Aerospace and Electronic Systems Magazine August 2016 - 27

Shifrin Figure 4. Angular distribution of scattered power Fsc given different values of errors' correlation radius. the angular distribution of power scattered due to the presence of errors. When the correlation radii are small, the errors create in the mean RP an almost constant background of the order of (ρ / L)α. For example, at the errors' standard deviation of 10°, the constant background will be approximately -23 dB within the first two sidelobes of the RP of an antenna with the uniform amplitude distribution. With an increase in the correlation radius of errors, the character of angular distribution of the scattered power rapidly varies and, at c → ∞, approaches the theoretical RP sin2 ψ / ψ2. Curves in Figure 4 can be considered an essential addition to the results of the first body of work on the tolerance theory [1], [2] wherein the consideration was restricted by the case c ≪ 1. After the mean power RP, the mean directivity of the antenna was thoroughly studied. It was shown that: C C C at small errors, the value = (1 −Δ) D0 (where D0 is the theoretical directivity at the absence of errors) and the value Δ varies from α at small с, to null at c → ∞; at small correlation radii, . This relation is suitable for both linear and aperture systems. Limits of its applicability are given in the book [5]; in the general case, , i.e. is equal to the mean power radiated in the MMD (see Figure 3). Further, the mean RP width was studied. The maximum of this value is reached at mean values of the correlation radius (i.e., c = 0.5...0.6, i.e., r = 0.3L). By an order of magnitude, the mean RP given the variance of errors α = 2..3 is 2-3 times wider than the theoretical one. The last mean characteristics considered were the mean RP extremes. The investigations here were carried out for small errors because the statement of the problem for large errors is senseless because the sidelobes join the mainlobe. In the course of investigations, it appeared that when using a statistical approach to the analysis of antennas, beside of inAUGUST 2016 Figure 5. MMD variance versus errors' correlation radius. troducing new notions and definitions, it was necessary either to correct conventional notions of the usual antenna theory or redefine them. For example, for the RP width, one should distinguish between the mean RP width for separate realizations and the width of mean RP. It turned out that one should also distinguish between the mean normalized RP and the normalized mean RP. The mean maximum directivity and a maximum value of the mean directivity are different notions, etc. In addition, new effects appeared in SAT, which were absent in the usual antenna theory: limiting directivity, minimum side radiation level (SRL), and effect of directivity saturation, etc. Some of these effects are considered in this article. Further in the book, the fluctuations of antenna parameters are investigated. Errors of sources are assumed to be small. Fluctuations of the field amplitude and phase in different directions, as well as the MMD fluctuations and their dependence on the correlation radius are discussed. Some of the results obtained include: On fluctuations of the field amplitude and phase. It is shown that at phase errors in the antenna, the amplitude fluctuations of the field in MMD, as a first approximation, are absent. The phase fluctuations in this direction vary from small values to α (when c → ∞); and in other directions, mutually-independent fluctuations of the amplitude and phase take place. On MMD fluctuations. Figure 5 shows the results of corresponding calculations. As seen from the figure, source errors for correlation radius с within the limits of from 0.2 to 0.6 (r = 0.1L..0.3L) are most unpleasant from the viewpoint of MMD departures. In this case, the maximum standard deviation of the MMD departure is approximately equal to that of phase errors. For example, at the phase error standard deviation of 10° (0.17 rad), the MMD departure standard deviation with respect to the theoretical width of the error-free RP (being equal to 2y0.5Р = 2.78) is of the order of 5...6%. The confidence interval that defines the MMD spread is approximately equal to one-third of the mainlobe width of the theoretical RP. IEEE A&E SYSTEMS MAGAZINE 27

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine August 2016