Phase Modulation Questions and Answers

Q: Which single change converts a PM transmitter into an FM transmitter?

Integrating the message is all that is required, and it is exactly what the Armstrong chain does. Differentiating would take an FM modulator to PM, which is the opposite conversion. Raising the sensitivity increases the index without changing the scheme. And a limiter affects amplitude, which is constant in both cases. The economy of the conversion is what makes the two schemes genuinely one family rather than two unrelated techniques.

Q: What does the sensitivity of a phase modulator specify?

Sensitivity is radians per volt, the constant that turns a message amplitude into a phase deviation and hence into the index. Hertz per volt is the corresponding figure for a frequency modulator. Volts per radian inverts the relationship into something a detector might specify. And radians per hertz would imply a frequency dependence that PM does not have. Checking that a quoted sensitivity has the right units is the quickest way to tell which kind of modulator a data sheet is describing.

Q: A phase modulator of \( 0.5 \ \mathrm{rad/V} \) is driven by \( 1.2 \ \mathrm{V} \) peak. Its index is

Multiplying out:\[ \beta_p = 0.5 \times 1.2 = 0.6 \ \mathrm{rad} \]so 0.6 radians, which sits just beyond the narrowband regime and would give a bandwidth somewhat above twice the message frequency. 2.4 divides the amplitude by the sensitivity. 1.7 inverts it the other way. And 0.42 corresponds to no correct combination. Because the answer is a pure number of radians, no message frequency was needed, which is the signature of a PM calculation.

Q: What is the equivalent frequency deviation of a PM signal?

Differentiating the phase gives an equivalent deviation of index times message frequency, which is the quantity to feed into Carson's rule. Dividing inverts the relationship and would give the FM index instead. Multiplying by the carrier frequency produces an enormous and meaningless figure. And the index has no units of frequency by itself. Converting a PM index into an equivalent deviation is the standard route to a bandwidth, and it makes the two angle schemes directly comparable.

Q: A PM signal with index 4 carries a \( 2.5 \ \mathrm{kHz} \) tone. Its equivalent deviation is

Multiplying index by message frequency:\[ \Delta f = 4 \times 2.5 = 10 \ \mathrm{kHz} \]giving 10 kHz, from which Carson's rule yields a bandwidth of 25 kHz. 1.6 kHz divides frequency by index. 0.625 kHz divides the other way and slips a factor. And 4 kHz reports the index as a frequency. The two-step route - equivalent deviation, then bandwidth - keeps PM arithmetic on the same footing as FM's.

Q: Which detector will demodulate PM without any additional processing?

A coherent phase detector reads phase directly against a reference, which is exactly what PM encodes. A frequency discriminator recovers the derivative and needs a following integrator. An envelope detector reads amplitude, which is constant here. And a ratio detector is a frequency discriminator with built-in limiting, so it too gives the derivative. Matching the detector to the modulated quantity, rather than to the family, is what makes these choices obvious. The parameter that varies and the parameter that does not are worth naming before any substitution is attempted.

Q: Why is a limiter still useful in a PM receiver?

Because PM's envelope is constant at the transmitter, any amplitude variation at the receiver is noise or fading and can be discarded, exactly as in FM. That is why the limiter belongs to the whole angle family rather than to FM alone. It performs no conversion. The index is a transmitter parameter that no receiver stage restores. And the phase ambiguity is resolved by a reference or by differential coding, not by limiting. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

Q: Which property makes both angle modulations efficient in the transmitter?

A constant envelope permits the output device to run saturated, so class C or switching amplifiers can be used and efficiency is high. The carrier is present in both schemes. Their bandwidths are wide rather than narrow. And a small index is a special case rather than a general property. This is the one advantage the angle family holds over single sideband, which is the most power-efficient amplitude scheme but insists on linear amplification.

41.

Which single change converts a PM transmitter into an FM transmitter?

A.Integrate the message before the modulator
B.Differentiate the message before the modulator
C.Increase the modulator's sensitivity
D.Add a limiter after the modulator

Answer: A

Integrating the message is all that is required, and it is exactly what the Armstrong chain does. Differentiating would take an FM modulator to PM, which is the opposite conversion. Raising the sensitivity increases the index without changing the scheme. And a limiter affects amplitude, which is constant in both cases. The economy of the conversion is what makes the two schemes genuinely one family rather than two unrelated techniques.

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42.

What does the sensitivity of a phase modulator specify?

A.Radians per hertz of message frequency
B.Radians of phase shift per volt of message
C.Hertz of deviation per volt of message
D.Volts of output per radian of input

Answer: B

Sensitivity is radians per volt, the constant that turns a message amplitude into a phase deviation and hence into the index. Hertz per volt is the corresponding figure for a frequency modulator. Volts per radian inverts the relationship into something a detector might specify. And radians per hertz would imply a frequency dependence that PM does not have. Checking that a quoted sensitivity has the right units is the quickest way to tell which kind of modulator a data sheet is describing.

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43.

A phase modulator of \( 0.5 \ \mathrm{rad/V} \) is driven by \( 1.2 \ \mathrm{V} \) peak. Its index is

A.1.7 radians
B.0.42 radians
C.0.6 radians
D.2.4 radians

Answer: C

Multiplying out:

\[ \beta_p = 0.5 \times 1.2 = 0.6 \ \mathrm{rad} \]

so 0.6 radians, which sits just beyond the narrowband regime and would give a bandwidth somewhat above twice the message frequency. 2.4 divides the amplitude by the sensitivity. 1.7 inverts it the other way. And 0.42 corresponds to no correct combination. Because the answer is a pure number of radians, no message frequency was needed, which is the signature of a PM calculation.

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44.

What is the equivalent frequency deviation of a PM signal?

A.The index divided by the message frequency
B.The index times the carrier frequency
C.The index alone, in hertz
D.The index times the message frequency

Answer: D

Differentiating the phase gives an equivalent deviation of index times message frequency, which is the quantity to feed into Carson's rule. Dividing inverts the relationship and would give the FM index instead. Multiplying by the carrier frequency produces an enormous and meaningless figure. And the index has no units of frequency by itself. Converting a PM index into an equivalent deviation is the standard route to a bandwidth, and it makes the two angle schemes directly comparable.

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45.

A PM signal with index 4 carries a \( 2.5 \ \mathrm{kHz} \) tone. Its equivalent deviation is

A.10 kHz
B.1.6 kHz
C.0.625 kHz
D.4 kHz

Answer: A

Multiplying index by message frequency:

\[ \Delta f = 4 \times 2.5 = 10 \ \mathrm{kHz} \]

giving 10 kHz, from which Carson's rule yields a bandwidth of 25 kHz. 1.6 kHz divides frequency by index. 0.625 kHz divides the other way and slips a factor. And 4 kHz reports the index as a frequency. The two-step route - equivalent deviation, then bandwidth - keeps PM arithmetic on the same footing as FM's.

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46.

Which detector will demodulate PM without any additional processing?

A.A ratio detector
B.A coherent phase detector
C.A frequency discriminator
D.An envelope detector

Answer: B

A coherent phase detector reads phase directly against a reference, which is exactly what PM encodes. A frequency discriminator recovers the derivative and needs a following integrator. An envelope detector reads amplitude, which is constant here. And a ratio detector is a frequency discriminator with built-in limiting, so it too gives the derivative. Matching the detector to the modulated quantity, rather than to the family, is what makes these choices obvious. The parameter that varies and the parameter that does not are worth naming before any substitution is attempted.

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47.

Why is a limiter still useful in a PM receiver?

A.It restores the constant index
B.It removes the phase ambiguity
C.Amplitude variation from noise and fading carries no information
D.It converts phase into amplitude for detection

Answer: C

Because PM's envelope is constant at the transmitter, any amplitude variation at the receiver is noise or fading and can be discarded, exactly as in FM. That is why the limiter belongs to the whole angle family rather than to FM alone. It performs no conversion. The index is a transmitter parameter that no receiver stage restores. And the phase ambiguity is resolved by a reference or by differential coding, not by limiting. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

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48.

Which property makes both angle modulations efficient in the transmitter?

A.The carrier is suppressed
B.The bandwidth is narrow
C.The index is small
D.The envelope does not vary

Answer: D

A constant envelope permits the output device to run saturated, so class C or switching amplifiers can be used and efficiency is high. The carrier is present in both schemes. Their bandwidths are wide rather than narrow. And a small index is a special case rather than a general property. This is the one advantage the angle family holds over single sideband, which is the most power-efficient amplitude scheme but insists on linear amplification.

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49.

What is the effect of doubling a PM signal's index at constant message frequency?

A.The bandwidth grows but less than twofold
B.The bandwidth doubles exactly
C.The bandwidth is unchanged
D.The bandwidth halves

Answer: A

The bandwidth is \( 2f_m(1+\beta_p) \), so doubling the index from say 3 to 6 takes it from \( 8f_m \) to \( 14f_m \): a large increase but less than twofold, because of the unity term. Exact doubling would require the unity term to be negligible, which it is at very large index. No change would contradict the formula, and halving inverts it. Noticing that the unity term matters most at small index is the practical value of keeping the full expression.

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50.

Which scheme would you expect to occupy more bandwidth for a high-pitched tone at fixed message amplitude?

A.Neither, as bandwidth is set by amplitude
B.PM
C.FM
D.Both equally

Answer: B

PM widens in direct proportion to the message frequency, while FM widens only through Carson's additive term because its index falls as the frequency rises. So at the top of the audio band PM is the wider of the two. Saying both equally ignores the different index behaviour. And bandwidth certainly is not set by amplitude alone, since the message frequency appears in both expressions. This asymmetry is what pre-emphasis in FM deliberately imitates.

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