Design of Two-Terminal Balancing Networks 



By K. G. VanWYNEN 



This paper describes a simple graphical method for designing a two-termi- 

 nal network, which will simulate a given line impedance to such a degree that 

 return losses of the order of 25 db or better will be readily obtained. The 

 method is particularly useful in those problems in which a reasonably accurate 

 balancing network is adequate, but a high degree of precision is not required. 



General 



IT 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 dis- 

 cussion 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 at- 

 tempting 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(X), where Z{\) is a fraction whose numerator and denominator are poly- 

 nomials in frequency in accordance with the customary usage in such prob- 

 lems. 



Origin of Problem 



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. Hence there 

 are also a large number of networks which will satisfy a given impedance 

 function. 



In designing networks for repeater circuits, it is generally satisfactory 



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