Design of Two-Terminal Balancing Networks

T IS the purpose of this paper to describe a graphical method which has been found useful in the design of simple two-terminal networks to simulate the impedance of transmission lines or equipment. The discussion which follows is intended to emphasize the simplicity of the method and the rapidity with which it may be employed to arrive at a solution; it will also indicate the analytical background without attempting to develop or establish the rigor of the procedure involved. A solution can frequently be obtained in a fraction of an hour and it is thought that the graphical analysis will appeal to the pragmatist and the engineer who has a job to do, but very little time in which to accomplish his aim, rather than the person interested in the rigor of the solution. The problem which is considered may be stated as follows: Design a two-terminal network with the minimum number of elements which will give a desired degree of approximation to a given impedance function Z(), where Z(X) is a fraction whose numerator and denominator are polynomials in frequency in accordance with the customary usage in such problems. ORIGIN OF PROBLEM I This problem has arisen most generally in providing balancing networks which will give satisfactory return losses against various types of telephone facilities. It is obvious that for a given impedance, (r + jx), at a given frequency there are an infinite number of networks which will satisfy the given impedance. It has also been pointed out that the network which simulates a given impedance function is not unique.