Realization method of approximate wave‐digital filter d‐section based on lumped/distributed network

Abstract

AbstractThis paper proposes a reduction method for the D‐section which realizes the complex attenuation poles in the wave digital filter (WDF) design. The reduction is based on the lumped/distributed network. First, an approximate lumped network (called A2‐section) is introduced for the transmission line (UE) with the length T where Richard's variable u = tanh TS is replaced by the rational function qrs/(p2 + t2S2) (p ± 1.6, q ± 2.8). The A2‐section has a set of complex attenuation poles if the values t, p, q are chosen so far as the attenuation pole s = (± y ± j ± ‐ y2)/2(y = q/t, ± = p/t) is complex. In this case, the A2‐section is called the A2‐section. Then it can be shown that the cascade connection 2‐port of two GA2‐sections and series coils is equivalent to the D‐section, and the D‐section is also approximately equivalent to the 2‐port composed of two UE's and LC elements: By applying the well‐known WDT realization method by Fettweis and Swammy, simultaneously, an approximate but very simple D‐section of WDF is obtained. When the length of UE is small, the deviation of WDF response from the design specification is small. As an example, the design of the WDF bandpass filter is shown and the low coefficient sensitivity property compared to the conventional cascade synthesis method is verified.