An upperbound for the stopband attenuation of switched-capacitor direct-form recursive filters subject to random coefficient errors

Since systematic capacitance matching errors can be substantially reduced by corrective layout procedures, random errors in capacitance ratios may be responsible for the greatest limitation on the achievable stopband attenuation of recursive switched-capacitor (SC) filters. Although coefficient random errors affect the frequency response of SC filters in all frequencies, it is in the stopband that their effect is more apparent, since in this region the desired signal magnitude is very small. This paper focus on the study of the effects of random coefficient errors in the stopband of recursive SC filters implemented in direct form. It is shown that, contrary to an intuitive belief, increasing the filter order with the purpose of compensating for the coefficient error effects may even decrease the stopband attenuation. All results shown in this paper have been corroborated by Monte Carlo simulations on a large number of sample filters.