Microelectronics and Reliability Pergamon Press 1972. Vol. 11, pp. 293-295. Printed in Great Britain ACTIVE DISTRIBUTED RC LOW-PASS FILTERS S. C. DUTTA ROY and R. P. SAH Electrical Engineering Department, Indian Institute of Technology, New Delhi-29, India Abstract--In the active distributed RC low-pass filter circuit studied by Wyndrum, a non-zero output impedance of the amplifier results in a rejection filter characteristic, instead of a low-pass characteristic. A simple method of avoiding this undesirable effect is reported in this note. 1. INTRODUCTION THE distributed RC network is an important by- product of the modern trend in electronics towards microminiaturization and integrated circuits. Using this circuit element together with active devices, one can obtain attractive solutions for micro- electronic filter problems. This note is concerned with such a circuit, consisting of a distributed RC network and a fractional gain amplifier, as c_l_ + R + vi v. o (a) shown in Fig. l(a). Kerwin Ill showed that this circuit can realize a sharp cut-off low-pass charac- teristic. Kerwin's analysis was based on the assumption of K being an ideal amplifier, i.e. with infinite input impedance and zero output impe- dance. Wyndrum 12) showed that the presence of a non-zero output resistance (R:) of a practical amplifier results in a notch type characteristic, instead of a low-pass one. Wyndrum demonstrated the presence of a notch even when R 1 is as small as lO-4R, where R is the total resistance of the distributed RC network. To overcome this diffi- culty, Wyndrum suggested using another distri- buted RC network in cascade. The purpose of this note is to show that the notch type response can be avoided by using a capacitor C 1 across the output of the amplifier, as shown in Fig. l(b). + R + v~ Vo 0 tb~ 2. ANALYSIS Assuming a negligibly small input admittance of the amplifier K, the equivalent circuit of Fig. l(b) can be drawn as shown in Fig. l(c). If R and C are the total resistance and capacitance of the (uniform) distributed RC network, then it can be characterized by the following Z-matrix: R o ~ ~ R reoth 0 cosech 01 * + [~] = -0 [cosech 0 coth 0J / / Vi R1 Vo - c K~,- o a where 0 = ~/(sCR). In Fig. l(c) we can replace (c:, the distributed RC network by its T equivalent circuit and the KVo, R1, C: combination by its FIG. 1. (a) Basic scheme for sharp cut-off low-pass filter. Thevenin equivalent circuit. This results in a (b) Modified scheme for avoiding notch response. (c) Equivalent circuit of Fig. l(b). single-loop network from which we get 293 (1)