#jsDisabledContent { display:none; } My Account |  Register |  Help

# Phase modulation

Article Id: WHEBN0000024772
Reproduction Date:

 Title: Phase modulation Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Phase modulation

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

Phase modulation is widely used for transmitting radio waves and is an integral part of many digital transmission coding schemes that underly a wide range of technologies like WiFi, GSM and satellite television.

PM is used for signal and waveform generation in digital synthesizers, such as the Yamaha DX7 to implement FM synthesis. A related type of sound synthesis called phase distortion is used in the Casio CZ synthesizers.

## Theory

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 m(t) and the carrier onto which the signal is to be modulated is

c(t) = A_c\sin\left(\omega_\mathrm{c}t + \phi_\mathrm{c}\right).

Annotated:

carrier(time) = (carrier amplitude)*sin(carrier frequency*time + phase shift)

This makes the modulated signal

y(t) = A_c\sin\left(\omega_\mathrm{c}t + m(t) + \phi_\mathrm{c}\right).

This shows how m(t) 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 modulation signal could here be

m(t) = \cos\left(\omega_\mathrm{c} t + k\omega_\mathrm{m}(t)\right)\

The mathematics of the spectral behavior reveals that there are two regions of particular interest:

2\left(h + 1\right)f_\mathrm{M},
where f_\mathrm{M} = \omega_\mathrm{m}/2\pi and h is the modulation index defined below. This is also known as Carson's Rule for PM.

## Modulation index

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:

h\, = \Delta \theta\,,

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

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.