Synthesis of N-Port 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. Several techniques have been proposed for the active RC realization of transfer and driving-point functions.1"18 It has been established t h a t any real rational fraction can be realized as the transfer or drivingpoint function of a transformerless active RC network containing one active element. In particular, Linvill's technique 3 has been the basis for much of the later work. Recently, Si press18 has shown that any two of the four short-circuit admittance parameters of a two-port network can be chosen arbitrarily and realized with a structure requiring only one active element. It follows that all four parameters can be realized with three active elements. The problem of determining the m i n i m u m number of controlled sources required to realize all N~ parameters of an arbitrary A l p o r t immittance matrix is of considerable theoretical importance and has been of interest to network theorists for several years. The solution to 329