CONSTANT RESISTANCE NETWORKS 



187 



These equations include the root at X = — 1 corresponding to 

 6 = T. Excluding this they will each have (n — l)/2 roots between 

 6 = and 6 = tt. The roots in p will then be given hy p = 2 cos 6. 



Equation (7) becomes 



(n-l)/2 



/3i = tan~^ X -\- J^ tan 



— 1 ymX 



1-^2' 



(11) 



where the quantities pm are the roots of the above equations, without 

 regard to sign. 



We require also the value of d^ijdx, which may be written 



dSi 

 dx 



1 



1 + X2 



(n-l)/2 



1+ L - 

 1 1 



p^ 



(4 - pj)x' 



(1 + x^Y J 



(12) 



A possible configuration for the first network is shown in Fig. 5 

 and for the second in Fig. 6. 



\AAr 



an-a^ 



Fig. 5 



R=l 



Fig. 6 

 Figs. 5-6 — A pair of constant resistance networks of the "M -derived" configuration. 



To find the elements it would be possible to expand the voltage 

 ratio and solve for the as as was done in the constant K illustration. 

 Another method would be to find the input admittance of the network 

 from the known input conductance, and find the a's from this ex- 

 pression. A simpler method, however, takes advantage of the fact 



