| Summary: | Simulating wave propagation in microstrip lines with Gyrotropic magnetic substrate is
considered in this thesis. Since the static internal field distribution has an important
effect on the device behavior, accurate determination of the internal fields are considered as well. To avoid the losses at microwave frequencies it is assumed that the magnetic substrate is saturated in the direction of local internal field. An iterative method to obtain the magnetization distribution has been developed. It is applied to a variety of nonlinear nonuniform magnetic material configurations that one may encounter in the design stage, subject to a nonuniform applied field.
One of the main characteristics of the proposed iterative method to obtain the static internal field is that the results are supported by a uniqueness theorem in magnetostatics.
The series of solutions Mn,Hn, where n is the iteration number, minimize the free Gibbs
energy G(M) in sequence. They also satisfy the constitutive equation M = χH at the end
of each iteration better than the previous one. Therefore based on the given uniqueness
theorem, the unique stable equilibrium state M is determined.
To simulate wave propagation in the Gyrotropic magnetic media a new FDTD formulation is proposed. The proposed formulation considers the static part of the electromagnetic field, obtained by using the iterative approach, as parameters and updates the dynamic parts in time. It solves the Landau-Lifshitz-Gilbert equation in consistency with Maxwell’s equations in time domain. The stability of the initial static field distribution ensures that the superposition of the time varying parts due to the propagating wave will not destabilize the code.
Resonances in a cavity filled with YIG are obtained. Wave propagation through a
microstrip line with YIG substrate is simulated. Magnetization oscillations around local internal field are visualized. It is proved that the excitation of magnetization precession which is accompanied by the excitation of magnetostatic waves is responsible for the gap in the scattering parameter S12. Key characteristics of the wide microstrip lines are verified in a full wave FDTD simulation. These characteristics are utilized in a variety of nonreciprocal devices like edgemode isolators and phase shifters.
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