4-8] AMPLITUDE, ANGLE, AND RANGE NOISE 203 



spectrum in Fig. 4-24 shows two peaks, not quite resolved completely, at 5 

 and 6.6 cps. In Fig. 4-25 the presence of a fundamental period in this region 

 can be seen clearly; and similar fundamental periods, but of progressively 

 lower frequency, can be seen in the 2810- and 1250-Mc plots. From an 

 examination of the drawings of the B-45, it was concluded that the observed 

 spectrum could be explained as the doppler beats between reflections from 

 the engine nacelle, the wing tank, and a portion of the fuselage near the tail 

 which was broadside at this aspect, all caused by a yaw rate of 0.14° /sec. 

 For a longer sample (i.e., longer period of observation) during which the 

 yaw rate varied, the discrete frequencies varied with time so that the 

 spectrum over such a time of observation was smeared out into a more or 

 less continuous band. Whether one should be concerned about a continuous 

 band or discrete frequencies in the design of a tracking radar depends, 

 therefore, on the time constant of the system — in other words, on the 

 passband of the servo loop. This problem will be discussed in more detail 

 in Chapter 9. 



Angle Noise. In a simultaneous lobing system (to be discussed in 

 more detail in Paragraph 6-2) the signals which are compared to obtain 

 angle information arrive simultaneously; thus amplitude fluctuations of the 

 target echo do not generate angle error signals. If the angle tracking servo 

 loop of a simultaneous lobing system is opened and the target is tracked 

 optically, it is found that error signals still occur. These must be caused, 

 therefore, by wandering of the eflFective center of reflection of the target. 

 The principle involved in the generation of angle noise may be explained 

 in terms of a target which consists of two point reflection centers, whose 



relative amplitude and phase vary as 



the target aspect changes. Fig. 4-26 

 'BoresightAxis illustrates this model. Consider the 



following type of tracking system. 



A dual-feed antenna produces lobes 

 Fig. 4-26 Physical Arrangement for on each side of the boresight axis. 

 Illustrating the Origin of Angle Noise. the gains being equal along that axis. 



The voltage from each lobe is passed 

 through an amplifier and square-law detector, and their diff"erence is used 

 to derive angular inform^'.tion. The sum of the detector outputs is used for 

 the AGC voltage of the receiver, so that the angular deviation of the 

 arriving signal is determined by the difi^erence divided by the sum of the 

 detector outputs. 



Let the boresight axis be directed at the center of the target (midway 

 between A and B) and let the angle of A (and of B) to the boresight axis 

 be d. For small d, the slope of the antenna lobes can be considered constant, 

 and will be denoted by-^. Denoting the received RF voltages due to A alone 



