Constant Resistance Networks with Applications to Filter 



Groups 



By E. L. NORTON 



The problem investigated is the determination of two finite 

 networks such that, when connected in parallel, they will have a 

 constant resistance at all frequencies. The admittance of any 

 network may be written as the ratio of two polynomials in fre- 

 quency. A network to be one of a constant resistance pair must 

 have certain restrictions imposed on its admittance. In case the 

 two networks are both filters of negligible dissipation, the expres- 

 sion for the input conductance of each may be written from a 

 knowledge of the required loss characteristic. 



The poles of the expression for the conductance are then found. 

 They will be identical for the two networks. The networks are 

 then built up by synthesis from those poles of the conductance 

 which have negative real parts, these corresponding to real network 

 elements. 



The methods which have been developed for this last process 

 are described in detail. 



ONE of the most useful principles available to the network design 

 engineer is that of constant resistance networks. The use of 

 these networks is widespread in the telephone system for purposes of 

 loss equalization and distortion correction, where they have the 

 advantage of providing a means for altering the transmission properties 



•Z2 



LATTICE SHUNT SERIES 



Fig. 1 — The three fundamental forms of constant resistance networks. 



of a circuit without affecting its impedance.' The three usual types 

 of constant resistance networks are shown in Fig. 1, where, in all 

 cases, Z1Z2 = R"^, a relationship which is always possible to fulfill if 



1 " Distortion Correction in Electrical Circuits with Constant Resistance Recurrent 

 Networks," Otto J. Zobel, Bell Sys. Tech. Jour., July 1928. 



178 



