Phase modulation

The phase modulation or MP or PM is a mode of modulation consisting in transmitting a Signal by the phase modulation of a carrying signal (carrying). This modulation is nonlinear.

Theory

That is to say carrying:

$x\_p\; (T)\; =\; has\; \backslash \; cos\; (\backslash \; omega\_p\; T\; +\; \backslash \; phi\; (T))\backslash ,$

The instantaneous phase of carrying is given by:

$\backslash \; Omega\; (T)\; =\; \backslash \; omega\_p\; T\; +\; \backslash \; phi\; (T)\; \backslash ,$

That is to say a modulating signal:

$m\; (T)\; \backslash ,$

To modulate in phase the signal amounts carrying out the following operation:

$\backslash \; phi\; (T)\; =\; K\_p.m\; (T)\; \backslash ,$

The modulated signal is written:

$e\; (T)\; =\; has\; \backslash \; cos\; (\backslash \; omega\_p\; T\; +\; K\_p\; m\; (T))\backslash ,$

Case of a sinusoidal signal

That is to say a sinusoidal signal modulating:

$m\; (T)\; =\; A\_m\; \backslash \; cos\; (\backslash \; omega\_m\; T)\; \backslash ,$

The modulated signal becomes then:

$e\; (T)\; =\; has\; \backslash \; cos\; (\backslash \; omega\_p\; T\; +\; K\_p\; A\_m\; \backslash \; cos\; (\backslash \; omega\_m\; T))\backslash ,$

It is noticed that $\backslash \; phi\; (T)$ varies between $\backslash \; phi\; (T)\; -\; \backslash \; Delta\; \backslash \; phi$ and $\backslash \; phi\; (T)\; +\; \backslash \; Delta\; \backslash \; phi$, where $\backslash \; Delta\; \backslash \; phi$ represents the maximum deviation of phase.

One will note the existing strong bond between the phase modulation and the frequency modulation.

See too

• Phase-shift keying

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