Phase Modulation Questions and Answers

Answer: A

Armstrong's indirect method integrates the audio, phase modulates a crystal-controlled carrier, and multiplies up to raise the small index, giving FM with crystal stability. The reactance modulator is the direct FM alternative, which pulls a free-running oscillator. A balanced modulator generates suppressed-carrier AM. And collector modulation is high-level amplitude modulation. The Armstrong chain is the clearest practical demonstration that the two angle schemes are interchangeable with the right pre-processing.

Answer: B

Radians of phase define the PM index, deviation over message frequency the FM index, and the amplitude ratio the AM index, so A-R, B-Q, C-P. Laying the three definitions side by side is the fastest way to avoid mixing them, and it shows why only the FM index carries a frequency dependence. The alternatives each swap two of the three, which is precisely the error the mapping exists to prevent.

Answer: C

Reading across, the PM index holds at six while the FM index falls from twelve to three, exactly as the definitions require: FM divides by the message frequency and PM does not. The second option inverts the finding. Both falling contradicts the PM row. And PM has the smaller index at 1 kHz here, so it is not uniformly larger. The table is the compact form of the single most examinable difference between the two schemes. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: D

PM gives a flat output noise spectrum because its detector measures phase directly, whereas an FM discriminator differentiates and so multiplies the noise by frequency. That difference is the entire reason pre-emphasis exists in FM broadcasting. Saying both would erase the distinction that motivates the shaping, and saying neither contradicts the detector mathematics. Naming which scheme has which noise shape is worth a moment's memorisation.

Answer: A

The PM index is a phase and therefore in radians, and it is unusual among modulation parameters for having a natural unit at all. FM deviation is a frequency in hertz. The AM index is a dimensionless amplitude ratio. And bandwidth is a frequency. Checking units is a quick way to spot a wrong formula, since an index and a deviation can never be interchanged without a frequency somewhere in between.

Answer: B

For PM the bandwidth is twice the message frequency times one plus the index, and since the index does not depend on that frequency, the whole expression scales with it. FM's bandwidth grows with message frequency too but only through the additive term, so it is not proportional. AM's bandwidth is twice the highest message frequency, which is a proportionality to the highest frequency rather than a per-tone one. And SSB occupies the message bandwidth itself. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: C

Narrowband PM requires an index well below one radian, in which case only the first sideband pair matters and the bandwidth approaches twice the message frequency, as in AM. The deviation condition is the FM form of the same idea. A high carrier is assumed throughout and is not what defines the regime. And a large index is the wideband case. Both angle schemes have the same two regimes, distinguished by their own index. The shared properties explain why these schemes form a family, and the differences explain why more than one exists.

Answer: D

Phase shift keying is phase modulation with a message restricted to discrete values, and it dominates digital radio because phase can be detected reliably at low signal-to-noise ratios. Pulse code modulation is a sampling and quantising scheme. Delta modulation encodes differences. And vestigial sideband is an amplitude technique. Recognising PSK as the digital descendant of analogue PM ties this topic to modern practice. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Only phase differences are observable, so a receiver cannot tell which absolute phase it has locked to and must either be given a reference or encode information in the change from one symbol to the next. That is the analogue phase ambiguity in digital dress. Carrier instability is a separate practical problem. Bandwidth is set by the symbol rate. And the index is a design parameter rather than something the receiver measures. Working one numerical case through both schemes side by side fixes the distinction better than any rule of thumb.

Answer: B

Applying the rule even at small index:

\[ B = 2 \times 3(1+0.3) = 7.8 \ \mathrm{kHz} \]

so 7.8 kHz, close to the narrowband limit of 6 kHz that the second option gives. That closeness is the point: below an index of about 0.3 the simple limit is adequate, and above it the full expression is needed. 1.8 kHz drops the factor of two and the unity term. And 12 kHz would need an index of one.