A closed-form analytical expression for evaluation of the output noise voltage of active-R filters has been developed. 7'he expression is applicable to any low-pass, band-pass or high-pass two amplifier second order active-R realization. The expression for the noise voltage has been derived in terms of the filter specifications and parameters of noise sources contained within the filter. Thus, it is very convenient for practical calculations. The expression is also useful for obtaining a design that minimizes the magnitude of the output noise. Experimental measurements indicate close agreement with the theroetical analysis.
I. Introduction
Recently considerable attention has been paid to the design of filter networks by using resistors and operational amplifiers (OA) only (l-4). These designs are known as active-R designs. Since the OA's and the resistors are easily integrable, such designs are attractive for IC implementation, particularly because of the absence of external capacitors in the resulting networks. Further, these designs considerably widen the frequency range of applications in comparison to the one obtainable from active-RC designs of filter networks.
However, the components of active-R filters, namely, the resistors and the OA's are noisy and hence would contribute noise to the filtered signal. The presence of this noise at the output will restrict the dynamic range of these filters. In addition, in view of this noise, the slew rate of the OA's will limit the maximum operating frequency obtainable from active-R filters. Thus, it is useful to be able to estimate the amount of noise generated by these filters.
An extensive literature search by the authors has failed to reveal any noise analysis of active-R filters. The techniques, that have been used for some specific RC-active filter circuits (57), can, of course, be used for active-R filters. However, the resulting analysis will be complex as, even for a simple realization, 10 or 15 noise sources are Isquired for a complete noise characterization. Consequently, the details are likely to obscure any clear insight into the noise behaviour of active-R filters.
The purpose of the present article is to determine a fairly general expression