A Contribution to the Theory of Network Synthesis

The design of corrective networks for transient conditions has been based to a great extent upon trial-and-error methods. Such a procedure has practical advantages at times, particularly when intuition may be relied upon for almost the entire solution of the problem. However, a procedure which eliminates trial-and-error methods not only provides a better understanding of the problem but also correlates and clarifies the basic theory involved in the solution of the problem. The results of the analysis presented in this paper extend O. Brune's systematic procedure of synthesizing electrical networks based upon steady-state requirements, to the synthesis of electrical networks satisfying transient requirements. The extension of the method is accomplished with the use of the generalized infinite-integral formula expressed in (16). This equation gives a unique solution for the impedance function in terms of the transient voltage and the transient current. The impedance function obtained by evaluating the infinite ineg rals of (16) may then be synthesized by using Brune's method.