MEASURING SYSTEM FOR VIDEO 



231 



in phase angle <p oi a. known direction. From equation (11) in the appendix 

 for equal amplitudes Ei and Ei 



(2) 



\Es\ - \Eo\ = 1 £i I [cos (^/2) - sin(<^/2)] 



Substituting (a) (p = x/2 + A(p and (b) ip = Z-w/l + A(p into eqyation (2) 

 it is evident that the sign of | £s | — 1 -Ed | in substitution (b) is the reverse 

 of substitution (a). 



\Es\ and | Ed \ are equal every 180° only if all arms of the phase bridge 

 are exactly equal. If the arms are unequal, balance exists for all angles 

 if = 7r/2 + 2w7r + A^i and ^ = 7r/2 + {In — l)7r + A^2 where A0 may be 

 called departure angle. 



Fig. 6 — The phase bridge. 



The phase detector can also be used as a deflection bridge. If the phase 

 indicating meter is calibrated according to equation (2), phase angle de- 

 partures from 7r/2 + n-n may be read directly on the indicator when | £i | = 

 I El I and the scale factor is adjusted for the amplitude of Ei which is 

 maintained constant by the overall automatic volume control circuit. 

 Equation (2) is almost a linear function and is plotted in Fig. 7. 



In using the deflection on the indicator to measure phase shift, an error 

 Ai/' is incurred if | £i | 9^ \E^\. The maximum permissible ratio of | Ei \J 

 I E\ I for a given error Ai/' is given by 



(3) 



£2 1 / I £i I = cos^/cos {ip -i- A^) + \/[cos ^lcos{<p + A^)]^ - 1 



