Communication Theory- I Course Code:17 EC 2206 Dr. G V Subbarao Professor Department of Electronics and Communication Engineering K L University

Angle Modulation

The phase angle of the carrier wave is varied in accordance with the amplitude of modulating signal is referred to as ‘Angle Modulation’. PM: The phase of carrier wave is varied in accordance with the amplitude of message signal. FM: The frequency of the carrier wave is varied in accordance with the amplitude of the modulating signal

Phase angle and Instantaneous Frequency The instantaneous frequency

Phase Modulation

The phase of carrier wave is varied in accordance with the amplitude of message signal. Assume Where Kp is phase modulation sensitivity constant. Then the resulting Phase Modulated wave is In this case the instantaneous angular frequency is given by Hence in PM the instantaneous angular frequency varies linearly with the derivative of the modulating signal.

Frequency Modulation

The frequency of carrier wave is varied in accordance with the amplitude of message signal. The instantaneous angular frequency is given by or where is frequency modulation sensitivity constant Then the resulting Frequency Modulated wave is

AM, PM and FM Waveforms

PM and FM Waveforms

Relationship between PM and FM Equations and show that in both PM and FM, the angle of a carrier is varied in proportion to some measure of m(t). In PM : Directly proportional to m(t) In FM : Directly proportional to integral of m(t)

Example1

Example 2

Single Tone Angle Modulation (PM) Let a message signal

Single Tone Angle Modulation (FM) For a single tone FM Modulation is given by

Brief Summary

Phase and Frequency Deviation

Phase and Frequency Deviation…

Narrowband F.M

Narrowband F.M.

Frequency spectrum of Narrow Band Frequency Modulation The time domain expression for NBFM is The frequency spectrum of Narrow Band Frequency Modulation is represented by

Spectrum of AM and NBFM

Phasor Diagrams

Bandwidth of NBFM The time domain expression for NBFM is It resembles the AM signal and hence bandwidth is twice of the message signal frequency

Narrow Band Angle Modulation for Base Band Signal Let a base-band signal represented by m(t) is band limited to ‘W’ Hz

NBFM for Base Band Signal and where Fo r

NBPM for Base Band Signal For and,

Comparison Similarities: Both have the same modulated bandwidth 2W, where W is the highest modulating signal frequency. The sideband spectrum for FM has a phase shift of 90 0 with respect to the carrier, whereas that of AM is in-phase with the carrier. Differences: In an AM signal, the oscillation frequency is constant and the amplitude varies with time, whereas in an FM signal, the amplitude stays constant and frequency varies with time.

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