Frequency Modulation Questions and Answers

Answer: A

The standard is plus or minus 75 kHz, giving a deviation ratio of five against a 15 kHz audio limit. Five kilohertz is narrowband FM for voice. Two hundred kilohertz is the channel spacing rather than the deviation. And fifteen kilohertz is the audio bandwidth. Confusing deviation with channel spacing is easy and consequential, since the two differ by more than a factor of two once Carson's rule is applied.

Answer: B

A phase-locked loop tracks frequency and its output depends on the oscillator's control voltage rather than on input amplitude, so it is largely immune once captured. The three alternatives all convert frequency to amplitude at some stage and are therefore sensitive to it, needing a limiter ahead of them. That practical difference, along with its integrability, is why the loop dominates modern FM receivers.

Answer: C

It is the index evaluated at the highest message frequency, which is the worst case for bandwidth and therefore the figure a system is designed around. The lowest message frequency gives the largest index but the narrowest spectrum in Carson terms, so it is not the design case. Channel spacing is a regulatory quantity. And FM power ratios are not what the term describes. It is a system parameter where the modulation index is a per-tone one.

Answer: D

Only the amplitude is constant. The instantaneous frequency varies with the message, which is the definition. The bandwidth varies with deviation and hence with modulation depth. And the index varies with both deviation and message frequency, so it differs for every tone in a complex message. Identifying the one invariant is the quickest route to answering questions about power, amplifier class and limiter action.

Answer: A

Differentiating before an FM modulator gives phase modulation, since frequency is the derivative of phase and the two operations cancel. The dual arrangement, integrating before a phase modulator, gives FM. Amplitude modulation needs an entirely different modulator. Single sideband is an amplitude scheme. And no pre-processing simply doubles the index. The pair of equivalences is why the two schemes are studied as one family.

Answer: B

A practical phase modulator is linear only over a small phase excursion, so the index produced is small and frequency multiplication is used to raise it to what broadcasting needs. That constraint is the whole reason the multiplier chain exists. Crystal tolerance affects centre frequency rather than deviation. Audio gain sets the drive but not the linear range. And antenna bandwidth is a matching matter far downstream.

Answer: C

Multiplying scales the radio-frequency waveform, so the carrier and the deviation both grow while the rate at which the deviation swings, set by the audio, is unchanged. The index therefore rises by the multiplication factor. The audio is not removed and not reinserted; it is carried through as deviation. And a multiplier is deliberately nonlinear, which is how it generates harmonics. This asymmetry between what scales and what does not is the key to the Armstrong method.

Answer: D

Multiplication scales the index with the frequency:

\[ \beta = 0.5 \times 64 = 32 \]

so 32, at a carrier of 6.4 MHz. The index staying at 0.5 would make the method pointless. 64 is the multiplication factor alone. And 128 doubles it. This is exactly how a stable crystal source is turned into a wideband FM signal, and it shows why the multiplier chain is a defining feature of the indirect method.

Answer: A

The loop holds the centre frequency against drift, comparing the oscillator with a crystal reference through a long time constant that does not fight the wanted modulation. Deviation is set by the modulator's sensitivity and is checked separately. Audio distortion is a linearity matter. And antenna mismatch is corrected by tuning the output network. Direct FM's simplicity is bought at the price of needing this loop, which is the trade against the Armstrong method.

Answer: B

The instantaneous frequency is the carrier plus a deviation proportional to the message amplitude. Multiplication would produce a quite different and unusable signal. A term in the message's derivative describes phase modulation written as a frequency deviation, which is the dual case. And dividing by the index is meaningless. Writing the expression down correctly is the starting point for deriving the index, and hence the spectrum, of any FM signal.