The Distortionless Line

and this velocity has been shown (page 226) to be the velocity of light

Figure 6. Attenuation of 19-gauge telephone cable pairs at various frequencies and temperatures. (Reference 4.).

in free space. Also, if LG = CR, then equation 49, page 201, becomes

and also, equation 50 becomes

Derivations of these equations will be found in references 5, 6, 7, and 8. Thus, if LG = CR, the wave velocity, the attenuation, and the characteristic impedance are independent of frequency. If complex voltage waves, such as of speech, are impressed on such a circuit, the current entering the line (determined by Z₀) will be independent of the frequency, the rate at which the various components travel along the line will be independent of frequency, and the attenuation will be independent of frequency. Thus a complex wave will be transmitted without a change in wave form (without distortion), and a transmission circuit in which LG = CR is known as a distortionless line.

Other characteristics of the distortionless line are that the attenuation becomes the least possible value, and the characteristic impedance becomes a value of pure resistance and is increased to a high value.