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model of nonlinear radiating electromagnetic crystal in a mixing regime


S. E. Bankov 1, M. D. Duplenkova 2

1 Kotel'nikov Institute of Radio-engineering and Electronics of RAS, Moscow

 2 National Research University Moscow Power Engineering Institute, Development Bureau

Received February 1, 2012


Abstract. Radiating electromagnetic crystal containing resistive capacitive non-linear two port elements is considered. The structure has a finite length along a coordinate axis and is infinite along another axis and it is excited by a free space plane wave with low amplitude that propagates at a signal frequency. Simultaneously the electromagnetic crystal is excited by its eigen mode with high amplitude that propagates at a heterodyne frequency. Two problems of linear and non-linear analysis are solved. Harmonic balance method is applied for solution of a non-linear problem. A system of non-linear equations relatively voltage amplitudes of heterodyne frequency harmonics at all elements of the crystal is obtained. The result of non-linear problem solution is presented in form of time dependencies of differential conductivities and capacities of non-linear elements. Linear analysis about excitation of the structure by a free space plane wave is carried out for given differential parameters. The result of linear analysis is loss of power transformation from signal frequency to intermediate frequency.

Keywords: electromagnetic crystal, non-linear electromagnetic crystal, harmonic balance method, transform loss.