Question 39 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

## Q39. The signal as shown is applied both to a phase modulator (with as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency.

## The ratio for the same maximum phase deviation is,

## (A)

## (B)

## (C)

## (D)

## Solution

To answer this question, let us understand basics of **Frequency modulation** and **Phase modulation**. Am referring to the discussion in Section 10 of **Electronic Communication, 4th Edition, Dennis Roddy, John Coolen **(buy from Amazon.com, buy from Flipkart.com).

**Frequency Modulation**

In frequency modulation, the modulation signal will cause a change in the instantaneous carrier frequency and is related as

where

is the frequency deviation constant expressed in hertz/volt (Hz/V) and is the carrier frequency in Hz.

The angular velocity radians per second.

Since the rate of change of phase is the angular velocity,

and so, the instantaneous phase is

.

The frequency modulated carrier signal is

**Phase modulation**

In phase modulation, the modulation signal will cause a change in phase and the instantaneous phase is

where

is the phase deviation constant expressed in radians/volt and is the carrier frequency in radians per second.

The phase modulated carrier signal is

.

**Now, applying the above equations to solve the problem :**

In frequency modulation case, the maximum phase deviation happens when the term hits the maximum.

In phase modulation case, the maximum phase deviation happens when the term hits the maximum.

.

The ratio is,

and so,

**Based on the above, the right choice is (B) **

## References

[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf

[2] **Electronic Communication, 4th Edition, Dennis Roddy, John Coolen **(buy from Amazon.com, buy from Flipkart.com).

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