14-13] RELATIVE IMPORTANCE OF DESIGN VARIABLES 767 



To illustrate the extent of this compromise, let us assume that trans- 

 mitter power and antenna size are fixed by other considerations. Utilizing 

 Equations 14-14, 14-19, and 14-22, we see that a 2-to-l increase in frequency- 

 provides a 64-to-l (18 db) increase in return power for clear air propagation 

 (7 = 0). Since we are interested in maximum system range, and storm cell 

 areas are generally a fraction of that required for beam filling at such ranges, 

 (target area <<C R'^4>6), we can set 



Rn... oc -^K. (14-23) 



In other words, doubling the frequency increases the range 2.8 times for 

 clear-air propagation. This conclusion is modified appreciably when 

 intervening meteorological attenuators are considered (see Fig. 14-14). 



Obviously if system and antenna size, weight, and power consumption 

 are of little consequence, a lower frequency would be more desirable. Since 

 this cannot be the case for airborne radar, the band of frequencies between 

 C band and X band are found to be the best compromise. The lower 

 frequency end is dictated principally by the required target definition 

 (nominally 8° maximum beamwidth) which is a function of antenna dish 

 size and frequency; and the size, weight, and power consumption of a 

 transmitter required to give sufficient range. On the other hand, the high 

 frequency end is limited by the significance attached to the ability to 

 penetrate extensive heavy-rainfall areas, and the distortion in displayed 

 storm cells, caused by two-way attenuation through the cell. This atten- 

 uation could reach as high as 30 to 40 db at a wavelength of 3.2 cm for a 

 particularly severe storm situation. The comparable attenuation at 5.7 cm 

 would be 8 db. 



Peak Transmitter Power. This parameter must be construed as 

 peak magnetron output power modified by losses in the duplexer and other 

 waveguide components. Because high power output can only be purchased 

 through larger, heavier magnetrons, modulators, and power supplies, this is 

 normally a highly undesirable means of improving airborne radar perform- 

 ance. Equation 14-20 indicates that maximum range varies with the fourth 

 root of peak power(Pr). Inasmuch as the weather targets at the maximum 

 range of most systems probably lie in a classification somewhere between 

 that of a point target and a beam-filling target, this expression may be more 

 nearly represented as a cube root function. A peak power increase of 2 to 1 

 therefore might only be expected to improve range by 19 to 26 per cent. 

 In the discussion above on frequency it was shown that return power drops 

 very rapidly with lowering of frequency. If peak transmitted power (Pt) 

 is to be increased to counteract this decrease in Pr it is readily seen that the 

 maximum permissible size and weight of the transmitter soon limits how 

 low in frequency the designer may go. 



