528 



BELL SYSTEM TECHNICAL JOURNAL 



point where the test is conducted. The method is unsatisfactory for 

 measuring extremely small amounts of envelope delay. It is particu- 

 larly suitable for measurements on correcting networks in the field 

 where special delay measuring apparatus is not available. 



TO IMPEDANCE* 



■BRIDGE 



SYSTEM 



TO BE 



MEASURED 



OPEN 



TO IMPEDANCE 

 -• BRIDGE 



SYSTEM 



TO BE 



MEASURED 



SHORT 



K = CHARACTERI5TIC IMPEDANCE OF SYSTEM 



Fig. 2 — Arrangement for special Impedance measurements. 



The system to be measured is connected to the impedance bridge as 

 indicated in Fig. 2. The termination (short or open) used at the far 

 end of the system constitutes a 100 per cent irregularity in its structure 

 and the alternating current transmitted by the system from the im- 

 pedance bridge to the far end is totally reflected at this irregularity and 

 retransmitted by the system to its input terminals. When a steady- 

 state has been established, this reflected current bears a definite phase 

 relation to the incident current at the input terminals, this relation 

 depending on the steady-state phase shift of the system at the fre- 

 quency used for the measurement. This phase relation varies with 

 frequency and, consequently, the measured impedance of the system 

 will also vary with frequency. These variations in impedance are 

 evident from the impedance-frequency curves plotted from the meas- 

 urements taken, and it can be seen that the impedance varies cyclically 

 over the frequency range. 



To begin with we shall assume that the impedance bridged across 

 the measuring trunk equals the characteristic impedance, K, of the 

 system, as shown in the figure, and that the characteristic impedance 

 is the same in both directions. Then if the variation of impedance 

 completes one half cycle when the frequency is increased from fx to f-y 

 cycles, it is evident that the steady-state phase shift of twice the sys- 

 tem is one half cycle greater at/2 than at/i. Now the envelope delay 

 of a system in seconds at any frequency / is approximately 



T.= 



AB 



A/' 



where AB — the change in phase shift in cycles for a small change 

 in frequency of A/ cycles per second. Here the change in the steady- 

 state phase shift of the system is one quarter cycle for a finite change in 

 frequency of /2 — f\. Dividing this change of phase shift by the change 



