MEASUREMENT OF DELAY DISTORTION 257 



that this length can be regarded as part of the balancing line I. Then at 

 point E we have 



2irf\tc 



<i>E — 4>A — 4>AB = <i>A 



<f>E — <t>B — <f>BE — <t>B — 



V 



27r/2 tc 



The primes indicate phase shifts at frequency /2. The phase 0''^ of the 

 beat note, A/ = /2 — /i, at E is 



4>E = <f>E — <f>E = (i>B — <f>A — A/ (10) 



V 



Similarly, at point D 



<l>o = 4>'b-4>a - ^^ + iThia -x) - (0' - ^) (11) 



K X is adjusted so that the A/'s in the two branches are in phase at the 

 oscilloscope then 



0"^ = 0% _ a (12) 



where a is the difference in the phase shifts in the two beat note circuits. 

 Substituting (10) and (11) in (12) and solving for (/3' - /3) yields 



(0' -0)= ?I^^ - M/ -/:(2. - a) +g] 



(13) 



The delay in the network is 



lirAf 



T = 



_ 1 Vtc ac i2x - a) _ ~| 



-717+2^/ -^^^-aT" ""J 



(14) 



The first two terms in (14) are independent of x and/i and therefore are 

 of interest only for absolute measurements. Relative measurements may 

 be made without evaluating these constants. The last two terms are 

 functions of x and yield the change in delay as / is varied. It is usually 

 most convenient to adjust a and ^ so that the average delay in the meas- 

 uring branch is given by (14) with 



(2x - a) = (15) 



In general this will minimize the variation of the slider and make the delay 

 distortion in the measuring branch roughly proportional to the slider 



