Operational amplifier gain - bandwidth product effects on the performance of switched-capacitor networks

Abstract

A method of analyzing switched-capacitor (SC) filters which incorporates a single-pole model of the operational amplifiers (op amp's) is presented. Closed-form algebraic expressions for filter transfer functions in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -domain are obtained which are computationally more efficient than time-domain methods. The necessity for including a frequency dependent model of the op amp rather than the common finite gain model in doing a performance analysis, especially when considering stability, is emphasized. To illustrate the method of analysis, an analog integrator, an analog second-order bandpass filter, and their SC counterparts are considered. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -domain performance of the analog \footnote[1]{circuits} is compared with the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -domain performance of the sampled-data configurations to show how the finite gain-bandwidth product (GB) of the op amp's affects the respective topologies. These comparisons show that the effects of switching rates and switching arrangements on filter performance are strongly dependent upon the GB product of the op amps. These comparisons also emphasize the fact that it is not sufficient to investigate the effect of the operational amplifiers on the performance of an analog filter to predict the performance of a SC filter derived from the analog configuration.