Discussion
Assertion (A) : From SNR point of view, FM is superior to PM by a factor of 3.
Reason (R) : Narrowband FM offers no improvement in SNR over AM.
Answer: B
The answer is both (A) and (R) are true but (R) is not the correct explanation of (A).
For sinusoidal modulation, the output SNR of FM is \(3\beta^{2}\) times a reference value, while that of PM with the same peak phase deviation is \(\beta^{2}\) times it. So with equal deviation, FM is better than PM by a factor of 3 (about 4.8 dB). Separately, narrowband FM (\(\beta\) well below 1) occupies the same bandwidth as AM and gives no SNR improvement over it; the FM advantage appears only in wideband operation.
Both statements are standard results, but the FM-over-PM factor of 3 comes from the different way noise is weighted after the discriminator, not from the comparison of narrowband FM with AM.
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