Input and ground as complements in active filters

Abstract

Active filters are frequently realized as grounded threeterminal networks. It will be shown that one can create the complementary transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t' = 1 - t</tex> by first synthesizing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> with a threeterminal network and then interchanging the network's input and ground leads, i.e., the former network ground is the new input and the former input is grounded. The output voltage continues to be taken with respect to common ground. If the active element in the network is a differential-input op amp, then this maneuver can be carried out without changing the dc power-supply common-ground connection. It is shown that this is not true in general of finite-gain amplifier networks or of single-input op amp networks. Several uses are suggested and the example of a 360° all-pass section is examined in detail. It is shown that in the particular case of a multiinput biquad all-pass section there is a small increase in the variability of the delay due to resistor changes, and experimental results are given which confirm this. Both the all-pass and band-reject realizations are attractive because the zero frequency is guaranteed to track the pole frequency. A proof of the results for an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -terminal network is outlined.