β is an important quantity used in understanding transmission lines and waveguides. It is not intuitive so this treatment presents a brief explanation of the quantity in the analysis of transmission lines, waveguide and other wave systems.

Sometimes β is referred to as the phase constant of the line or guide. If the cartesian coordinate system is used and a coordinate, say “z” is used as the direction of wave propagation then βz measures the instantaneous phase at point z on the line with respect to z =0.

In addition, voltage or current on the line is the same at any two points separated in z such that βz differs by multiples of 2π. Since the shortest distance between points where voltage or current is at the same phase is a wavelength, then:

βλ = 2π

( replacing z by λ),

β = 2π/λ

_____________________________________________________________