266 TECHNIQUES FOR SIGNAL AND NOISE ANALYSIS 



In analyzing the effects of the remaining circuits in the loop on this signal, 

 it is convenient to make certain simplifying approximations. First, it is 

 assumed that the fractional modulation kt is small enough that its square 

 may be neglected. Second, when determining the spectrum of the video 

 noise, the target is assumed centered in the beam so that ke is zero. This 

 reduces the expression above to the case already considered in Paragraph 

 5-7 (Equation 5-74). 



The average value of the video signal plus noise during a pulse will consist 

 of a d-c term and the a-c error signal: 



Average video = ^2 ^ ^2 j^ 2(j^ -[- la'ke cos (co./ + ip). (5-86) 



The AGC loop will act to maintain the value of the d-c part of the video at 

 a constant level which we may conveniently assume to be unity. Thus, 

 ideally, the effect of the AGC is to divide the video by its d-c level. We 

 assume that the AGC loop does indeed operate in this manner, although 

 in an actual system only an approximate quotient would be formed. This 

 assumption is sufficiently accurate for our purposes. In this case the 

 effective a-c error signal during a pulse becomes 



/ S/N \ 



\\ + s/n) 



A-C error signal = f , , c/at ) ^^e cos (co^/ + <p). (5-87) 



One effect of the noise is to introduce a factor depending upon the signal- 

 to-noise ratio which attenuates the a-c error at low values of this ratio. 

 The net result of this suppression of the signal by the noise is to decrease 

 the gain around the angle tracking loop. 



A pulse stretcher is used to generate a signal suitable for use in the low- 

 frequency control circuits from the pulsed signal delivered by the range 

 gate. The pulse stretching operation will introduce some distortion of the 

 angular error modulation, but because the scanning frequency is normally 

 much smaller than the pulse repetition frequency, this distortion can be 

 neglected and the pulse stretcher assumed to generate the fundamental 

 component of the pulsed signal. Thus the a-c error signal delivered to the 

 phase-sensitive demodulator is essentially of the form given in Equation 

 5-87. 



We suppose the demodulator to be a simple product type consisting of a 

 multiplication of the modulated error signal by a sinusoidal reference, 

 (1 Ik) cos oist. The factor 1 jk is incorporated in order that the output may 

 be equal to the angular error. The properties of such a device with noise 

 inputs were established in Paragraph S-6. The demodulator output is 

 filtered so that only the very low frequencies are retained (components of cog 

 and above are eliminated) as the angular error signal. The development of 

 the error signal in the demodulator can be represented by the following 

 operations: 



