Unit - 2 : Chapter - 3

Angle Modulation
Prepared by
Dr. L. Bhargava Kumar

1
Refer class notes for PM, NBFM and WBFM, Bandwidth concepts.
Plots of Bessel functions of the first kind
For a more accurate assessment of the bandwidth requirement of an FM signal, we
may use a definition based on retaining the maximum number of significant side
frequencies whose amplitudes are all greater than some selected value. A convenient
choice for this value is 1 percent of the unmodulated carrier amplitude.

The transmission bandwidth of an FM wave is the separation between the two

frequencies beyond which none of the side frequencies is greater than 1 percent of
the carrier amplitude obtained when the modulation is removed.

BT = 2 nmax fm

where fm is the modulation frequency and n is the largest value of the integer n that
satisfies the requirement |Jn(β)|>0.01. The value of nmax varies with the modulation
index β and can be determined readily from tabulated values of the Bessel function
|Jn(β)|.
Universal curve for evaluating the 1 % bandwidth of
an FM wave.
Bessel Functions of the First Kind
Deviation ratio (D)

It is defined as the ratio of the frequency deviation ∆f to the highest modulation frequency
W

D = ∆f / W

The deviation ratio D plays the same role for non-sinusoidal modulation that the modulation
index β plays for the case of sinusoidal modulation.

From a practical viewpoint, Carson’s rule somewhat underestimates the bandwidth

requirement of an FM system, whereas using the universal curve yields a somewhat
conservative result.

Thus, the choice of a transmission bandwidth that lies between the bounds provided by these
two rules of thumb is acceptable for most practical purposes.
Example: In North America, the maximum value of frequency deviation ∆f is fixed
at 75 kHz for commercial FM broadcasting by radio. If we take the modulation
frequency W - 15 kHz, which is typically the “ maximum” audio frequency
of interest in FM transmission
Relationship between PM and FM waves:

Phase-modulated
signal

Frequency-
modulated signal
 FM Wave
Generation

PM Wave
Generation
Generation of FM waves:

There are two techniques to generate FM signals.

(i) Indirect method

NBFM wave is first generated by phase modulating the carrier by the integral
of the message signal. The resulting signal is frequency multiplied to get
WBFM signal.

(ii) Direct method

The instantaneous frequency of the carrier wave is varied directly in
accordance with the message signal by means of a device known as a voltage-
controlled oscillator (VCO).
Indirect Method

• Recall NBFM,

• The NBFM is given to frequency multiplier to increase the frequency

deviation to the desired level.
• Let s1(t) be the NBFM

13
Generation of NBFM waves:
Generation of WBFM waves:

NBFM
 Frequency
Multiplier

After substituting s1(t) in the above equation and simplifying it, s2(t) have a DC
component and n frequency modulated waves having carrier frequencies f1 , 2f1 , 3f1 , ….,
nf1 with frequency deviations ∆f1 , 2∆f1 , 3∆f1 , ….. , n ∆f1

The BPF has two functions:

1. To pass the FM wave centered at carrier frequency nf1 and having frequency deviation
n∆f1
2. To supress all other FM spectra.

Direct Method

In direct method, fi(t) is varied directly in accordance with the amplitude of the message
signal. This is achieved by using a VCO.

VCO is basically a oscillator with high resonant network where the capacitance varies in
accordance with the modulating signal.
This configuration permits the attainment of

• Good oscillator stability

• Constant proportionality between output frequency change and input
voltage change
• The necessary frequency deviation to achieve wide-band FM.

The disadvantage is that the carrier frequency is not obtained from a highly
stable oscillator.

It is therefore necessary, in practice, to provide some auxiliary means by

which a very stable frequency generated by a crystal oscillator will be able
to control the carrier frequency.
A feedback scheme for the frequency stabilization of a frequency modulator.
Hartley oscillator

The capacitive component of the frequency-determining network in the oscillator

consists of a fixed capacitor shunted by a voltage-variable capacitor. The resultant
capacitance is represented by C(t).

A voltage-variable capacitor, commonly called a varactor or varicap, is one whose

capacitance depends on the voltage applied across its electrodes.
The frequency of oscillation of the Hartley oscillator is given by

L1, and L2 are the two inductances in the frequency-determining network of

the oscillator and C(t) is the total capacitance of the fixed capacitor and the
variable-voltage capacitor and is given as

C0 is the total capacitance in the absence of modulation and ∆C is the

maximum change in capacitance.

Substituting C(t) in fi(t) gives

 Where f0 is unmodulated frequency of oscillation

Using the Binomial Theorem

Letting the above equation becomes

Frequency Discrimination (Simple Slope Detection) technique:
H(f)

sc(t) Envelope sd(t)

s(t) Detector

t t

S(t) Sc(t)

Sd(t)
t
Problems:-
1.The detector also responds to spurious amplitude variation of the input FM.

2. The range of linear slope is quite small.

|H(f)|

fc f0 f
Balanced/ Dual slope detection
Balanced/ Dual slope detection
Frequency response
Advantages of FM

• Amplitude of the FM wave remains unaffected.

• Large decrease in noise, hence increase in SNR.

• Frequency allocation allows for a guard band which reduces adjacent

channel interference.

• FM permits several independent transmitters on the same frequency with

negligible interference.
Disadvantages of FM

• FM wave can’t cover large area.

• Transmitting & receiving equipments for FM are complex & costly.
• A much wider channel, typically 200 kHz, is needed for FM.
Applications of FM and PM:

FM PM

ü Radio broadcasting ü Data communications

ü Sound signal transmission in TV ü Generating FM in FM transmitters.
broadcast ü Television broadcast:
ü Two-way fixed and mobile radio VSB-AM TV video signal,
systems FM for the sound signal associated
ü Analog cellular communications with video signals, and
systems and satellite PM for the transmission of colour
communications. information along with video and
sound signals.
References:

• Haykin, Simon. Communication systems. John Wiley & Sons, 2008.

• Bhat K. N. Hari. Analog Communication. DK, 2012.