Synthesis of active RC networks

A basic theorem is derived for RC networks containing active elements. It is shown that no more than one active element, embedded in a passive RC network, is needed to realize any driving-point function. Sufficiency of only one active element is shown by developing a synthesis method. A synthesis technique for n-port passive RC networks is developed in order to establish the sufficiency proof of the basic theorem. A more practical method of realizing driving-point functions, using active RC networks, termed the “cascade” method, is also presented. This method is applied to the design of a tenth-order Tchebycheff parameter filter.