If the modulating signal is a constant DC voltage, the output of a Phase Modulator will be:
A constant frequency signal with a fixed phase shift.
Phase Modulation (PM) encodes information by varying the instantaneous phase of the carrier in proportion to the modulating signal. The modulated wave is:
s(t) = Ac cos(2πfct + kpm(t))
where Ac is the carrier amplitude, fc the carrier frequency, m(t) the message, and kp the phase sensitivity (radians per volt). A key relationship in angle modulation is that instantaneous frequency is the time-derivative of the total phase:
fi(t) = fc + (kp/2π) × dm(t)/dt
Now apply a constant DC input, m(t) = Vdc:
- The total phase becomes 2πfct + kpVdc. The extra term kpVdc is a fixed constant, i.e. a static phase offset.
- Since dm(t)/dt = 0 for a constant, the frequency deviation term is zero, so the instantaneous frequency stays at exactly fc.
Therefore the output is a constant-frequency carrier carrying a fixed phase shift of kpVdc radians — which is the correct choice.
A signal with increasing frequency would require the phase to grow faster than linearly in time; that happens only if m(t) itself increases, not for a constant. A zero output is impossible because the carrier amplitude Ac is unchanged. And PM does not alter amplitude — the envelope stays constant at Ac — so an amplitude-varying output does not describe a phase modulator at all.
Important Questions from Phase Modulation
In phase modulation, frequency deviation is-
Which of the following phase modulation applications is INCORRECT?
A message signal m(t) = A msin (2πf mt) is used to modulate the phase of a carrier A ccos (2πf ct) to get the modulated signal y(t) = A ccos (2πf ct + m(t)). The bandwidth of y(t)
