800 BELL SYSTEM TECHNICAL JOURNAL 



more simply if we reject the image impedance statement of the problem 

 in favor of its alternative. For the time being, therefore, we will as- 

 sume that we are attempting to design a reactive network having a 

 preassigned input impedance when terminated by a given load imped- 

 ance. 



In accordance with a principle originally stated by O. J. Zobel,^ 

 this problem of impedance correction can be simplified if we consider 

 separately the resistance and reactance of the corrected circuit. To 

 be more explicit, since a reactance in series with the circuit will change 

 its reactance without changing its resistance, it is simplest to consider 

 first the construction of a network which will produce the required 

 resistance characteristic. Of course the reactance characteristic 

 furnished by such a structure will not in general be ideal, but we may be 

 able to correct it to the proper value by the later addition of a series 

 reactive network. Quite obviously, it is equally easy to base the analy- 

 sis upon admittances and construct first a network which will give the 

 required conductance characteristic and make up any faults in its 

 susceptance characteristic by a final shunting branch. 



This division of the network into two separate structures is, of 

 course, not a necessary one and in view of the extremely limited range 

 of reactance or susceptance characteristics which can be compensated 

 for by a final, physically realizable, two-terminal reactive network may 

 seem scarcely desirable. An alternative procedure in which this divi- 

 sion is not attempted is mentioned in the concluding section. The 

 reason for assuming separate correction of the real and imaginary com- 

 ponents of impedance and admittance in the present discussion is 

 simply one of convenience. The difficulties which might be antici- 

 pated in the design of the final reactive compensator do not appear in 

 filter impedance correcting problems, at least. On the other hand, the 

 division has the advantage that it makes each step simple and allows 

 us to meet fairly severe impedance requirements with a small number 

 of variables. As we shall see later the method has the further advan- 

 tage in its application to filters that it lends itself readily to the modifi- 

 cations necessary when a number of filters must operate together. 



The Resistance or Co?iductance Controlling Network 



Since the characteristics of two-terminal reactance networks are well 



understood, the construction of the final reactive branch demands no 



2 See, for example, U. S. Patents No. 1,557,229 and 1,557,230 where he applies 

 it to "x-terminated" filters. The method of this paper is in some respects merely 

 a generalization of that analysis. The relation of "m-derived" sections and '^x- 

 terminations" to the filter terminations developed in this paper is indicated in the 

 following section. In this connection, the previous work of R. S. Hoyt on loaded 

 lines should also be mentioned. See this Journal, Vol. 3, p. 414, 1924. 



