21.

Deduce the expressions for characteristic impedance and propagation constant of a

line of cascade identical and symmentrical T sections of impedances?
R, L, C, G – Primary Constants Consider a transmission lines as a two conductor
separated by dielectric
 In a transmission line the terminal behaviour is not be same
Where ∆V is the drop in series arm and ∆I is a drop in short arm.
 Due to the drop, the voltage between the i/p and o/p there is a presence of resistor in
the series arm.
 Since the two wires separated by dielectric. There is capacitance and this capacitance
not ideal and it has leakage inductance which should be ideally zero.
 Initially the voltage and current on a line are in phase and later there is a phase shift
which is due to the presence of inductance.
R, L, C, G are called primary constants of transmission line.
Z – Series impedance
Y – Shunt admittance
Note: Since the transmission line is introducing delay the signal is distorted. Since it is a wire
it having some resistance and attenuation in the signal.

22. Discuss the types of waveform distortion introduced by a transmission line?

 WAVEFORM DISTORTION: When a signal is transmitted over the line, it will
not have all frequency with equal attenuation and equal time delay.
∴ the received waveform will not be identical with the input waveform.
This variation is known as distortion 2 types of distortion
1. Frequency distortion
2. Phase distortion
FREQUENCY DISTORTION:


A complex applied voltage containing many frequency will not have equal
attenuation. ∴ received waveform will not be identical with the input waveform.
This is known as frequency distortion. It can be reduced using equalizers.
Equalizers are network whose frequency & phase characteristics are adjusted to be
inverse to that of line resulting in uniform frequency response over the desired
band.
PHASE DISTORTION:

 For an applied voltage, received waveform will not be identical with the input
waveform, since some components will be delayed more than others. This is
known as delay or phase distortion.
23. Explain the significance of reflection coefficient and insertion loss?
 As the frequency increases insertion loss and return loss are more relevant in the
systems due to the characteristics of microwave frequencies. The voltage standing
wave ratio (VSWR) and reflection coefficient (Γ) are an important factor involved
in return loss.
 Insertion loss and return loss are widely used terms in the field of microwave
technologies. Insertion loss and return loss plays an important role in designing
and development of high-frequency devices such as filters, power dividers,
amplifier, etc.
 These are quite similar concepts, it is an advanced form of the basic electronics we
have learned in network theorems.

If the power transmitted to the load is PT and the incident power received by the load is
PR,

24. Describe the line not terminated to Z0?

 The insertion loss of a line or network is defined as the number of nepers or decibels
by which the current in the load is changed by the insertion . Insertion loss=Current
flowing in the load without insertion of the Network Current flowing in the load with
insertion of the network.

Coaxial cable
 Coaxial lines confine the electromagnetic wave to the area inside the cable, between
the center conductor and the shield. The transmission of energy in the line occurs
totally through the dielectric inside the cable between the conductors. Coaxial lines
can therefore be bent and twisted (subject to limits) without negative effects, and they
can be strapped to conductive supports without inducing unwanted currents in them.
  In radio-frequency applications up to a few gigahertz, the wave propagates in the
transverse electric and magnetic mode (TEM) only, which means that the electric and
magnetic fields are both perpendicular to the direction of propagation (the electric
field is radial, and the magnetic field is circumferential). However, at frequencies for
which the wavelength (in the dielectric) is significantly shorter than the circumference
of the cable, transverse electric (TE) and transverse magnetic (TM) waveguide modes
can also propagate.

Microstrip
 A microstrip circuit uses a thin flat conductor which is parallel to a ground plane.
Microstrip can be made by having a strip of copper on one side of a printed circuit
board (PCB) or ceramic substrate while the other side is a continuous ground plane.
The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the
dielectric constant of the insulating layer determine the characteristic impedance.
Microstrip is an open structure whereas coaxial cable is a closed structure.

Waveguide
 Waveguides are rectangular or circular metallic tubes inside which an electromagnetic
wave is propagated and is confined by the tube. Waveguides are not capable of
transmitting the transverse electromagnetic mode found in copper lines and must use
some other mode. Consequently, they cannot be directly connected to cable and a
mechanism for launching the waveguide mode must be provided at the interface.
 25.Adopt the condition for minimum attenuation?
 To calculate the value of L,the other line parameter R,C,G & ω are considered as
constant,only L may be varied solving and reducing we get,
 R/L= G/C If only L is variable, the attenuation is minimum when
 L=RC/G H/Km
 In practice L is normally less than the desired vlue
 Similarly, C= LG/R F/Km
 When R=0 and G=0, the attenuation constant is zero.

21.Explain the parameter of open wire line and coaxial wire line?

The line parameters of open wire line at radiofrequency:

 Loop inductance for open wire line: consider an open wire line having two
circular conductors parallel to each other. Let a-be radius of the conductor and d
be the spacing between the two conductors In general, The self inductance of the
parallel wire line system L={µr+9.21 logd/a}10-7 henry/meter
 Where µr is the relative permeability of the conducting material for nonmagnetic
material But at high frequency due to skin effect, the internal inductance of the
open wire line is Li=0 -7 Hence the self inductance at RF=L=9.21 10 log(d/a)
henry/m 2. Shunt capacitance: The value of capacitance of a line is not affected by
a skin effect or frequency, hence given as C=πεd/(ln(d/a))
 Loop resistance: At radio frequency due to appreciable skin effect, the current
flows over the surface of the conductor in a thin layer with a resultant reduction in
effective cross section area or an increase in resistance of the conductor
Rac=Rdc/2 (πfµ)
 Shunt conductance: since the lines are well constructed that is filled with solid
dielectric between the conductors there is no shunt conductance. G=0

Parameters of coaxial lines at RF:

At radio frequency due to skin effect, the current flows on the outer surface of the
inner conductor and the inner surface of the outer conductor, which eliminates
flux linkages due to internal conductor flux and the

 Loop inductance: for the co-axial line L = /2 loge (b/a) henrys/m Where a- radius
of a inner solid conductor b-inner surface radius of the outer hollow tubular
conductor c-the outer surface radius µrd- relative permeability of the dielectric
material µo- absolute permeability.
 Shunt capacitance: the capacitance of a co-axial line is not affected by frequency,
except the relative permittivity of the dielectric , so that C = 2 d/ ln(b/a) farad/m =
µ / Where, - is the dielectric constant of the dielectric material - is the relative
dielectric constant of the dielectric material.

22. Explain Line  of zero  dissipation,  voltage  and  current  on  the dissipation?

 Internal inductance, due to skin effect Li = 0

 The inductive reactance is comparatively large with loop resistance, ≫
 Shunt conductance G = 0

 LOW DISSIPATION LINE: these lines are used where resonance properties are
involved. Example transmission line as simple resistor, inductance, capacitor If
the loop resistance R is negligible in comparison with then the line is termed as
ZERO DISSIPATION LINES or LOSSLESS LINES.
 Example: transmission of power at high efficiency is done through zero
dissipation lines only. That is the transmission line which is used to transfer the
power signal between the power amplifier and the antenna section at transmit end.
  Shunt capacitance per unit length, in farads per metre.
 

 Series inductance per unit length, in henrys per metre.

 Characteristic impedance in ohms (Ω). Neglecting resistance per unit length for
most coaxial cables, the characteristic impedance is determined from the
capacitance per unit length (C) and the inductance per unit length (L). Those
parameters are determined from the ratio of the inner (d) and outer (D) diameters
and the dielectric constant (ε). The characteristic impedance is given by

23. Brief notes on standing waves, nodes, standing wave ratio?

 If the transmission is not terminated in its characteristic impedance ,then there
will be two waves traveling along the line which gives rise to standing waves
having fixed maxima and fixed minima.
 The ratio of the maximum to minimum magnitudes of current or voltage on a
line having standing wave is called the standing-wave ratio S. That is, S=
E max = I max; Emin =I min.
 For coaxial lines it is necessary to use a length of line in which a longitudinal
slot, one half wavelength or more long has been cut. A wire probe is inserted
into the air dielectric of he line as a pickup device, a vacuum tube voltmeter or
other detector being connected between probe and sheath as an indicator. If
the meter provides linear indications, S is readily determined. If the indicator
is non linear, corrections must be applied to the readings obtained.

 The relation between standing wave ratio S and reflection co-efficient k is, S
=1+ k/1-k.

24. Derive the power and impedance measurement on lines?

 Forward and backward travelling wave.

 
 The wave equations are partial differential equations (PDEs) of two variables t  an d x
and can b e solved by Laplace transform method. By taking Laplace transform of

 and assuming zero initial condition s, the two PDEs become ordinary differential
equations (O DEs) with respect to variable  (with   treated as a parameter):

 Combining t hese two firs t order OD Es, we get t he voltage w ave equation as a
second order ODE:
25. Explain how measurement of VSWR and wavelength?
 Standing Waves
 
 Standing waves on the transmission line. Assuming the propagation constant is purely
imaginary (lossless line), We can re-write the voltage and current waves as:

 If we plot the voltage along the transmission line, we observe a series of peaks and
minimums, which repeat a full cycle every half-wavelength. If gamma equals 0.5
(purely real), then the magnitude of the voltage would appear as:

 Hence, this ratio, known as the Voltage Standing Wave Ratio (VSWR) or standing
wave ratio is a measure of how well matched a transmission line is to a load. It is
defined as:

 The reflection coefficient may also be established using other field or circuit
quantities.
 
 The reflection coefficient can be given by the equations below, where ZS is the
impedance toward the source, ZL is the impedance toward the load:

 Simple circuit configuration showing measurement location of reflection coefficient.

 Notice that a negative reflection coefficient means that the reflected wave receives a
180°, or π, phase shift.

 Thus the absolute magnitude (designated by vertical bars) of the reflection coefficient
can be calculated from the standing wave ratio.