8-16] STATIC REGULATION REQUIREMENTS OF AGC LOOPS 421 



The constant B in this equation gives the slope of the gain control charac- 

 teristic in decibels per AGC bias volt. Differentiating with respect to eg-. 



(201ogio.)i^' = B 

 Gi a eg 



(8-10) 



i^' =0.1155. 

 Gi deg 



Multiplying and dividing the LHS by eiK:i allows us to express it simply as 

 the ratio of the loop gain K2 and the video output <?« by utilizing Equation 

 8-4. 



1 ;^n 



0.1155 



(8-11) 

 0.1155. 



For the d-c or static case with G^iO) equal to unity, changes in the bias are 

 directly proportional to changes in the output. Thus the slope B can be 

 expressed as the ratio of the total change in gain to the change in output 

 voltage : 



„ gain- change (db) gain change (db) 



^O.max ^fl.min ^o.max ^o.min 



(8-12) 



Substituting Equation 8-12 into Equation 8-11 yields the following expres- 

 sion for the AGC loop gain: 



K^ = — fMHf^ X [gain change (db)] (8-13) 



^o.max ^o,min 



It is apparent from this expression that with the linear gain control charac- 

 teristic shown in Fig. 8-17, the loop gain will vary somewhat with the video 

 output eg. Normally, the video output will be well enough controlled that 

 its variation can be neglected and an average value used in Equation 8-13. 

 It is possible to compensate for this variation in the loop gain K2 by 

 introducing a slight curvature in the gain control characteristic. Generally, 

 though, uncontrolled departures from linearity with accompanying uncon- 

 trolled variations in the loop gain are a much more important design factor 

 to consider. 



To illustrate the use of Equation 8-13, suppose that static input varia- 

 tions of 100 db must be regulated by the AGC loop to output variations of 

 only ±1 db or between 0.89^<, and 1.122 eo. Substituting these numbers 

 into Equation 8-13 yields 



Mmm= 49.5 = 33.4 db. (8-14) 



'^' 1.122 - 0.89 



