Low-Noise, Low-Sensitivity Active-RC Allpole Filters Using MATLAB Optimization

The application of Matlab, combining its symbolic and numeric calculation capabilities, to calculate noise and sensitivity properties of allpole active-RC filters is shown. Transfer function coefficients calculations, as well as plotting of amplitude-frequency and phasefrequency characteristics (Bode plots) have been performed using Matlab. Thus, using Matlab a comparison of different design strategies of active-RC filters is done. It is shown that active-RC filters can be designed to have low sensitivity to passive components and at the same time possess low output thermal noise. The classical methods were used to determine output noise of the filters. It was found that low-sensitivity filters with minimum noise have reduced resistance levels, low Q-factors, low-noise operational amplifiers (opamps) and use impedance tapering design. The design procedure of low-noise and lowsensitivity, positiveand negative-feedback, secondand third-order low-pass (LP), highpass (HP) and band-pass (BP) allpole filters, using impedance tapering, is presented. The optimum designs, regarding both performances of most useful filter sections are summarized (as a cookbook programmed in Matlab) and demonstrated on examples. The relationship between the low sensitivity and low output noise, that are the most important performance of active-RC filters, is investigated, and optimum designs that reduce both performances are presented. A considerable improvement in sensitivity of single-amplifier active-RC allpole filters to passive circuit components is achieved using the design technique called 'impedance tapering' (Moschytz, 1999), and as shown in (Jurisic et al., 2010a) at the same time they will have low output thermal noise. The improvement in noise and sensitivity comes free of charge, in that it requires simply the selection of appropriate component values. Preliminary results of the investigation of the relation between low sensitivity and low thermal noise performances using impedance tapering on the numeric basis using Matlab have been presented in (Jurisic & Moschytz, 2000; Jurisic, 2002). For LP filters of secondand third-order the complete analytical proofs for noise properties of the desensitized filters are given in (Jurisic et al., 2010a). By means of classical methods as in (Jurisic et al., 2010a) closed-form expressions are derived in (Jurisic et al., 2010c), providing insight into noise characteristics of the LP, HP and BP active-RC filters using different designs. LP, HP and BP, low-sensitivity and low-noise filter sections using positive and negative feedback, that have been considered in (Jurisic et al., 2010c) are presented here. These filters are