9-13] 



RANGE TRACKING DESIGN EXAMPLE 



507 



Two additional derivatives lead to the impulses of Fig. 9-20c. The mathe- 

 matical expression for the steady-state frequency-domain equivalent of 

 these impulses becomes 



\Ri*f J > |2 sin wtI 



(9-10) 

 (9-11) 



The low-frequency upper bound is found by using the small angle sin x ^> x 

 approximation. Thus, 



ID * I 



-^0 [ ojtJ 



(9-12) 



The high-frequency upper bound is found by using the maximum value 

 (+1) for the sine function. Thus, 



\R^ 



(9-13) 





</2 



Figure 9-21 shows the results given by Equations 9-12 and 9-13 on a 

 g-magnitude, log-frequency plot. The low-frequency upper bound for 



0.01 



Pass course: 



k-M 



KV 



K = 0.5626 for Rq in yards 

 \^ in knots 



0.1 1.0 



COT (Log scale) 



10 



Fig. 9-21 Asymptotic Upper Bound Frequency Domain Representation of Pass- 

 Course Range Tracking. 



