A theoretical study for estimating the order required for a group delay allpass equalizer based on global optimization of variables.

摘要

This dissertation develops an empirical formula from theoretical considerations for the order of a group delay equalizer needed to achieve a constant group delay response with a desired equiripple group delay error. It is desirable to predict the number of equalizer stages as a function of (1) the peak group delay in a given bandwidth of the original circuit, (2) the average group delay in the given bandwidth of the original circuit, and (3) the desired ripple in the group delay after equalization. The existence of an empirical equation for group delay order estimation would eliminate time consuming trial-and-error optimization methods in which the equalizer order is guessed and the optimization proceeds only to find that the resulting group delay ripple is either too large or unnecessarily small. The estimation formula will assume global minimization of a set of simultaneous non-linear equations that must be solved to find the coefficients of the all-pass sections in the group delay equalizer.; The first few chapters of this dissertation will review filter theory that leads up to the physical realization of active, passive, digital, and switched capacitor group delay equalizers. A theoretical expression for the prediction formula is developed in Chapter VII and refined in Chapter VIII by finding the global minimum of the resulting simultaneous non-linear equations for several hundred filter examples. Once the form of the equation is known from theoretical considerations, the coefficients of the prediction formula are finally determined by a least-squares fit between the actual data and the theoretical form of the equation that was derived earlier.