Design and analysis of bilinear digital ladder filters

Methods for designing bilinear switched-capacitor (SC) ladder filters are well known. However, they cannot be directly extended to digital filters because of the delay-free loops allowed in SC filters. In the present paper, design methods for low-sensitive bilinearly transformed voltage-current ladder filters are developed. The matrix approach for SC filter design is extended to digital filters, and the delay-free loops are eliminated. Design equations for general order low-pass, high-pass, bandpass, bandstop, and allpass filters are obtained in a simple closed form. The design procedure gives a canonical number of delays and a number of distinct multipliers equal to the number of reactive elements in the prototype. A number of test filters are analyzed with respect to magnitude sensitivity, magnitude response with respect to coefficient quantization, occurrence of limit cycles, stability, quantization noise levels, and structural complexity. The results are compared to wave digital filters (WDF), and cascade-form filters. It is found that bilinear digital ladder filters (BDLF) in most cases perform better than WDFs, while they at the same time have a simpler structure.