜷=
𝛌
The group delay 𝜏𝑀𝑎𝑡 can be written by substituting the value of β for 𝑘 = 1⁄2𝜋𝜆 as,
𝑳 𝒅𝒏
𝝉𝑴𝒂𝒕 = (𝒏 − 𝛌 )
𝒄 𝒅𝛌

 The material dispersion for unit length (L = 1) is given by,

−𝛌 𝒅𝟐 𝒏
𝑫𝑴𝒂𝒕 = × 𝟐
𝒄 𝒅𝛌
𝒅𝟐 𝒏
Where, C- is the velocity of light, 𝛌 – center wavelength, 𝟐 – first order derivative ofindex of
𝒅𝛌
refraction w.r.to wavelength. Negative sign shows that the upper sideband signal (lowest
wavelength) arrives before the lower sideband (highest wavelength).

 Figure below shows index of refraction as a function of optical wavelength

Fig: Index of refraction as a function of wavelength

 Figure below shows the variation of material dispersion as a function of wavelength
 Fig: Material Dispersion as a function of wavelength
 From the figure we understand that the amount of material dispersion depends upon the chemical
composition of glass.
Waveguide Dispersion
 Waveguide dispersion is caused by the difference in the index of refraction between the core and
cladding, resulting in a ‘drag‘ effect between the core and cladding portions ofthe power.
 Waveguide dispersion is significant only in fibers carrying fewer than 5-10 modes. Sincemultimode
optical fibers carry hundreds of modes, they will not have observablewaveguide dispersion.
 The group delay (τwg) arising due to waveguide dispersion.
𝐿 𝒅𝜷 𝐿 𝒅(𝒌𝒃)
𝜏𝑊𝑔 = = [𝒏𝟐 + 𝒏𝟐 ∆ ]
𝑐 𝒅𝒌 𝑐 𝒅𝒌

Where, 𝒃 – normalized propagation constant𝑘 = 1⁄2𝜋𝜆 and

Normalized frequency, 𝑽 = 𝒌𝒂(𝒏𝟏 𝟐 − 𝒏𝟐 𝟐 )𝟏/𝟐 = 𝒌𝒂𝒏𝟐 √𝟐∆
For small values of ∆,Vinstead of k in group delay yields,
𝐿 𝒅𝜷 𝐿 𝒅(𝑽𝒃)
𝜏𝑊𝑔 = = [𝒏𝟐 + 𝒏𝟐 ∆ ]
𝑐 𝒅𝒌 𝑐 𝒅𝒌
The first term is constant and the second term is group delay arising from waveguide dispersion
Signal Distortion in single-mode fiber
 The final factor giving rise to signal degradation is intermodal distortion, which is a result of
different values of the group delay for each individual mode at a single frequency.
 The variation in the group velocities of the different modes results in a group delay spread or
intermodal distortion. This distortion mechanism is eliminated by single-mode operation, but is
important in multimode fibers.
 The pulse broadening arising from intermodal distortion is the difference between the travel time
𝑻𝒎𝒂𝒙 of the longest ray congruence paths ( the highest-order mode) and the travel time 𝑻𝒎𝒊𝒏 of the
shortest ray congruence paths ( the fundamental mode). This is simply obtained from ray tracing and
is given by,
𝒏𝟏 ∆𝑳
𝝈𝒎𝒐𝒅 = 𝑻𝒎𝒂𝒙 − 𝑻𝒎𝒊𝒏 =
𝒄

Mode Coupling
  After certain initial length, the pulse distortion increases less rapidly because of mode coupling. The
energy from one mode is coupled to other mods because of:
- Structural imperfections.
- Fiber diameter variations.
- Refractive index variations.
- Microbends in cable.
 Due to the mode coupling, average propagation delay become less and intermodal distortion
reduces.
 Suppose certain initial coupling length = Lc, mode coupling length, over Lc = Z. Additional loss
associated with mode coupling = h (dB/ km). Therefore the excess attenuation resulting from mode
coupling = hZ. The improvement in pulse spreading by mode coupling is given as :
𝝈𝒄 𝟐
𝒉𝒁 ( ) = 𝑪
𝝈𝒐
where, C is a constant, 𝜎𝑜 is the pulse width increase in the absence of mode coupling, 𝜎𝑐 is the
pulse broadening in the presence of strong mode coupling, and hZ is the excess attenuation resulting
from mode coupling.
For long fiber length‘s the effect of mode coupling on pulse distortion is significant. For a graded index
fiber, the effect of distance on pulse broading for various coupling losses is shown in Figure below.

Fig: Mode coupling effects on pulse distortion in long fibers for various coupling losses
Polarization Mode Dispersion (PMD)
 Polarization Mode Dispersion (PMD) is a broadening of the input pulse due to a phase delay between input
polarization states. Single-mode optical fiber and components support one fundamental mode, which consists
of two orthogonal polarization modes.
 Ideally, the core of an optical fiber is perfectly circular, and therefore has the same index of refraction for
both polarization states. However, mechanical and thermal stresses introduced during manufacturing result in
asymmetries in the fiber core geometry. This asymmetry introduces small index of refraction differences for
the two polarization states, a property called birefringence.
 External mechanical stresses and environmental conditions exacerbate the problem. Birefringence creates
differing optical axes that generally correspond to the fast and slow axes. (These axes can also be thought of
as corresponding to the Linear Polarization (LP) modes or Principal States of Polarization (PSP).)
Birefringence causes one polarization mode to travel faster than the other, resulting in a difference in the
propagation time called the differential group delay (DGD).
  DGD is the unit that is used to describe PMD. DGD is typically measured in picoseconds.
 When mode coupling is present, both the PSP and the DGD are also dependent on optical frequency. Mode
coupling refers to an exchange of power among propagating polarization modes. This is usually seen in long
lengths of single-mode fiber, and is sometimes observed even in short optical components.
 PMD effects resemble those of chromatic dispersion, but with some key differences: Chromatic dispersion is
a rather stable, linear effect, making compensation relatively easy, but PMD is a linear effect that is time-
varying in fiber links, making compensation difficult. PMD is very stable in components.
 Unlike chromatic dispersion, the effects of PMD are dependent on the launched polarization state. In high-bit-
rate systems, PMD may introduce errors as pulses spread into one another.

Design Optimization in Single-mode fibers

 Features of single mode fibers are :
- Longer life.
- Low attenuation.
- Signal transfer quality is good.
- Modal noise is absent.
- Largest BW-distance product.
 Basic design – optimization includes the following :
- Cut-off wavelength.
- Dispersion.
- Mode field diameter.
- Bending loss.
 Single-mode fibers waveguide dispersion is of importance and can be of the same order of
magnitude as material dispersion.
 The pulse spread occurring over a distribution of wavelengths is obtained from the derivative of the
group delay with respect to wavelength,
𝒅𝝉𝑾𝒈
𝝈𝑾𝒈 = 𝝈𝝀 = 𝝈𝝀 𝑳𝑫𝒘𝒈(𝝀)
𝒅𝝀
𝑽 𝒅𝝉𝑾𝒈 𝒏𝟐 𝑳∆𝝈𝝀 𝒅𝟐 (𝑽𝒃)
= − 𝝈𝝀 =− 𝑽
𝝀 𝒅𝑽 𝒄𝝀 𝒅𝑽𝟐
𝒅 𝟐 (𝑽𝒃)
 Where, 𝑫𝒘𝒈(𝝀) − 𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛. 𝑽 𝒅𝑽𝟐 is plotted as a function ofV as shown in figure
below: This factor reaches a maximum at V=1.2 but runs between 0.2 and 0.1 for a practical single-
mode operating range of V = 2.0 to 2.4. thus for values of ∆ = 0.01 and 𝑛2 = 1.5,
 𝝈𝑾𝒈 0.003𝝈𝝀
= −
𝐿 𝒄𝝀
The figure above shows that fused –silica –core single mode fiber having V=2.4

Fig: Group Delay of waveguide dispersion as function of V number of step-index fiber

Refractive Index Profile
 Dispersion of single mode silica fiber is lowest at 1300 nm while its attenuation isminimum at 1550
nm. For archiving maximum transmission distance the dispersion null should be at the wavelength
of minimum attenuation.
 The waveguide dispersion is easier to control than the material dispersion. Therefore a variety of core-
cladding refractive index configuration fivers. Such as 1300 nm – optimized fibers, dispersion shifted fibers,
dispersion – flattened fibers and large effective core area fibers.
1300 nm – Optimized Fibers
 These are most popularly used fibers. The two configurations of 1300 nm – optimized single
mode fibers are :
- Matched cladding fibers.
- Dressed cladding fibers.
 Matched cladding fibers have uniform refractive index throughout its cladding. Typical diameter
is 9.0 μm and Δ = 0.35 %.
 Dressed cladding fibers have the innermost cladding portion has low refractive index than
outercladding region. Typical diameter is 8.4 μm and Δ1 = 0.25 %, Δ2 = 0.12 %.

Fig: (a) 1300 nm – Optimized (b) dispersion-shifted

 The addition of wavelength and material dispersion can shift the zero dispersion point of longer
 wavelength. Two configurations of dispersion shifted fibers are :
 Step index dispersion shifted fiber.
 Triangular dispersion shifted fiber.
Dispersion Flattened
 Dispersion flattened fibers are more complex to design. It offers much broader span of wavelengths
to suit desirable characteristics. Two configurations are :

Fig; Dispersion Flattened in single mode fibers

 Figure below shows total resultant dispersion.

Fig: Total Resultant Dispersion

Dispersion Calculations
 The total dispersion consists of material and waveguide dispersions. The resultant intermodal
dispersion is given as,
𝒅𝝉
𝑫(𝝀) =
𝒅𝝀
Where, 𝝉is group delay per unit length of fiber
 The broadening𝝈 of an optical pulse is given as,
𝝈 = 𝑫(𝝀)𝑳𝝈𝝀
Where, 𝝈𝝀 – half power spectral width of the source
 As the dispersion varies with wavelength and fiber type. Different formulae are used to calculate
dispersions for variety of fiber at different wavelength.
 For a non –dispersion shifted fiber between 1270 nm to 1340 nm wavelength, the expression for the
dispersion is given as,
𝝀 𝝀𝒐4
𝑫(𝝀) = 𝑆𝑜 [1 − ]
4 𝝀
 Where, 𝝀𝒐 – zero dispersion wavelength,So is the value at dispersion at slope at 𝝀𝒐
 Figure below shows dispersion performance curve for non-dispersion shifted fibers in 1270 –1340
nm region.

 Maximum dispersion specified as 3.5 ps/(nm . km) marked as dotted line.

Cut-off Frequency of an Optical Fiber
 The cut-off frequency of an optical fiber is determined not only by the fiber itself (modal dispersion
in case of multimode fibers and waveguide dispersion in case of single mode fibers) but also by the
amount of material dispersion caused by the spectral width of transmitter.
Bending Loss Limitations
 The macro bending and micro bending losses are significant in single mode fibers at 1550 nm
region, the lower cut-off wavelengths affects more. Figure below shows macro bending losses.

Fig: Fiber attenuation due to micro bending and Macro bending Loss
 UNIT-V OPTICAL NETWORKS
SONET/SDH
The ANSI standard is called the Synchronous Optical Network (SONET). The ITU-T standard is
called the Synchronous Digital Hierarchy (SOH). SONET was developed by ANSI; SDH was developed by
ITU-T. SONET/SDH is a synchronous network using synchronous TDM multiplexing. All clocks in the
system are locked to a master clock.
ARCHITECTURE
Architecture of a SONET system contains: signals, devices, and connections.
Signals: SONET defines a hierarchy of electrical signaling levels called synchronous transport signals
(STSs). Each STS level (STS-l to STS-192) supports a certain data rate, specified in megabits per second.
The corresponding optical signals are called optical carriers (OCs). SDH specifies a similar system called a
synchronous transport module (STM).
SONET Devices: SONET transmission relies on three basic devices: STS multiplexers/demultiplexers,
regenerators, add/drop multiplexers and terminals.
STS Multiplexer/Demultiplexer: It marks the beginning points and endpoints of a SONET link. They
provide the interface between an electrical tributary network and the optical network. An STS multiplexer
multiplexes signals from multiple electrical sources and creates the corresponding OC signal. An STS
demultiplexer demultiplexes an optical OC signal into corresponding electric signals.
Regenerator: Regenerators extend the length of the links. A regenerator is a repeater that takes a received
optical signal (OC-n), demodulates it into the corresponding electric signal (STS-n), regenerates the electric
signal, and finally modulates the electric signal into its correspondent OC-n signal. A SONET regenerator
replaces some of the existing overhead information (header information) with new information.
Add/drop Multiplexer: It allows insertion and extraction of signals. An add/drop multiplexer (ADM)
can add STSs coming from different sources into a given path or can remove a desired signal from a path
and redirect it without demultiplexing the entire signal. Instead of relying on timing and bit positions,
add/drop multiplexers use header information such as addresses and pointers (described later in this section)
to identify individual streams.
In the simple configuration shown by Figure, a number of incoming electronic signals are fed into
an STS multiplexer, where they are combined into a single optical signal. The optical signal is transmitted
to a regenerator, where it is recreated without the noise it has picked up in transit. The regenerated signals
from a number of sources are then fed into an add/drop multiplexer. The add/drop multiplexer reorganizes
these signals, if necessary, and sends them out as directed by information in the data frames. These
demultiplexed signals are sent to another regenerator and from there to the receiving STS demultiplexer,
where they are returned to a format usable by the receiving links.
Terminals: A terminal is a device that uses the services of a SONET network. For example, in the
Internet, a terminal can be a router that needs to send packets to another router at the other side of a SONET
network.
Connections: The devices are connected using sections, lines, and paths.
Sections: A section is the optical link connecting two neighbor devices: multiplexer to multiplexer,
Multiplexer to regenerator, or regenerator to regenerator.
Lines: A line is the portion of the network between two multiplexers: STS multiplexer to add/drop
multiplexer, two add/drop multiplexers, or two STS multiplexers.
Paths: A path is the end-to-end portion of the network between two STS multiplexers. In a simple
SONET of two STS multiplexers linked directly to each other, the section, line, and path are the
same.
SONET LAYERS
The SONET standard includes four functional layers: the photonic, the section, the line, and the path
layer. The headers added to the frame at the various layers are discussed later in this chapter. SONET
defines four layers: path, line, section, and photonic.
Path Layer: The path layer is responsible for the movement of a signal from its optical source to its optical
destination. At the optical source, the signal is changed from an electronic form into an optical form,
multiplexed with other signals, and encapsulated in a frame. At the optical destination, the received frame is
demultiplexed, and the individual optical signals are changed back into their electronic forms. Path layer
overhead is added at this layer. STS multiplexers provide path layer functions.
Line Layer: The line layer is responsible for the movement of a signal across a physical line. Line layer
overhead is added to the frame at this layer. STS multiplexers and add/drop multiplexers provide line layer
functions.
Section Layer: The section layer is responsible for the movement of a signal across a physical section. It
handles framing, scrambling, and error control. Section layer overhead is added to the frame at this layer.
Photonic Layer: The photonic layer corresponds to the physical layer of the OSI model. It includes
physical specifications for the optical fiber channel, the sensitivity of the receiver, multiplexing functions,
and so on. SONET uses NRZ encoding with the presence of light representing 1 and the absence of light
representing O.
SONET FRAMES
Each synchronous transfer signal STS-n is composed of 8000 frames. Each frame is a two-
dimensional matrix of bytes with 9 rows by 90 x n columns. For example, STS-l frame is 9 rows by 90
columns (810 bytes), and an STS-3 is 9 rows by 270 columns (2430 bytes). Figure 17.4 shows the general
format of an STS-l and an STS-n.

A SONET STS-n signal is transmitted at 8000 frames per second. If we sample a voice signal and
use 8 bits (l byte) for each sample, we can say that each byte in a SONET frame can carry information from
a digitized voice channe1. In other words, an STS-l signal can carry 774 voice channels simultaneously
(810 minus required bytes for overhead). Each byte in a SONET frame can carry a digitized voice channel.
Wavelength division Multiplexing (WDM): A powerful aspect of an optical communication link is that many
different wavelengths can be sent along a single fiber simultaneously in the 1300 to 1600nm spectral band. The
technology of combining a number of wavelengths on to the same fiber is known as wavelength division multiplexing
or WDN.
Features of WDN:
Capacity upgrade: If each wavelength supports an independent network signal of perhaps a few giga bits per
second, then WDN can increase the capacity of fiber optic network dramatically.
Transparency: Using different wavelengths, fast (Or) slow asynchronous and synchronous digital data and analog
information can be sent simultaneously and independently, over the same fiber, without the need for a common signal
structure.
Wavelength routing: The use of wavelength sensitive optical routing devices makes it possible to use wavelength as
another dimension, in addition to the time and space in designing communication networks and switches. In
wavelength routed networks, use the actual wavelength as intermediate (or) final address.
Wavelength switching: Wavelength routed network-rigid configuration (can not be altered) Wavelength switched
network (WSN)-allow the reconfiguration of optical network. Key components needed for WSN add drop
multiplexed. Optical cross connects and wavelength converters.
Operation principle of WDM.
  Here N fibers come together at an optical combiner (or)wavelength multiplexer, each with its energy
present at different wavelength.
 The N light beams are combined (or) multiplexed on to a single shared fiber for transmission to a
distance destination.
 At far end, the beam is split up over many fibers as there were on the input side. Each output fiber
contains a short, specially constructed core that filters act all but one wavelength.
 The resulting signals can be rated to their destination (or) recombined in different ways for
additional multiplexed transport
 The only difference with electrical FDM is that on optical system using a diffraction grating is
completely passive and thus highly reliable.
 The first commercial system had eight channels of 2.5 Gpbs per channel. By 2001, there were
products with 96 channels of 10 Gpbs , for a total of 960 Gbps.
 When the number of channels is very large and wavelength is spaced close together, for example
0.1nm, the system often referred to as DWDM (Dense WDM).
 By running many channels in parallel on different wavelength, the aggregate bandwidth is increased
linearly with the no. of channels. Since the bandwidth of single fiber band is about 25,000 GHZ,
there is theoretically room for 2500 10 GPPS channels even at 1 bit/HZ. (for DWDM, write same
explanation with the diagram)
Wavelength division Multiplexing (WDM): A powerful aspect of an optical communication link is that many
different wavelengths can be sent along a single fiber simultaneously in the 1300 to 1600nm spectral band. The
technology of combining a number of wavelengths on to the same fiber is known as wavelength division multiplexing
or WDN.
Features of WDN:
Capacity upgrade: If each wavelength supports an independent network signal of perhaps a few giga bits per
second, then WDN can increase the capacity of fiber optic network dramatically.
Transparency: Using different wavelengths, fast (Or) slow asynchronous and synchronous digital data and analog
information can be sent simultaneously and independently, over the same fiber, without the need for a common signal
structure.
Wavelength routing: The use of wavelength sensitive optical routing devices makes it possible to use wavelength as
another dimension, in addition to the time and space in designing communication networks and switches. In
wavelength routed networks, use the actual wavelength as intermediate (or) final address.
Wavelength switching: Wavelength routed network-rigid configuration (can not be altered) Wavelength switched
network (WSN)-allow the reconfiguration of optical network. Key components needed for WSN add drop
multiplexed. Optical cross connects and wavelength converters.
Operation principle of WDM.

 Here N fibers come together at an optical combiner (or)wavelength multiplexer, each with its energy
present at different wavelength.
  The N light beams are combined (or) multiplexed on to a single shared fiber for transmission to a
distance destination.
 At far end, the beam is split up over many fibers as there were on the input side. Each output fiber
contains a short, specially constructed core that filters act all but one wavelength.
 The resulting signals can be rated to their destination (or) recombined in different ways for
additional multiplexed transport
 The only difference with electrical FDM is that on optical system using a diffraction grating is
completely passive and thus highly reliable.
 The first commercial system had eight channels of 2.5 Gpbs per channel. By 2001, there were
products with 96 channels of 10 Gpbs , for a total of 960 Gbps.
 When the number of channels is very large and wavelength is spaced close together, for example
0.1nm, the system often referred to as DWDM (Dense WDM).
By running many channels in parallel on different wavelength, the aggregate bandwidth is increased
linearly with the no. of channels. Since the bandwidth of single fiber band is about 25,000 GHZ, there is
theoretically room for 2500 10 GPPS channels even at 1 bit/HZ. (for DWDM, write same explanation with
the diagram)

 OPTICAL CDMA TECHNIQUE Optical code division multiple access (OCDMA) combines the
beneficial aspects of optical fiber and the flexibility of the CDMA to achieve reliable high speed
connectivity. CDMA was first applied to optical domain in the mid 1980s.
 The optical code division multiple access is continuously gaining more and more interest due to its
potential for improved information security, simplified and decentralized network control, improved
spectral efficiency and increased flexibility in the granularity of bandwidth that can be provided.
 The main difference of O-CDMA systems from wireless CDMA is the code structure. Optical
systems are mainly intensity modulated and hence the chips in the O-CDMA system are alternating
‘1’s and ‘0’s instead of '-1’s and '+1’s In Optical CDMA system, each bit is divided up into n time’s
periods called chips.
 An optical signature sequence or codeword is created, by sending a short optical pulse during some
chip interval but not for others. Each user on the O-CDMA system has a unique signature sequence.
 The encoder of each transmitter represents each “1” bit by sending the signature sequence where as
binary “0” bit is represented by all zero sequence. Since each bit of the original signal is represented
by a pattern of lit and unlit chips, the bandwidth of the data stream is increased
Optical CDMA is therefore a spread spectrum technique. The optical CDMA encoded data is then sent to
the N x N star coupler in a local area network or 1 x N coupler in an access network and broadcast to all
nodes as shown in fig.
In optical CDMA, different users whose signals may be overlapped both in time and frequency share
common communication medium; multiple accesses is achieved by assigning unlike minimally interfering
code sequence to different transmitter, which must subsequently be detected in the presence of multiple
access interference from the users.
The crosstalk between different users sharing the common fiber channel known as the multiple access
interference is usually the dominant source of bit errors in an O-CDMA systems.
The intelligent design of the code word sequence is important to reduce the contribution of MAI to the total
received signal. Performance of O-CDMA communications is clearly dependent on the Multiple User
Interface, the type of modulation used and the receiver topology.
Coherent and Incoherent OCDMA OCDMA system can be classified as
 coherent
 incoherent
Depending on the nature of superposition of the optical signal.
Incoherent systems use intensity-modulation/direct-detection (IM-DD) receivers that detect the power
of the optical signal but not the instantaneous phase variations of the optical signal. Thus uses the
presence of light signal energy or no light signal energy to represent the binary “1” and “0”. Incoherent
OCDMA systems use only uni-polar codes.
In coherent OCDMA system, the phase information of the optical carrier is crucial for the dispreading
process. It increases the complexity of receiver. However the performance of the coherent system is
superior to the incoherent since the receiver are more sensitive to signal to noise ratio, which makes the
overall system performance better. Early O-CDMA networks were developed based upon code
 sequences of incoherent pulses and intensity modulation. The signals were therefore uni-polar with no
negative components due to the incoherent nature of the system. Each user had a unique spreading
sequence: coded transmission was sent to represent data bit “1” and null was used for a “0” bit.
Nevertheless, the signature codes used, i.e. optical orthogonal codes (OOCs), generally had much
poorer correlation properties than their bipolar counterparts, and their availability was severely
restricted. Later coherent systems often relied on phase coding of the optical signal field and coherent
detection. Bipolar signaling was used in the form of ‘+1’ or ‘-1’, which could be obtained by
manipulating the polarization or phase of the optical coherent carrier signal. B.
A. Synchronous and Asynchronous OCDMA: The optical CDMA system may be synchronous or
asynchronous.
In a synchronous OCDMA (S-OCDMA) the bit and chip are synchronized and the receiver
examines the correlator output only at one instant in the chip interval. The codeset for S-OCDMA
are described by the (N, w, λ). S-OCDMA dramatically improves efficiency by trading off between
code length, MAI and address space. In the asynchronous OCDMA the bit are not synchronized but
the chips may be transmitted synchronously. The codeset for A-OCDMA are described as (N, w, λa
, λc). The cardinality of /Ca / for A-OCDMA can be used as a codeset of Cs with (N, w, max (λa ,
λc)) and cardinality /Cs / = n. /Ca / for S-OCDMA, since each of the n time shifts of each code
sequence of Ca can be used as a unique code sequence in Cs with the same correlation properties.
OCDMA for PON and LAN In data communication systems, the access network directly link with the
customer premises and is responsible for delivering and collecting traffic.
Optical access network can be categories into two:
 Active optical network (AON)
 Passive optical network (PON)
In AON electrical de-multiplexer are used where as in PON optical de-multiplexer are employed. PON
avoid the effect of electromagnetic interference and thunder, economize the cost of operation and
maintenance, very good transparency and is suitable for signals with any format and any bit rate, thus
provide improved reliable systems. In fiber-to-the-home (FTTH) application, optical access networks are
considerable choice. The all optical CDMA system is usually a fiber optic non-coherent system. It usually
has no separate modulation operation
The combination of three potential advantages makes OCDMA attractive from a networking perspective:
i. Large channel count.
ii. Asynchronous transmission simplifies access control to the medium.
iii.Multiclass multi-rate services can be implemented by using variable code lengths code weight
System Parameters Various parameters to be considered in the design and implementation of OCDMA
communication systems - are:-
a) Bit rate
b) Chip rate
c) Power handling
d) Processing gain
e) Multiple access interference
OPTICAL CDMA CODING TECHNIQUE

In order to implement OCDMA communication network, address codes with sufficient performance are
required. OCDMA is the use of optical network technology to arbitrate channel access among multiple
network nodes in a distributed fashion.

Passive Optical Network (PON):

 PON use some form of passive components such as optical star coupler or static wavelength router as the
remote node.
 Simple PON architecture uses a separate fiber pair from the CO to each ONU.The main problem with this
approach is that cost of CO equipment scales with the number of ONU’s.
 Moreover,the operator needs to install and maintain all these fiber pairs.This type of architecture used to
provide high speed service.
 Instead of providing a fiber pair to each ONU,a single fiber can be used with bidirectional
transmission.However the same wavelength cannot be used to transmit data simultaneously in both the
directions because of the uncontrolled reflection in the fiber.One way is to use time division multiplexing so
that both the ends does not transmit simultaneously.Another is to use different wavelength (1.3 and
 1.55µm,for example)for the different directions.
 In PON architecture,fiber pair can also shared by many users.Common example for such network is
SONET/SDH rings.This type of network provides high speed services to large business customers.An ONU
is a SONET add drop multiplexer(ADM),which can drop its information at particular wavelength.
PON architecture types:
 T PON-Passive Optical Network for Telephony.
 W PON-Wavelength Division Multiplexing (WDM) Passive Optical Network.
 WR PON-Wavelength Routing Passive Optical Network.
Passive Optical Network for Telephony (TPON):
 The CO broadcasts its signal downstream to all the ONU’s using a passive star coupler. The ONU
shares an upstream channel in a time multiplexed fashion. In this case, upstream and downstream
signals are carried using different wavelength over a single fiber.
 In TDM approach, the ONU’s need to be synchronized to a common clock.This is done by a process
called ‘RANGING’, where each ONU measures its delay from CO and adjusts its clock such that all
the ONU’s are synchronized relative to the CO.
 The CO transmitted can be LED or fabry penot laser and receiver is PIN FET receiver.ONU’s
transmitter and receiver can also be LED or laser and PIN FET receiver.
 Number of ONU’s is limited by splitting loss in the star coupler.
 There is a trade off between transmitted power, receiver sensitivity, bit rate and the number of
ONU’s and total distance covered.
 TPON’s may be cost effective at offering low speed services compared to SONET/SDH rings or
Ethernet based offerings.
b.WDM PON:
 It is an upgraded version of the basic PON architecture.In this case,the CO broadcasts multiple
 wavelengths to all the ONU’s and each ONU select a particular wavelength.
 In this case,a single transceiver at the CO with WDM array of transmitters or single tunable
transmitter to yield(WDM PON).
 This approach allows each ONU’s to have electronics running only at the rate it receives data,and
not at the aggregate bit rate.
 However it is still limited by the power splitting at the star coupler.
c. WR PON- Wavelength routing PON:
 In this case, a passive arrayed waveguide grating (AWG) is used to route different wavelength to
different ONUS in the down stream directions, without is curring a splitting loss.
 AS in the TPON and WPON architectures, the ONUS time shared wavelength for upstream
transmission
 It allows point to point dedicated services to be provided to ONUS.
Disadvantages of PON:
 The cost of CO equipment scales with number of ONU’s.
 Operator needs to install and maintain all the pair of fibers coming from each ONU’s to CO.
Advantages of PON:
 Since this architecture is made from passive components, its reliability is very high.
 Ease of maintainence.
 Fiber infra structure itself is transparent to bit rate modulation formats and the overall network can
be upgraded in the future without changing the infra structure itself.
FTTH: Fiber to the home
 IN FTTC ie Fiber to the curb (or) Fiber to the building, data is transmitted digitally over optical
fiber from the hub, or central office, to fiber terminating nodes called optical network units(ONU).
The expectation is that fiber would get much closer to the subscriber with this architecture.
 IN FTTH (fiber to the home) architecture, the ONUS would perform the function of NIU> Here the
optical fiber is used to transmit data from central office to remote node(RN) and RN to home.
 In network from the co to ONU is typically a passive optical network(PON). The remote node is a
simple passive device such as an optical star coupler and it may some be collocated in the central
office itself rather than in the field.
 Although many different architectural alternatives can be used for FTTC, the term FTTC is usually
used to describe a version where the signals are broadcast from the central office to the ONUS, and
 the ONUS share a common total bandwidth in time division multiplexed fashion.
 In FTTC, the fiber is within about 100m of the end user. In this case, there is an additional
distribution network from the ONUS to the NIUS with the fiber to the cabinet(FTTcab) approach,
the fiber is terminated in a cabinet in the neighbourhood and is within about 11cm of the end user.

Optical network management functions

All optical network (AON) consisting of AT&T Bell laboratories, digital equipment co-operation and
Massachusetts institute of technology developed a test bed for
light wave communication. the aim of the test bed was to demonstrate a single routing mode in a network operating
at a transmission rate of 100 lib/s.
 Packet interleaving was used and packets from electronic sources at 100 Mb/s were optically compressed to the 100
lib/s rate using optical time division multiplexing.
AON supported different classes of service, specifically guaranteed bandwidth service and bandwidth-on-demand
service.
The topology used in the above diagram is bus topology where users transmit in the top half of the bus and receive
from the bottom half. However, each user is attached for transmission to two points on the bus such that the
guaranteed bandwidth transmission are always upstream from the bandwidth-on-demand transmission since it
having helical shape, the name helical LAN(HLAN) for this network.
network management consists of several functions, all of which are important to the operation of the network:
1. Performance management deals with monitoring and managing the various parameters that measure the
performance of the network. Performance management is an essential function that enables a service provider to
provide quality-of-service guarantees to their clients and to ensure that clients comply with the requirements imposed
by the service provider. It is also needed to provide input to other network management functions, in particular, fault
management, when anomalous conditions are detected in the network.
2. Fault management is the function responsible for detecting failures when they happen and isolating the failed
component. The network also needs to restore traffic that may be disrupted due to the failure, but this is usually
considered a separate function.
3. Configuration management deals with the set of functions associated with managing orderly changes in a
network. The basic function of managing the equipment in the network belongs to this category. This includes
tracking the equipment in the network and managing the addition/removal of equipment, including any rerouting of
traffic this may involve and the management of software versions on the equipment.
Another aspect of configuration management is connection management, which deals with setting up, taking down,
and keeping track of connections in a network. This function can be performed by a centralized management system.
Alternatively, it can also be performed by a distributed network control entity. Distributed network control becomes
necessary when connection setup/take-down events occur very frequently or when the network is very large and
complex.
Finally, the network needs to convert external client signals entering the optical layer into appropriate signals inside
the optical layer. This function is adaptation management.
4. Security management includes administrative functions such as authenticating users and setting attributes such as
read and write permissions on a per-user basis. From a security perspective, the network is usually partitioned into
domains, both horizontally and vertically. Vertical partitioning implies that some users may be allowed to access only
certain network elements and not other network elements.
 For example, a local craftsperson may be allowed to access only the network elements he is responsible for
and not other network elements. Horizontal partitioning implies that some users may be allowed to access
 some parameters associated with all the network elements across the network.
 For example, a user leasing a lightpath may be provided access to all the performance parameters associated
with that lightpath across all the nodes that the light path traverses. Security also involves protecting data
belonging to network users from being tapped or corrupted by unauthorized entities. This part of the problem
needs to be handled by encrypting the data before transmission and providing the decrypting capability to
legitimate users.
5. Accounting management is the function responsible for billing and for developing lifetime histories of the
network components. This function is the same for optical networks.