PHASE DISTORTION IN TELEPHONE APPARATUS 



519 



minals 1 and 2 and Wh at 3 and 4. For these terminating conditions 

 let the input current be /„' and the output current h' . The image 

 transfer constant, 6, of the network then is 



la' 



Let 



d = log. 



d = A' +jB' 



(1) 

 (2) 



lo- 



ll— 



Fig. 28 — Network connected between a generator of impedance Z^ and a load of 



impedance Zj. 



A' is the real part of the image transfer constant and B' is the ima- 

 ginary part. We have 



h' 



Wa' 



W,' 



= e' = e^'\B\ 



(3) 



B' is the image transfer phase shift of the network.^^ Its value as a 

 function of frequency gives the image transfer phase characteristic of 

 the network. 



There is another type of phase shift of more frequent use. Let h 

 be the current through the load before insertion of the network, i.e., 

 when the generator and load are connected directly together or con- 

 nected together by means of an ideal transformer of the best turns 

 ratio. Let lb" be the current through the load with the network in 

 place as shown in Fig. 28. Then 



h 



JT,= t 



\B' 



(4) 



B" is the insertion phase shift?"^ It will be noted that when the 

 terminating impedances are the image impedances that B' and B" 

 are the same.-^ 



In most practical cases the phase shifts as defined above are deter- 

 mined for pure resistance terminations hence the phase shifts may 

 equally well be said to relate the applied voltage to the received cur- 

 rent. The angle of lag of the received current is regarded as positive. 



-^ 20 logio eA' gives the image transfer loss in decibels. 



^* 20 logio eA" gives the insertion loss in decibels. 



^' The term insertion loss and insertion phase shift is here extended to include cases 

 where apparatus is designed to work between resistance impedances of different 

 values. 



34 



