506 BELL SYSTEM TECHNICAL JOURNAL 



ance component of a two-terminal network impedance is constant, 

 independent of frequency, it is not necessary that the reactance com- 

 ponent be zero throughout the frequency range. This may be seen 

 from the relations above. A simple example is series resistance and 

 inductance. 



Theorem II: If the iterative impedance of a network is real at all 

 frequencies, it must be constant according to the latter impedance 

 theorem above. 



For the second part of Theorem II we have as assumptions regarding 

 the propagation constant, T = A -\- iB, and iterative impedance, K, 

 effectively 



B = TOO 



and (98) 



K = a constant = R, 



where t is some positive constant. The transfer admittance com- 

 ponents with respect to a resistance R which terminates the transducer 

 are then 



-A 



a{w) = —5- cos rco 

 K 



)3(w) = B"Sin TOO. 



(99) 



By means of these and (95) we shall prove that A is uniform at all 

 frequencies. 



To satisfy (95) with (99) at all frequencies the transducer must be 

 such as to give the relations 



h(o) = 0, 



h'(t) = 0, I 9^ T, 

 and (100) 



I 



'•+ g-A 



h'(y)dy = -^ 



Since the left-hand member of the last relation is independent of 

 frequency, it follows necessarily that the attenuation constant. A, 

 must be uniform. That uniform attenuation together with (98) is 

 also sufficient to satisfy the other relations of (100) can be seen if the 

 parameter characteristics at all frequencies are 



A = a constant, 



B = TOO (101) 



and 



X = a constant = R. 



