Synthesis of Active Time-Variable Networks

Existing procedures for the synthesis of an arbitrary rational function are extended to the case of time-variable networks via differential operator techniques. The procedures yield a realization of an arbitrary regular differential operator as a network of operational amplifiers and passive (time-variable) Foster forms, or alternatively as a network of operational amplifiers, constant components, and time-variable controlled sources. The procedures require only that algebraic operations be carried out on the coefficients of the given differential operator: the differential equation is neither solved nor are any properties of its fundamental solutions assumed.