A systematic method to approximate capacitance ratios to improve capacitance matching in SC filters

Abstract

A critical issue in the design of switched-capacitor (SC) filters is the capacitance matching, because the filter coefficients depend on capacitance relative values - capacitance ratios. The most successful design method to achieve an accurate capacitance matching employs a parallel arrangement of identical unit capacitors to implement each filter capacitor. This method, combined with a careful layout design, can achieve a capacitance matching accuracy of 0.1%. However, the procedure can be directly applied only if the filter coefficients can be written as rational numbers, since each capacitor is implemented as an integer number of capacitors in parallel. This paper presents a systematic procedure, with low computational effort, to approximate the filter coefficients by integer ratios without causing significant errors in the filter frequency response, whereas keeping the total number of unit capacitors small, in order to save die area. This procedure is applied in a design example of a SC band-pass filter, which has been fabricated in a 0.35 mm CMOS technology.