DISTORTION CORRECTION 



443 



would appear to be that of interposing between the circuit and the 

 receiving resistance a transducer having the requisite corrective propa- 

 gation constant and an iterative impedance, R. By so doing, the 

 transfer exponent at the end of the circuit proper would remain un- 



It 



"to j^ 



Qjngular Frequency, cv, (rad/ians per second) 



Fig. 1 — Non-ideal and ideal transfer exponents of circuits. 



altered, irrespective of the exact nature of the network beyond, since the 

 latter has the impedance R; but the total transfer exponent would 

 become ideal through the addition of the complementary propagation 

 constant of the transducer. Stated analytically, 



let a -\- ib = transfer exponent of the distorting circuit at a ter- 

 minating resistance R, 

 A -{- iB = propagation constant of the correcting transducer of 

 iterative impedance R, 



and a' -\- ib' = resultant ideal transfer exponent at the receiving re- 

 sistance R. 



Then the correcting transducer must be so designed that A and B 

 satisfy over the required frequency range the conditions 



and 



a' = a -\- A = constant, 

 b' = b + B = to:, 

 where r is a positive constant. Or, explicitly, 

 A = a' — a, positive, 



B = b' - b = TCO - b. 



and 



(8) 



