The Center Frequency ω0and Normalized Curves of Z0, , γ, θγ, α, β, and Velocity of Propagation for Electrical Transmission Lines

Transmission lines exhibit a center frequency about which several interesting phenomena can be observed when plotted on double log paper. The magnitude of the characteristic impedance manifests "double mirror" symmetry, with the impedance being greater below this frequency than above, when , and less if the converse is true. The impedance angle has a mirror symmetry about ω0, and is constrained to values between , with negative values when . Further, the angle of the propagation functions, α and β, and the velocity of propagation all possess double mirror symmetry. γ is asymmetrical. The behavior of all of these parameters is such that each can be presented in a normalized plot of the form ( ) and centered upon ω0.