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Electromagnetic field representations and computations in complex structures. III: Network representations of the connection and subdomain circuits. (English) Zbl 0993.78027

Summary: When complex structures are divided into subdomains for electromagnetic field computations, it is necessary to specify which of the tangential electromagnetic field components at the boundaries may be regarded as independent and which have to be treated as dependent. In this third of our three-part study, we establish some rules for the choice of primary and secondary fields at the connection interface, i.e. at the interface between adjacent subdomains. The discretized field continuity equations at the connection interface provide the connection network whose canonical forms are illustrated, and it is shown that the normalized scattering matrix is symmetric, orthogonal and unitary.
Tellegen’s theorem is introduced in order to provide the basis for consistent choice of primary and secondary fields and for deriving canonical forms of the connection network. The field problem is systematically treated by partitioning and by specifying canonical Foster representations for the subcircuits. Connection between different subdomains is obtained by selecting the appropriate independent field quantities via Tellegen’s theorem. For each subdomain, as well as for the entire circuit, an equivalent circuit extraction procedure is feasible, either in closed form for subdomains amenable to analytical treatment or via the relevant pole structure description when a numerical solution is available. Moreover, circuit-based resonant expansions in the complex frequency plane are provided here for the analytic dyadic Green’s functions in part I [ibid. 15, 93-107 (2002; Zbl 0992.78037)].

MSC:

78M99 Basic methods for problems in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
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References:

[1] Felsen, International Journal of Numerical Modelling 15 pp 109– (2002) · Zbl 1001.78028
[2] Felsen, International Journal of Numerical Modelling 15 pp 93– (2002) · Zbl 0992.78037
[3] Righi, IEEE Transactions on Microwave Theory and Techniques 43 pp 854– (1995)
[4] Mongiardo, IEEE Microwave Guided Wave Letters 3 pp 241– (1993)
[5] Mittra, IEEE Transactions on Microwave Theory and Techniques 20 pp 96– (1972)
[6] Eleftheriades, IEEE Transactions on Microwave Theory and Techniques 42 pp 1896– (1994)
[7] Schmidt, IEEE Transactions on Microwave Theory and Techniques 43 pp 2910– (1995)
[8] Tellegen, Philips Research Reports 7 pp 259– (1952)
[9] Tellegen, Proceedings of the Institution Radio and Engineers 14 pp 265– (1953) · Zbl 0051.19301
[10] Tellegen’s Theorem and Electrical Networks. MIT Press: Cambridge, Massachusetts, 1970.
[11] Linear and Nonlinear Circuits. McGraw Hill: New York, 1987.
[12] Field Theory of Guided Waves. IEEE Press: New York, 1991. · Zbl 0876.35113
[13] Theorie der Linearen Wechselstromschaltungen. Akademie-Verlag: Berlin, 1954.
[14] Classical Network Theory. Holden-Day: San Francisco, California, 1968. · Zbl 0172.20404
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