Phase modulation

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Phase modulation (PM) is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.

Unlike its more popular counterpart, frequency modulation (FM), PM is not very widely used. This is because it tends to require more complex receiving hardware and there can be ambiguity problems with determining whether, for example, the signal has 0° phase or 180° phase.

[edit] Theory

An example of phase modulation. The top diagram shows the modulating signal superimposed on the carrier wave. The bottom diagram shows the resulting phase-modulated signal.

Suppose that the signal to be sent, the modulating signal with frequency ω_m and phase φ_m, is

,

and the carrier onto which the signal is to be modulated is

.

Then the modulated signal,

,

which shows how m(t) modulates the phase. Clearly, it can also be viewed as a change of the frequency of the carrier signal. PM 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 spectral behaviour of phase modulation is difficult to derive, but the mathematics 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 f_M = ω_m / 2π and h is the modulation index defined below. This is also known as Carson's Rule for PM.

[edit] Modulation index

As with other modulation indices, in PM this quantity indicates by how much the modulated variable varies around its unmodulated level. For PM, it relates to the variations in the phase of the carrier signal:

h = Δθ,

where Δθ is the peak phase deviation. Compare to the modulation index for frequency modulation.

[edit] See also

• Modulation for a list of other modulation techniques
• Phase-shift keying (PSK), the digital version of PM
• Electro-optic modulator for Pockel's Effect phase modulation for applying sidebands to a monochromatic wave