In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal.
, a particular solution to given equation is Consider the following concepts used in physics and signal processing mainly.
Suppose a circuit has an input voltage described by the equation where ω equals 2π×100 Hz, i.e., the input signal is a 100 Hz sine wave with an amplitude of 1 volt.
If the circuit is such that for this frequency it doubles the signal's amplitude and causes a 90 degrees forward phase shift, then its output signal can be described by In complex notation, these signals can be described as, for this frequency, j·1 V and 2 V, respectively.
The complex gain G of this circuit is then computed by dividing output by input: This (unitless) complex number incorporates both the magnitude of the change in amplitude (as the absolute value) and the phase change (as the argument).