Nonlinearly Loaded Antennas

Franceschetti, Giorgio; Pinto, I. M.

doi:10.1016/b978-0-12-709660-5.50015-3

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…Using this property, substitution of (14) into (12) yields where all sums are from 1 to n. The solution of our differential equation 9has thus been reduced to determining the transfer functions. This is straightforward but algebraically tedious and will only be outlined here (see, e.g., Sarkar and Weiner, 1976, Graham and Ehrman, 1973, Franceschetti and Pinto, 1980. Using 10…”

Section: Volterra Series Solutionmentioning

confidence: 99%

“…Do not return copies of this report unless contractual obligations or notices on a specific document requires that it be returned. (Franceschetti and Pinto, 1980, Landt et al, 1983, Liu and Tesche, 1976, Kanda, 1980, Sarkar and Weiner, 1976 have focused on scattering by a nonlinearly loaded antenna. This effort extends this previous work by considering the scattering from an active circuit.…”

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Nonlinear Electromagnetic Scattering from a Diode Circuit

Beland¹

1984

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Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, if different from Report) IS. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side it necesery and identify by block number) electromagnetic scattering: nonlinear scattering: Volterra series: diode circuit: of-7 20 ABSTRACT (ContInue on reverse side If necessary end identify by block number) Electromagnetic scattering from an active diode circuit is considered. The focus is on the nonlinear interaction between the incident fields and the internal circuit sources. This interaction results in a mixing of frequencies between the incident and internal sources. An equivalent circuit model of the diode circuit and dipole antenna Is presented and a nonlinear differential equation derived. This equation is solved approximately by a Volterra series to third order. This solution is simulated and numerical values of total scattered power at the various frequencies are calculated.-k e.- , .

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Section: Volterra Series Solutionmentioning

confidence: 99%

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confidence: 99%

Nonlinear Electromagnetic Scattering from a Diode Circuit

Beland¹

1984

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“…It will prove advantageous to describe such nonlinear systems by means of Volterra series [17]. See also related work by Franceschetti and Pinto [20] and earlier studies cited therein. See also related work by Franceschetti and Pinto [20] and earlier studies cited therein.…”

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Scattering by Weakly Nonlinear Objects

Censor¹

1983

SIAM J. Appl. Math.

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An attempt is made to construct a consistent scattering theory for systems involving nonlinear objects. Weak nonlinearity is assumed, such that harmonic generation is present, but shock wave formation is excluded. Mathematically this is described by constitutive relations in the form of Volterra series. For periodic (as opposed to monochromatic) waves, this procedure facilitates algebraic constitutive relations and dispersion equations in the transform space. Weak nonlinearity, as defined here, implies phase matching, i.e., all harmonics of the tundamental wave possess the same phase velocity (this is the reason that shock waves cannot be formed). Due to this stipulation superposition is allowed in a restricted sense, facilitating the construction of arbitrary wave solutions, e.g., cylindrical and spherical waves, by using sums (integrals) of plane waves.Using wave solutions from the linear theory, various boundary value problems can be discussed. Plane interfaces are considered, displaying well known properties relevant to new technological applications, such as bistability, and nonlinearly induced transparency. Scattering from cylinders and spheres is discussed, pointing out the new phenomena that should be observed, due to the presence of nonlinearity.Deterministic multiple scattering theory is extended to include the present class of problems. Propagation of waves in random media of distinct nonlinear objects is discussed in a cursory manner, essentially to demonstrate that the Foldy-Twersky method of medium synthesis can be extended to the present case. This suggests a new area of interest for future research. Introductory remarks. The status of scattering theory in the presence of objects involving nonlinear media is radically different from what we have in the linear case. Although there are many open problems in the linear theory, it has been around for many decades and is in a quite advanced stage. References to early results are well documented, e.g., see Stratton [1]. The mathematical methods and the properties of the relevant special functions are given, e.g., Morse and Feshbach [2]. This maturity reached for the class of linear problems is not matched in the case of scattering in the presence of nonlinear media, probably because of the complexity of the latter subject. Many aspects of nonlinear wave propagation have been discussed, but a thorough review of the literature is out of the scope of the present study. Some linkage to the existing (mostly early) literature is provided by the books cited here [3]-[12].It appears that a scattering theory as we know it for the linear case is practically nonexistent, except for specialized discussions, mainly concerning plane waves and plane interfaces (and their logical extension in the context of geometrical optics).An attempt is made here to construct a scattering theory for nonlinear systems, along the lines of the classical linear theory. In order to achieve this goal, the principle of superposition, valid for linear systems, must be salvaged. This is feas...

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