Phase modulation (PM) is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave. In Telecommunications, modulation is the process of varying a periodic Waveform, i In Telecommunications, modulation is the process of varying a periodic Waveform, i Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave Single-sideband modulation ( SSB) is a refinement of Amplitude modulation that more efficiently uses electrical power and bandwidth. Space modulation is a radio Amplitude Modulation technique used in Instrument Landing Systems that incorporates the use of multiple antennas fed with various radio In Telecommunications, modulation is the process of varying a periodic Waveform, i On-off keying ( OOK) is a type of Modulation that represents Digital Data as the presence or absence of a Carrier wave. Frequency-shift keying (FSK is a Frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a Carrier wave Amplitude-shift keying ( ASK) is a form of Modulation that represents Digital Data as variations in the Amplitude of a Carrier Phase-shift keying (PSK is a Digital Modulation scheme that conveys data by changing or modulating the phase of a reference signal In Digital modulation, Minimum-shift keying (MSK is a type of continuous phase Frequency-shift keying that was developed in the late 1960s Continuous phase modulation ( CPM) is a method for modulation of data commonly used in Wireless modems In contrast to other coherent digital Phase Pulse-position modulation is a form of signal Modulation in which M message bits are encoded by transmitting asingle pulse in one of 2^M possible time-shifts In Telecommunication, trellis modulation (also known as trellis coded modulation, or simply TCM) is a modulation scheme which allows highly efficient Orthogonal frequency-division multiplexing ( OFDM) — essentially identical to Coded OFDM ( COFDM) and Discrete multi-tone modulation ( Spread-spectrum techniques are methods by which Energy generated in a particular bandwidth is deliberately spread in the Frequency domain, resulting Frequency-hopping spread spectrum ( FHSS) is a method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using In Telecommunications direct-sequence spread spectrum ( DSSS) is a Modulation technique In Telecommunications, modulation is the process of varying a periodic Waveform, i 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 In Telecommunications, a carrier wave, or carrier is a Waveform (usually Sinusoidal) that is modulated (modified with an input signal

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. This article describes the unit of angle For other meanings see Degree.

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

. Frequency is a measure of the number of occurrences of a repeating event per unit Time.

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. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change

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. In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave In Signal processing, baseband is an adjective that describes signals and systems whose range of Frequencies is measured from zero to a maximum bandwidth Bandwidth is the difference between the upper and lower Cutoff frequencies of for example a filter, a Communication channel, or a Signal spectrum
• 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. In Telecommunication, Carson 's bandwidth rule defines the approximate bandwidth requirements of Communications system components for a carrier

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.

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