PRINCIPLE OF COMMUNICATIONS

CS=2 δ
ANGLE MODULATION
INTRO TO FREQUENCY MODULATION

A major problem in AM is its susceptibility to

noise superimposed on the modulated carrier
signal. To improve on this, the first frequency
modulation (FM) radio communication
system was developed in 1936, which is
much more immune to noise than its AM
counterpart. Unlike the AM, FM is difficult to
treat mathematically due to the complexity
of the sideband behavior resulting from the
modulation process.

Angle Modulation
In AM, the amplitude of the carrier signal
varies as a function of the amplitude of the
modulating signal. But when the modulating
signal can be conveyed by varying the
frequency or phase of the carrier signal, we
have angle modulation. Angle modulation
can be subdivided
by
a. frequency modulation (FM) and
b. phase modulation (PM).

A. Frequency Modulation- the carrier’s

instantaneous frequency deviation from its
unmodulated value varies in proportion to
the instantaneous amplitude of the
modulating signal.

B. Phase Modulation, the carrier’s

instantaneous phase deviation from its
unmodulated value varies as a function of v C ( t )=V c sin 2 π f c t
the instantaneous amplitude of the
modulating signal.
Below is the figures illustrates the FM and PM
waveforms for sine wave modulation v m ( t )=V m sin 2 π f m t

FREQUENCY MODULATION V FM (t )
- Type of angle modulation wherein the
frequency of the constant-amplitude carrier
signal is varied or changed according to the
instantaneous amplitude of the modulating
signal. Modulation Index,
mf
- As the amplitude to the information varies,
the carrier frequency varies above and below - The modulation index for an FM signal
its normal center frequency. is defined as the ratio of the maximum
frequency deviation to the modulating
signal frequency.
Frequency Deviation, δ
δ
mf =
- the peak frequency shift that occurs in fm
the carrier.
- - is the amount by which the carrier Where:
frequency is varied from its mf =¿ modulation index of fm
unmodulated value.
δ=¿ maximum frequency deviation of the

Carrier swing - is the peak to peak carrier by the amplitude of the modulating
frequency deviation. signal.
 f m=¿ frequency of the modulating signal
For a FM signal with a modulation index of
0.5, draw the frequency spectrum of the FM
signal. (Bessel Function Table)

FM was developed to cope with the BANDWIDTH REQUIREMENT FOR AN FM

undesirable noise, which competed with the SIGNAL
desired signal when it is amplitude
modulated. The exact bandwidth obtained using the
Bessel function is given by the equation,

BW =2 x n sideband pairs x f m
MATHEMATICAL DESCRIPTION OF AN FM
SIGNAL
The instantaneous frequency of the FM signal Approximate minimum bandwidth using
is given by the equation, Carson’s rule is
f =f c ( 1+k V m sin 2 π f m t )
δ +f m ( max❑ )
Where: BW =2¿
f c =¿ unmodulated carrier frequency, HZ
K=¿ Narrow Band FM with low modulation index
proportionality constant values, the minimum bandwidth is given by
V m sin 2 π f m t =¿ the equation,
instantaneous modulating
voltage, V BW =2 f m

The instantaneous value of the FM signal is

given by the equation, Wideband FM with high modulation iindex
2π f mt values, the minimum BW is given by the
equation,
δ
2 π f c t+ sin ¿
fm BW =2 δ
¿
¿
V FM ( t ) =V c sin ¿

Where: PERCENT MODULATION

fc = unmodulated carrier frequency, Hz
- Ratio of the actual frequency deviation to
f m = modulating signal frequency, Hz the maximum allowable frequency deviation
allowed by law.
δ = Frequency deviation
- For FM broadcast band, the maximum
V c = peak amplitude of the carrier voltage, allowable frequency deviation is 75KHz.
V - For sound portion of TV broadcast, the
maximum allowable frequency deviation is
Recall that in AM, the frequency component 25KHz
consists of a fixed carrier frequency with
upper and lower sidebands equally displayed δ actual
above and below the carrier frequency. The %M= x 100
frequency spectrum of the FM wave is much δ maximum
more complex, that it will produce an infinite
number of sidebands DEVIATION RATIO, DR
In expanded form, - - is the worst-case modulation index
and is equal to the maximum peak
frequency deviation divided by the
maximum modulating signal
frequency.
- - The worst case modulation index
FREQUENCY SPECTRUM OF A FM SIGNAL produces the widest output frequency
The frequency spectrum of the FM spectrum.
signal can be obtained using the Bessel
function table. (Please refer to the book) δ MAX
DR=
f m ( max❑)
Example:
For FM broadcast band, the maximum
allowable frequency deviation is 75KHz.

For sound portion of TV broadcast, the

maximum allowable frequency deviation is
25KHz.

- For FM broadcast band and sound portion of

TV broadcast, the maximum modulating
signal frequency is 15KHz.
Expression for PM signal:
POWER CONTENT OF AN FM SIGNAL

PT =P C + P 1+ P2 +…+ P n

V 2c V 21 V 22 V 2n
PT = + + + …+
2R 2R 2R 2R

Comparison between PM and FM:

1. Modulation Index is defined differently in

ADVANTAGES OF FM OVER AM
1.FM is more immune to noise than AM. each systems
2.Rejection of interfering signals because of
mp = is proportional to the amplitude of the
“capture effect”.
3.Lower power output requirements. modulating signal.
4.Better transmitter efficiency since class C
amplifier may be used. Note: In PM, the max frequency deviation
5.Improved signal to noise ratio. takes place at the crossing points. While in
FM, maximum frequency deviation takes
DISADVANTAGES OF FM OVER AM place t the peak amplitude of the modulating
1. Wider channel is required for FM signal. The value of change in the carrier fm;
2. FM transmitter and receiver circuits are
more complex and expensive. mf - indirectly proportional to fm.
3. Since the reception is line of sight, the
area of reception for FM is smaller than for 2. FM is a form of PM.
AM.
4. Maximum deviation is limited. 3. mf indicates the amount of frequency
deviation, while mp indicates the phase
PHASE MODULATION change introduced by the modulating signal.
– modulation technique in which the amount
mp is independent of the modulating
of phase shift of a constant frequency carrier
is varied in accordance with the modulating frequency.
frequency.
Example: A 25 MHz carrier is modulated by
-FM can be obtained from PM by the use of
a 400 Hz audio sine wave. If the carrier
the Armstrong systems. voltage is 4V and the maximum deviation is
10 KHz, Write the equation of this modulated
Phase shift – the separation between two
wave.
sinewaves of the same frequency. a. FM
b. PM
Principle of PM c. if the modulating frequency is increased to
In PM, when the modulating signal goes
2 KHz,
positive, the amount of phase lag increases
What is now the resulting FM and PM
with the amplitude of the modulating signal.
equation?
The effect is the frequency being increased,
when the modulating signal goes negative, Noise Triangle
the amount of phase decreases thus -triangular noise distribution for FM
frequency is lowered.
There is a non- uniform distribution of noise.
Noise of the higher modulating frequencies is
inherently greater in amplitude than noise at
lower frequencies.

For information signal with a uniform signal

level, a uniform S/N is produced. The higher
modulating frequencies have lower S/N than
the lower than the lower frequencies. To
Compensate for this pre-emphasis is used.
Advantage of Pre-emphasis and De-
emphasis Network:

1. increased S/N ratio

2. increases fidelity
3. increased intelligibility of FM signals.
4. uniform S/N indicates stable flow of
signals.
Pre-emphasis – process of emphasizing or
boosting in amplitude of the high frequency
signals prior to performing modulation. Fu = upper break frequency where the signal
enhancement flatten.
Pre-emphasis circuit:

De-emphasis – reciprocal of pre-emphasis;

restores the original amplitude vs. frequency
The break frequency, (the frequency
characteristics of the information signal.
whrere pre emphasis and de emphasis
begins) is determined by the RC and L/R time
constant of the network. The break
frequency occurs at the frequency Where Xc
or XL equal R.
De-emphasis circuit: Mathematically:

FM DUE TO AN INTERFERING SINUSOID

Pre-emphasis Network:
- A high pass filter that amplifies the
high frequency components more than
the low frequency components.
- A differentiator circuit.
The noise vector is super imposed on the
carrier circulating about it with a relative
angular Wn-Wc
Peak phase:

De-emphasis Network First derivative:

- A low pass filter or an integrator.
 c. Linear Integrated-circuit direct FM
modulators

The peak frequency deviation b. Indirect method - producing FM by use

of phase modulation

forward bias – current will flow depletion

region collapses
The S/N ratio at the output of an FM
demodulator due to unwanted frequency
deviation from an interfering sinusoid is the
ratio of the peak frequency due to the
information signal to the peak frequency
deviation due to the interfering signal. reverse bias – no current will flow in the
depletion region, acts as a capacitor
S/N =

Note: Width of the depletion region depends

upon the amount of reverse bias, the wider
the depletion the lower the reverse bias, the
Example: thinner the depletion region.
For an angle modulated carrier
Vc(t )=0.5 cos (2 π 200.01 MHzt ) FM modulator w/ Wc
Determine: a. the frequency of the 1
demodulated interference signal. f0 = 2 π √ LC
b. Peak phase and frequency deviation due
to the interfering signal
c. S/N at the output of the demodulator. LC 1 +C
¿
L¿
Solution: f0 = 2π √¿
1
¿

FM GENERATION Note: Capacitance of the Wc ( D1) is

controlled by:
a. Direct Method – producing FM by directly a.) Fixed dc voltage (set by R1 and R2)
varying the output frequency of a carrier b.) Modulating signal voltage(that adds to
oscillator.
and subtracts from the fixed dc bias)
-is angle modulation in which the
frequency of the carrier is varied (deviated) - If reverse bias increases, the
directly by the modulating signal.
capacitance of D1 is lowered, thus the
frequency of the oscillator is increased
- If the reverse bias decreases, the
Three common methods: capacitance of D1 is increased and the
a. Varactor diode Modulators frequency is decreased.

Reactance
- employs a reactance circuit that presents
inductive or capacitive reactance to the tank
circuit of an oscillator.
- the variation in reactance causes the
b. FM Reactance Modulator
frequency of the oscillator to shift in
accordance with the modulating signal
thereby producing FM.
 Note: The equivalent capacitance depends in
the device transconductance as given by Ceq2
gmRc and can therefore be varied, with bias
id
voltage since gm = vg , also the gate-to-

drain impedance (Xc) is made 5 to 10 times

Basic FET reactance modulator greater than gate-to-source impedance ( R ),
The impedance is entirely reactive. The value that is Xc = nR where n = multiplying factor.
of the reactance is proportional to the Therefore,
transconductance of the device which is
gm
dependent on the gate voltage and its
Ceq = 2 πfn
variations.
to det. Z:
v
z= i impedance looking at

the terminals
Note: For z to be pure reactance
1. The bias network current in must be TYPES OF REACTANCE MODULATOR
negligible compared to the drained current, Name Zgd Zgs Condition
id. The impedance of the bias network must Reactance Formula
RC Capacitive C R Xc>>R Ceq =
be large to be ignored.
gm RC
2. The drain-to-gate impedance (Xc) must be RC Inductive R C R>>Xc Leq = Rc/gm
greater than the gate to source impedance RL Inductive L R XL>>L Leq =
(R) L/gm R
By analysis: RL Capacitive R L R>>XL Ceq= gmL/R

V
Vg = Rib where: ib = R− jXc
Indirect FM
- The frequency of the carrier is deviated
indirectly by the modulating signal and is
VR
Vg = accomplished by changing the phase of the
R− jXc
carrier, which is a farm of direct FM.
id= gmVg - With the use of FM, carrier oscillator can be
ophimized per frequency accuracy and of the
id = gm ( R−VRjXc ) stability.

Note:
then, Primary disadvantage of direct FM is that
relatively unstable LC oscillators are used to
V
V produce carrier frequency.
VR
z= id = gm (
R− jXc ) Advantage of direct FM is the relatively high
frequency deviation and modulation indices
attainable because of the LC oscillators’
R− jXc 1 R− jXc
= −¿ instability.
z= gm R gm R gm Primary Advantage of direct PM (indirect FM)
is the use of high stable crystal oscillators.
1 − jXc
z= gm R( ) Disadvantage of direct PM the difficulty to
achieve high phase deviation and modulation
indices because of the inherent stability of
The impedance is a capacitive reactance the crystal oscillator.
Xc Indirect FM uses RC Phase Shifting Circuits
Xeq = R gm

1 1 /2 π fc
=
2 π f ceq R gm Ceq= gmRc
 and negative voltage if input frequency is
lower.
- Voltage output of the discriminator is in
series with the AF input of the reactance
modulator and therefore the
A VVC Phase Modulator Circuit transconductance will either increase or
decrease. The output capacitance or
Direct FM transmitter inductance is increase or decrease, thus
- uses AFC to meet FCC specifications on lowering or increasing the frequency of the
oscillator stability. master oscillator. Any unwanted shift in the
frequency is connected.

Up-Conversion Method
1. Heterodyning or Mixing
- change the fc only
1. Crosby Direct FM Transmitter
2. Frequency Multiplication
- used in commercial broadcast band
- changes fc, mf, δ, etc.
transmitter.
- includes an AFC Loop

AFC – Automatic Frequency Control

- provides the necessary correction in
case of unwanted frequency drifts
- uses discriminator circuit.

AFC Operation:
- Discriminator will give positive dc voltage if
input frequency is higher than what is tuned