Phase modulation

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Phase modulation

Phase modulation (PM) is a form of modulation

Modulation

In telecommunications, modulation is the process of varying a Periodic function waveform, i.e. a tone, in order to use that signal to convey a message, in a similar fashion as a musician may modulate the tone from a musical instrument by varying its volume, timing and Pitch ....
that represents information as variations in the instantaneous phase

Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
of a carrier wave

Carrier wave

In telecommunications, a carrier wave, or carrier is a waveform that is Modulation with an signal for the purpose of conveying information....
.

Unlike its more popular counterpart, frequency modulation

Frequency modulation

In telecommunications, frequency modulation conveys information over a carrier wave by varying its frequency . In analog signal applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal....
(FM), PM is not very widely used. This is because it tends to require more complex receiving hardware and there can be ambiguity problems in determining whether, for example, the signal has changed phase by +180° or -180°.

ose that the signal to be sent (called the modulating or message signal) is .

The carrier onto which the signal is to be modulated is

Then the modulated signal is This shows how modulates the phase.

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Theory

Suppose that the signal to be sent (called the modulating or message signal) is .

The carrier onto which the signal is to be modulated is

Then the modulated signal is This shows how 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

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point....
of the phase modulation.

The spectral

Spectral density

In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per Hz, or energy per Hz....
behaviour of phase modulation is difficult to derive, but the mathematics reveals that there are two regions of particular interest:

For small amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
signals, PM is similar to amplitude modulation
Amplitude modulation

Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave....
(AM) and exhibits its unfortunate doubling of baseband
Baseband

In signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from zero to a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies starting at zero....
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

Carson bandwidth rule

In telecommunication, John R. Carson's bandwidth rule defines the approximate Bandwidth requirements of communications system components for a carrier wave signal that is frequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency....
for PM.

Modulation index

As with other modulation indices

Modulation index

The modulation index of a modulation scheme describes by how much the modulated variable of the carrier signal varies around its unmodulated level....
, 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

Frequency modulation

Phase modulation

Theory

Modulation index

See also