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Unlike frequency modulation (FM), phase modulation is not widely used for transmitting radio waves. This is because PM requires more complex receiving hardware, and there can be ambiguity problems in determining whether, for example, the signal has changed phase by +180° or -180°.
PM changes the phase angle of the complex envelope in direct proportion to the message signal.
Suppose that the signal to be sent (called the modulating or message signal) is and the carrier onto which the signal is to be modulated is
- carrier(time) = (carrier amplitude)*sin(carrier frequency*time + phase shift)
This makes the modulated signal
This shows how modulates the phase - the greater m(t) is at a point in time, the greater the phase shift of the modulated signal at that point. It can also be viewed as a change of the frequency of the carrier signal, and phase modulation can thus be considered a special case of FM in which the carrier frequency modulation is given by the time derivative of the phase modulation.
The mathematics of the spectral behavior reveals that there are two regions of particular interest:
- For small amplitude signals, PM is similar to amplitude modulation (AM) and exhibits its unfortunate doubling of baseband bandwidth and poor efficiency.
- For a single large sinusoidal signal, PM is similar to FM, and its bandwidth is approximately
- where and is the modulation index defined below. This is also known as Carson's Rule for PM.
As with other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase of the carrier signal:
where is the peak phase deviation. Compare to the modulation index for frequency modulation.