508 



AUTOMATIC TRACKING CIRCUITS 



\Ri*(s) /Ro\ ^ T is a straight line with a —2 or double-integrator slope 

 which, when projected to a log unity or zero value, crosses the abscissa at 

 COT = ^2= 1.414. The high-frequency upper bound has a —3 slope 

 through COT = -x/l— 1.2599. These asymptotic segments intersect at 

 COT = 1 at a value \Ri*is) /Ro\ ^ t = 2. 



The asymptotic upper bound of the amplitude distribution shown in 

 Fig. 9-21 may be expressed by the equation 



Ri*(s) = 2R 



m 



m 





in units of yard seconds. If the definition of a coj-ner frequency 



1 KV ■ 

 coi = - = -^ 



T /<0 



is introduced, Equation 9-14 may be written in the form 



2Rf) I coi VI coi 



Rr 



, . 2R, /^COlVY COI \ 



Gain level 



Frequency characteristic 



.(9-14) 



(9-15) 



(9-16) 



The pass course qualifies as an excellent test signal for investigation of 

 the performance of automatic range tracking servo systems. At times that 

 are widely removed from crossover, the input approaches a constant range 

 rate. In the vicinity of crossover there is a transition from the approxi- 

 mation of a constant rate to a zero range rate at the instant of crossover. 

 In the sense that all circles (or parabolas, etc.) have a fixed shape, all pass 

 courses may be characterized by one general function. This fact is empha- 

 sized by Fig. 9-19 which specifies, in the time domain, the nature of all pass 

 courses in a fully normalized manner. One needs only to evaluate the time 

 constant t = {RqJKV) for a particular case. Fig. 9-21 specifies, in the 

 frequency domain, the upper bound for the pass-course range tracking input 

 information important in design of the automatic tracking servo system. 



9-14 PRACTICAL DESIGN CONSIDERATIONS 



For range tracking, the low-frequency asymptotic slope should be that of 

 a double integrator. To this basic fact one adds the practical considerations 

 that airborne radar systems employ electronic range tracking systems that 

 have a definite gain limit. This means that the —2 slope cannot be extended 

 indefinitely, and in practice a zero slope at extremely low frequencies 

 results. An additional practical consideration is the ever-present require- 

 ment that the feedback system be stable. This requirement means, in 



