Propagation Constant - Phase Constant

In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave. It represents the change in phase per metre along the path travelled by the wave at any instant and is equal to real part of the angular wavenumber of the wave. It is represented by the symbol β and is measured in units of radians per metre.

From the definition of (angular) wavenumber;

For a transmission line, the Heaviside condition of the telegrapher's equation tells us that the wavenumber must be proportional to frequency for the transmission of the wave to be undistorted in the time domain. This includes, but is not limited to, the ideal case of a lossless line. The reason for this condition can be seen by considering that a useful signal is composed of many different wavelengths in the frequency domain. For there to be no distortion of the waveform, all these waves must travel at the same velocity so that they arrive at the far end of the line at the same time as a group. Since wave phase velocity is given by;

it is proved that β is required to be proportional to ω. In terms of primary coefficients of the line, this yields from the telegrapher's equation for a distortionless line the condition;

However, practical lines can only be expected to approximately meet this condition over a limited frequency band.