Synthesis of Driving-Point Impedances with Active RC Networks

It is often desirable to avoid the use of magnetic elements in synthesis procedures, since resistors and capacitors are more nearly ideal elements and are usually cheaper, lighter and smaller. This is especially true in control systems in which, typically, exacting performance is required at very low frequencies. The rapid development of the transistor has provided the network synthesist with an efficient low-cost active element and has stimulated considerable interest in active RC network theory during the past decade. 1,2 ' 3 ' 4,5 The present paper considers the active RC synthesis of driving-point impedances. Transfer functions are not treated directly, but are covered at least in principle, since it is always possible, and indeed sometimes convenient, to reduce the synthesis of transfer functions to the synthesis of two-terminal impedances. It is now well known that any driving-point impedance function expressible as a real rational fraction in the complex frequency variable can by synthesized as an active RC network requiring only one ideal active element. Two proofs of this result are already in the literature. 6 '* The present paper provides a third proof, although its main objective is to present a new and more practical realization network. The synthesis * Another proposed proof 8 is in fact concerned only with those impedance functions which are positive on some section of the negative-real axis of the complex frequency plane. 947