MEASUREMENT OF PHASE DISTORTION 529 



of frequency gives for the envelope delay of the system 



1 



T.= 



4(/2 - h) 



Ta here is not the envelope delay of frequency /i or of frequency f-z, but 

 it is the envelope delay of some intermediate frequency. For our 

 purpose, it is sufficiently accurate to assume that T^ is the envelope 

 delay of the system at the frequency (/o +/i)/2. The envelope delay 

 of the system at any frequency can thus be determined from the 

 impedance curves by making measurements over a sufficient frequency 

 range to find the length in cycles per second of one half an impedance 

 cycle with its mid-point at the frequency of which the delay is to be 

 determined. 



If a system has constant envelope delay and attenuation over the 

 frequency range involved, then the impedance curves are periodic. 

 The resistance and reactance curves are in quadrature with each other. 

 The resistance and reactance curves for an open termination are 180° 

 out of phase, respectively, with those for a short-circuit termination. 

 In the usual case, however, there is attenuation in the system and this 

 varies with frequency. The change caused by this attenuation in the 

 impedance curves is in the amplitude of the impedance variations. 

 The amplitude varies inversely with the attenuation of twice the 

 system, expressed in terms of current ratio. Due to the variation of the 

 envelope delay of the system with frequency, the length of an impedance 

 cycle in cycles per second of frequency varies with frequency. The 

 efifect of this variable delay on the impedance curves is that the im- 

 pedance cycles are concentrated more and more along the axis of the 

 curve as the delay increases, the length of the impedance cycle varying 

 inversely with the envelope delay of the network. 



By way of illustration, Fig. 3 shows the computed impedance curves 

 for short and open terminations on a 100-mile unit of phase corrector 

 for 19-gauge, H-174 side circuit. Fig. 3 also gives the corresponding 

 envelope delay-frequency curve. The characteristic impedance of this 

 particular network is 600 ohms resistance. It will be noted that for 

 this case the resistance curves for open and short terminations at the 

 far end intersect on the line -|-300 ohms, while the corresponding reac- 

 tance curves intersect on the zero line. The curve passing through the 

 points of intersection of the curves for open and short terminations 

 should be used as the axis for determining the length of impedance 

 cycles. The delay obtained in this way is, of course, the delay of the 

 system between its characteristic impedances. 



