By R. C. Majam-Majumdar
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The erf (x) is the integral of the standard normal distribution with the standard deviation compressed by a factor of \12. 4 Probability of detection and false-alarm probability function associated with the normal curve. 5. 020" below the mean of the S + N distribution Let the radar be in the process of design. 98 are specified. 5 dB Detailed curves of P d VS P fa with SIN as a parameter have been worked out by many (Barton, 1988, p. 62; Marcum, 1960; Skolnik, 1980, p. 28). I have used a home computer to generate curves using the approach discussed previously.
By comparing the ratio of an integration from 0 to 1T and from 0 to 00, we can note that just under 50 percent of the farfield power is contained in the first beamwidth and 90 percent of the power is between the peak and the first null on either side. Having already . A 211. 311. noted that the null pomts are at D' D ' D ' and so forth, we can check that 24 Radar Principles for the Non-Specialist . 3'\ 5,\ the maXIma are at 0, 2D' 2D' and so forth. ) We can solve for these maxima. The first maximum is the antenna mainlobe.
Because there are about 40,000 square degrees in a sphere, an antenna with a I-degree beamwidth has a gain of 40,000 or 46 dB. Thus, a radar with a 60-ft. aperture diameter at a frequency where A = 1 ft. (L-band) has a beamwidth of about 1 degree and its gain is (before losses) about 46 dB. The effective area of an antenna will be less than its physical area. Good antennas have an effective area about 60 percent of the physical area. The preceding quantities derived are approximately applicable to many kinds of antennas, even though real antennas are usually not uniformly illuminated.