Analysis and synthesis algorithms for the electric screen Jauman electromagnetic wave absorber

Du Toit, Leendert Johannes (1993-11)

Thesis (PhD)--Stellenbosch University, 1993


ENGLISH ABSTRACT: An extensive literature study revealed numerous Jauman absorber examples with reasonable absorption properties. Unfortunately, tractable and detailed design techniques were found to be scarce, and often only applicable to absorbers with two or three layers. The research described in this report was therefore aimed at, and culminated in, general design methods for multilayered electric screen J auman absorbers. As a starting point, the synthesis problem is formulated by idealizing the spacers (assumed lossless and commensurate) and resistive sheets (assumed to have zero thickness), and by considering the absorption of a normally incident plane wave. An equivalent circuit model is derived, using the analogy between plane waves in stratified media, and guided waves in TEM transmission lines. The network is analyzed using Richard's frequency surrogate, S = tanh(s = cr +jw), and concise equations and algorithms are presented for symbolic and numerical analysis. Maximum bandwidth synthesis of the classic one-layer absorber, or Salisbury screen, proved to be simple, clearly illustrates the analytic approach, and apparently has not been published before. The two-layer absorber was also found to be algebraically simple enough to be synthesized in closed form, is dealt with comprehensively, and the treatment consolidates and formalizes many of the design techniques available in the literature. Networks comprising commensurate transmission lines and conductances have been investigated by Richardsl , but unfortunately the topology-driven realizability constraints on the input impedance of the Jauman network is only dealt with briefly. Fruitless investigations by the author showed this to be a formidable problem, and as a result the research concentrated on tractable and iterative synthesis algorithms for multilayered absorbers, instead of formal filter synthesis techniques. These algorithms may be summarized as follows: • A key concept in the multilayer zero-placement synthesis methods that will be presented, is the ability to physically realize a given set of reflection coefficientzeros. This involves solving a set of highly non-linear equations, and a gradientmethod iterative algorithm has been developed to achieve this . • The first application of the aforementioned algorithm is to synthesize all reflection zeros at S →∞, thereby obtaining a maximally flat reflection coefficient magnitude response. Stable and rapid convergence was found for up to at least 20 layers, thereby extending the two- and three-layer algebraic solutions available in the literature. It was found that a stringent restriction exists on the maximum dielectric constant (Er) of the spacers, thereby limiting the practical implementation of these solutions . • Through judicious manipulation of reflection zeros at distinct physical frequencies, an equiripple absorption response may be obtained. An elegant algorithm is presented to facilitate this, and it was found that these solutions represent substantial improvements over examples available in the literature. Restrictions still apply to the spacer Er, but these are more relaxed and practical equiripple absorbers are possible. In addition, the spread in sheet resistivities is much smaller than in comparable maximally flat solutions. • Numerical searches indicated that the aforementioned equiripple responses are very close to, but not absolutely optimal, in the sense of maximum bandwidth. The small bandwidth and/or absorption improvements that were found were almost negligible from a practical viewpoint, but the optimal synthesis problem is academically very important. Through use of the general Chebyshev approximation method, an algorithm is developed which finds the local optimal response in the vicinity of such a parent equiripple solution. Although it might be tempting to classify the algorithm as a brute force method, it will be shown that this is not the case, and that its solutions provide the answer to the fundamental and unsolved optimal design problem. These algorithms have been implemented, and tables of resistive sheet values are presented for N up to 8, a range of Er values corresponding to low loss foams, and for various absorption levels.


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