Angle modulation

Angle modulation is a class of carrier modulation that is used in telecommunications transmission systems. The class comprises frequency modulation (FM) and phase modulation (PM). The technique is based on altering the'phase or frequency of a carrier signal to encode the message signal. This is opposed to varying the amplitude of the carrier, such as in amplitude modulation transmission.

Formalism

In general form, an analog modulation process of a sinusoidal carrier wave may be described by the following equation:

$m(t)=A(t)\cdot \cos(\omega t+\phi (t))\,$.

Here, A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its instantaneous angle $\phi (t)$. $\omega$ is the circular frequency. This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In amplitude modulation, the angle term is held constant, while in angle modulation the term A(t) is constant and the second term of the equation has a functional relationship to the modulating message signal.

The functional form of the cosine term, which contains the expression of the instantaneous phase $\omega t+\phi (t)$ as its argument, provides the distinction of the two types of angle modulation, frequency modulation (FM) and phase modulation (PM). In FM the message signal causes a functional variation of the carrier frequency. These variations are controlled by both the frequency and the amplitude of the modulating wave. In phase modulation, the instantaneous phase deviation $\phi (t)$ of the carrier is controlled by the modulating waveform, such that the principle frequency remains constant.

For frequency modulation, the instantaneous frequency of an angle-modulated carrier wave is given by the first derivative with respect to time of the instantaneous phase:

${\frac {d}{dt}}[\omega t+\phi (t)]=\omega +\phi '(t)\,\!$,

in which $\phi '(t)$ may be defined as the instantaneous frequency deviation, measured in rad/s.

See also

• Polar modulation