PHASE DISTORTION AND PHASE DISTORTION CORRECTION 205 



such as loading, for instance. Fig. 7 is a schematic diagram of the 

 arrangement of the given transducer of transfer impedance Z{iw) 

 with phase angle B{w) and the terminal phase distortion corrective 

 network of transfer impedance N{io3) with phase angle ^(co). In 



Vaiiiu) 



Vo(iu)) 



Fig. 7 



response to the impressed voltage Fo(?co), the voltage Fi(ico) at the 

 output terminals of the transducer, which is assumed proportional to 

 the current, is then 



Z(ico) I 



and the final voltage V^ii^) is 



Thus 



F2(iC0) 



1 

 1 1 



FoM \Z{i^)\\N{io:)\ 



e-^*(")Fi(za;). 



g-i[S(w)+<^(co)] 



(14) 



In practical applications, it is usually found advisable to take both 

 t' and n of equation (12) equal to zero. Then the required phase 

 characteristic, <A(w), of the transfer impedance of the corrective 

 network is 



0(a)) = — (r(co). , 



The function — o-(co) is drawn in Fig. 5 for the submarine cable 

 where < co < w^ and com/2T = 25 cycles per second. This may 

 be represented quite closely analytically by the expression 



(f>(co) = tan ^ 



ax 



where 

 Thus 



and 



X = 



1 -\-bx^' 



,^ 2 



1 - 



(15) 

 (16) 



when CO = 0, X = — co and 0=0, 

 when CO = com, x — and 0=0, 



when < CO < co„j, — co < .t < and < 0. 



