This document discusses Carson's bandwidth rule and methods for generating frequency modulation (FM). Carson's rule defines the bandwidth requirement of communication system components based on the peak frequency deviation and highest modulating frequency. There are two main methods for generating FM: direct and indirect. The indirect, or Armstrong, method uses an integrator followed by a phase modulator rather than a voltage controlled oscillator, allowing for more stable oscillations than the direct method. Phase modulation is also discussed as an alternative technique where the carrier phase rather than frequency varies with the information signal.

1. EC 403: Communication Systems
Term paper
FREQUENCY MODULATION
Prepared By:-
GEET PATEL (13BEC072)
DARP RAITHATHA (13BEC084)

2. CARSON’S BANDWIDTH RULE:
 Carson’s Bandwidth rule defines the bandwidth
requirement of communication system components.
 Carson’s rule is very useful to optimize the signal
power in limited bandwidth.
 Carson’s rule can be defined as follows:
Where:
CBR = Bandwidth requirement
Δf = Peak frequency deviation
fm = Highest frequency in the modulating signal

4. EXAMPLE:-
 An FM signal with 5 kHz peak deviation, and a
maximum audio frequency of 3 kHz, would require
an approximate bandwidth 2(5+3) = 16 kHz.
 Applications:- Designing transmitters, antennas,
optical sources, receivers, photo detectors and
other communication system components.

5. METHODS FOR GENERATING FM
 There are mainly two methods for generating FM:
1. Direct
2. Indirect
Direct method uses normal VCOs. Also the input
signal is message signal m(t).
Disadvantage: Poor
frequency stability.

6. ARMSTRONG METHOD FOR FM:-
 It is also known as indirect method for FM
generation.
 Because instead of using VCO(voltage controlled
oscillator) it uses integrator followed by a phase
modulator.

7. WHAT IS PHASE MODULATION ?
 Phase Modulation is the modulation technique in
which carrier phase varies based on analog
baseband information signal to be transmitted using
wireless device.

8. ADVANTAGES AND DISADVANTAGES :
 Advantage –1. Phase modulation & demodulation
is easy compared to Frequency modulation.
 2. Phase modulator is used in determining velocity
of moving target by extracting Doppler information.
Doppler information needs stable carrier which is
possible in phase modulation but not in frequency
modulation.
 Disadvantage –1. Phase ambiguity comes if we
exceed its modulation index pi radian(180 degree).
 2. we need frequency multiplier to increase phase
modulation index.

9. Mathematical Output of an integrator is :
As name suggests Phase modulator or Phase shifter
shifts the carrier wave by π ⁄ 2 radians.
The output of the Armstrong modulator is of the form,
Equation can be approximated as follows

10. Where,
OR
Where,
β = Modulation index
VDSB = rms voltage of double-sideband (DSB) component at
modulator output
Vc = rms voltage of residual carrier (C) component at modulator
output
 Armstrong Modulator can produce a good approximation of
FM when the desired modulation index β is small.
 However, the well-known performance advantage of FM over
AM occurs only when β is large.
 However, there is a way to use an Armstrong modulator and
yet still achieve a large β . This is illustrated below.

11. Advantage:- More stable oscillations than normal VCOs
( It uses Crystal oscillator )

12. REFERENCES:-
 ieeexplore.ieee.org
 www.ieee.org
 www.daenotes.com