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.

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