8-7] CONTINUOUS-CORRECTION AFC 411 



where Eo is the maximum output voltage required 



T is the interpulse period 



fe is the static error due to finite gain of the loop 



r is the pulse length 



K is the discriminator gain. 



For a static error of 50 kc, a pulse length of 1.0 Msec, and an interpulse 

 period of 1000 Msec a typical gain required is 250,000. The required gain can 

 be reduced by the use of a pulse lengthener following the frequency discrimi- 

 nator. With a circuit like that described in Paragraph 7-17 the filter gain is 

 reduced to about 250 \i T = Tp and a = 0. A gain of 250 can be provided 

 with an operational amplifier. This d-c gain can be reduced if the discrimi- 

 nator is designed with higher output or if a video amplifier is employed 

 between the pulse lengthener and the discriminator. Although the loop can 

 provide a static accuracy of 50 kc, the tuning accuracy also includes the 

 inherent accuracy of the reference. With thermionic diodes in the 

 discriminator circuit and with stable capacitances and inductors a reference 

 accuracy on the order of 50 kc can be achieved for the assumed discrimi- 

 nator characteristic. The static accuracy is then expected to be 70 kc, 

 provided that means for adjusting the reference initially to the IF frequency 

 of the receiver exist. 



The dynamic accuracy will depend on hold-in and pull-in requirements. 

 A single lag network is usually employed; i.e., the operational amplifier is 

 made an integrator. An error only appears as a signal sampled at the pulse 

 repetition frequency; therefore the integrator time constant that can be 

 employed depends on the allowable overshoot. At a given time /i the error 

 in frequency might be /i. This error is applied as a voltage to the integrator. 

 The integrator output will change at a rate determined by the RC and the 

 input voltage corresponding to/i. 



An overshoot of about 50 per cent of the initial error is a reasonable 

 compromise to obtain good dynamic response. The introduction of a step 

 frequency error then results in an output frequency which is 50 per cent of 

 the initial error but of opposite sign. The output of the AFC thus oscillates 

 about the desired frequency with diminishing error. Inputs incident to 

 pulling of the transmitter may occur at the lobing frequency or multiples 

 thereof. The error reduction that can be accomplished by the AFC thus 

 depends on the ratio of the PRF to the pulling frequency. In typical cases 

 there might be 10 to 20 samples during a cycle of the pulling frequency, and 

 error reductions on the order of 10 to 1 are attained when 50 per cent 

 overshoot is allowed. 



