Frequency Modulation Questions and Answers

Answer: A

Regulators specify maximum deviation, since it is deviation that sets how far the spectrum extends and hence how much energy falls into the neighbours. A minimum power would help nobody's interference case. A minimum audio bandwidth is a quality matter. And the index at low audio frequencies is large but corresponds to a narrow spectrum in Carson terms, so constraining it would target the wrong quantity. Deviation is the single lever that controls occupied bandwidth.

Answer: B

Constant amplitude fixes the deviation, so the index, being deviation over message frequency, falls as the tone rises, while Carson's rule adds the growing message frequency and the bandwidth increases. The two quantities move in opposite directions, which is the single most counter-intuitive result in the topic and the reason worst-case bandwidth is computed at the highest audio frequency rather than at the largest index.

Answer: C

The Bessel function \( J_0 \) vanishes at particular indices, so a carrier null with a known modulating frequency fixes the index and hence the deviation exactly - the classical calibration method, needing no calibrated amplitude measurement at all. The outermost visible sideband depends on the analyser's noise floor. Equal first and second sidebands occur at one particular index and is a less sharp criterion. And constant total power is true of all FM and so distinguishes nothing.

Answer: D

Because the amplitude carries nothing, so distorting or clipping it costs no information and the amplifier can run at maximum efficiency. That single property separates the angle family from every amplitude scheme, where the envelope is the message. Bandwidth is wide rather than narrow. The carrier is present throughout. And the index is frequently far greater than one, as broadcasting's five demonstrates.

Answer: A

They pull in opposite directions and that is why their order matters: pre-emphasis boosts treble and therefore increases deviation on bright material, and the limiter placed after it holds the peak deviation inside the channel. Putting the limiter first would let pre-emphasis push the signal back over the limit. Saying both reduce deviation misses the purpose of pre-emphasis, and the reversed description inverts both stages. The audio chain's order is a genuine design constraint rather than an arbitrary convention.

Answer: A

The bandwidth is \(2(f_{m} + f_{d})\), Carson's rule.

An FM signal has, in theory, infinitely many sidebands, but almost all of its power lies within a band of \(2(\Delta f + f_{m})\), where \(\Delta f = f_{d}\) is the frequency deviation and \(f_{m}\) the highest modulating frequency. This approximation is Carson's rule.

For example, broadcast FM with \(f_{d} = 75\) kHz and \(f_{m} = 15\) kHz needs about \(2(75 + 15) = 180\) kHz. \(f_{m} + f_{d}\) is only half of that band, the average \(\frac{f_{m} + f_{d}}{2}\) has no physical meaning here, and \(2f_{m}\) is the bandwidth of AM or of very narrowband FM.

Answer: C

The correct statement is that narrowband FM offers no improvement in SNR over AM.

The noise advantage of FM comes from trading bandwidth for signal to noise ratio: the output SNR improvement grows with the square of the modulation index \(\beta\). In narrowband FM, \(\beta\) is small (well below 1) and the signal occupies about the same bandwidth as AM, \(2f_{m}\), so it offers essentially no SNR advantage over AM.

The statements that NBFM is better than AM, or augments SNR, describe wideband FM. Saying it is worse than AM is also wrong; its performance is comparable.