Estimation of group delay ripple of physical networks using a fast, band-limited Hilbert transform algorithm and scalar transfer function measurements

Abstract

A set of PC based programs has been developed for use with a standard scalar network analyser (SNA) to measure and display relative group delay. The core of the data processing algorithm is a form of the Hilbert transform which uses the Fast Fourier Transform (FFT) for computational speed and ease of implementation. This is used to derive the equivalent minimum phase response for the circuit, and calculate the group delay associated with this new phase response. Results derived in this way are given for two examples and are found to compare favourably with measurements made with a vector network analyser (VNA). In each case it is found that the difference between the minimum phase response and the actual response can be approximated by a constant delay. The technique described here enables group delay variation to be accurately estimated in an rapid and economical manner from scalar data.