A General Method for Time Domain Network Synthesis

This paper presents one approach to the general problem of synthesis in the time domain. Given an arbitrary time function as the speci- fied input to an electrical network and another such time function as the desired output, it shows how to go about designing the net- work. These arbitrary time functions may be prescribed either graphically, analytically, or merely as sequences of values at stated intervals of time. The first step is to write the input and output time functions in time-sequence form. Then synthetic division of the output time se- quence by the input time sequence yields the sequence of areas under the impulse curve. The power series expansion of the Laplace trans- form is obtained from this sequence. A rational-function approxima- tion to this power series may then be calculated and, as a result of the special constraints used, the inverse Laplace transform of this ra- tional function will be a close approximation throughout the time domain to the required impulse response. The paper contributes to network theory a simple and straight for- ward synthesis method for the time domain, which is economical of computational time and effort. Examples are included to illustrate the method.