Low‐passband‐sensitivity switched capacitor filters using a parallel connection of two structurally lossless networks

Abstract

The low-sensitivity property of IIR digital filters designed using a parallel connection of two allpass sections has already been demonstrated in the past few years. This property is closely related to the use of a particular type of allpass structures, called structurally lossless networks, which remain allpass regardless of the coefficient quantization. In this paper we provide a general theory for the synthesis of low-passband-sensitivity switched capacitor (SC) filters using a similar technique. The design of stray-insensitive structurally allpass SC sections is emphasized, ensuring the passivity property for the overall filter. Design examples are presented with computer simulations and experimental results to compare the performance of the different proposed structures. Analytical sensitivity calculations are also derived yielding useful formulae for the prediction of the filter sensitivities with respect to capacitor ratios, particularly in the stopband.

Digitally programmable switched-capacitor equalizers

“…2 guarantees low passive pole/zero sensitivities. This important feature has been confirmed theoretically and by simulations, and has been reported elsewhere [5]. The existing degrees of freedom can then be used to minimize the effects of finite bandwidth and gain of the op amps, and to reduce the capacitor ratio spread.…”

“…As a result, the pole sensitivities with respect t o the transfer function coefficients achieve very low values [5], specially for small pole angle, where the direct form is known to have high sensitivities. This feature is particularly important in SC filters since, in order to alleviate the prefiltering and postfiltering specifications, the sampling frequency is usually set much higher than the cutoff frequency.…”

“…The allpass circuit is based on the direct form structure and has been designed using the pole transformation technique [5], which consists of implementing a digital transfer function using accumulator type elements as basic building blocks rather than unit delays. As a result, the pole sensitivities with respect t o the transfer function coefficients achieve very low values [5], specially for small pole angle, where the direct form is known to have high sensitivities.…”