Phase and Amplitude Distortion in Linear Networks

Abstract

All practical communication networks exhibit distortions from the ideal linear phase and flat amplitude (all-pass) characteristics. When linear phase together with finite amplitude bandwidth prevail, the build-up time of the step transient response equals the reciprocal of twice the amplitude bandwidth. However, when phase distortion together with all-pass amplitude characteristics prevail, the finite (rather than zero) step-response build-up time is ascribed to the concept of phase bandwidth. Certain relations between phase and amplitude bandwidths are shown necessary to avoid step and impulse transient response overshoot arising from excessive phase distortion. In particular, attention is confined to networks comprising identical sections in cascade. For most cases of practical interest, it is shown that, as the number of sections increases, cascaded networks have a transmission characteristic approaching that of three networks in cascade. The first network is distortionless and accounts for the pure delay in the system. The other two networks, which account for the distortion in the system, are of two basic species: (1) all-pass networks with a monotonic phase distortion proportional to ω <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , and (2) zero-phase-shift networks with a monotonic attenuation proportional to ω <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> . Graphs are given of the impulse and step transient responses for such networks with monotonic phase and attenuation distortion. From these are obtained important design data such as the phase bandwidth, the overshoot in the transient responses, the narrowing in effective bandwidth obtained on cascading, etc. An important design parameter determining the transient behavior is the phase distortion at the frequency of amplitude cutoff.