Phase modulation (PM) is a form of modulation which 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 (except perhaps for in the inappropriately named FM-synthesis for musical instruments, introduced by Yamaha around 1982.) 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.

Theory

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Suppose that the signal to be sent, the modulating signal with frequency $\backslash omega\_\backslash mathrm\{m\}$ and phase $\backslash phi\_\backslash mathrm\{m\}$, is

$m(t)\; =\; M\backslash sin\backslash left(\backslash omega\_\backslash mathrm\{m\}t\; +\; \backslash phi\_\backslash mathrm\{m\}\backslash right)$,

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

$c(t)\; =\; C\backslash sin\backslash left(\backslash omega\_\backslash mathrm\{c\}t\; +\; \backslash phi\_\backslash mathrm\{c\}\backslash right)$.

Then the modulated signal,

$y(t)\; =\; C\backslash sin\backslash left(\backslash omega\_\backslash mathrm\{c\}t\; +\; m(t)\; +\; \backslash phi\_\backslash mathrm\{c\}\backslash right)$,

which shows how $m(t)$ modulates the phase. Clearly, it could also be viewed as a change to the frequency of the signal and PM can be considered a special case of FM where the carrier frequency modulation is the time derivative of the modulating signal.

The spectral behaviour of PM 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

$2\backslash left(h\; +\; 1\backslash right)f\_\backslash mathrm\{M\}$Hz,

where $f\_\backslash mathrm\{M\}\; =\; \backslash omega\_\backslash mathrm\{m\}/2\backslash pi$ and $h$ is the modulation index defined below. This is also known as Carson's Rule for PM.

Modulation index

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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:

$h\; =\; \backslash Delta\; \backslash theta$,

where $\backslash Delta\; \backslash theta$ is the peak phase deviation. Compare to the modulation index for frequency modulation.

See also

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• 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

Radio modulation modes

Fasemodulation | Phasenmodulation | Modulación de fase | 위상 변조 | Fasemodulatie | 位相変調 | Modulacja fazy | PM | Fasmodulering