DISTORTION CORRECTION 505 



Corollary II: The iterative impedances of a wave-filter recurrent 

 section are such as to give maximum energy transfer from sec- 

 tion to section in all transmitting bands. 



When the section is symmetrical, Xa = Xb, and therefore Ka = Kb = r, 

 a resistance in those frequency ranges. 



Non-Reactive Impedance Theorem: The impedance oj any two-terminal 

 network whose reactance component is zero at all frequencies must have a 

 resistance component which is constant, independent of frequency. To 

 prove the theorem, let the impedance of any two-terminal network 

 whose reactance component is zero at all frequencies be represented as : 



Z = r, (94) 



where r is a real function of frequency. 



The general relations between the components of the steady-state 

 admittance, a{(X)) -f i^{u}), of a network and the corresponding indicial 

 admittance, h{t), are known from electric circuit theory to be: 



and 



also 



a{io) = h{o) + I cos coyh'(y)dy 

 Jo 



^((jo) = — I Sin coyh' (y)dy ; 

 Jo 



h{t) = a{o) +-1 ^^cos/ojJco, / > 0. 



(95) 



(See pages 18 and 180 of the reference in footnote 5.) 



In the passive network under discussion here, the admittance com- 

 ponents at all frequencies from (94) are 



o!(co) = 1/r, 

 and (96) 



^(co) = 0. 



Upon substituting them in (95) it is found that 



h{i) = a{o) = a constant, / > 0, 



h'{t) = (97) 



and 



a{(ji) = 1/r = h{o) = a constant. 



This relation demands that the resistance component r be constant, 

 independent of frequency, as stated in the theorem. 



The converse of the above theorem does not follow, that is, if the resist- 



