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Eigenmodes and Eigenmode Solvers

Analysis of resonators.

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Business Management Powerful business-wide solutions for growing and large businesses that have outgrown their financial solution. The graph below shows a typical Eigenmode result for a 2-resonator model.

The width of the coupling aperture opening of the common wall between the resonators has been varied to see the dependency between this physical parameter and the coupling bandwidth. The y-axis unit is MHz. The center frequency is taken to be the geometrical mean of the two Eigenmode frequencies. The coupling opening affects the center frequency as can be seen in the graph below. The negative slope of the graph above is perhaps best explained by considering the effect of the aperture as an inductive loading of the resonators.

A larger equivalent resonator inductance leads to a lower resonant frequency. Eigenmode analysis of couplings between two resonators necessitates full symmetry of the structure.

Any lack of symmetry will lead to limited accuracy or invalid results. One way to check the effects of imperfect symmetry is to close the coupling aperture and observe the two natural modes. If these deviate significantly in frequency then the Eigenmode analysis is invalid and other methods of coupling analysis must be used. The page on planar filters contains more information on Eigenmode analysis and on alternatives to Eigenmode analysis if the latter is not available.

A CST simulation data file for two coupled planar resonators can also be obtained here. The physical TEM-mode 2-resonator structure has a lumped-element LC equivalence in the form of the circuit model shown below. The 2-resonator circuit also exhibits two distinct resonances that are centered around the single-resonator frequency. The offset between the two resonant frequencies depends on the strength of the coupling: We can demonstrate this by simple circuit analysis.

Rather than just stating that the mutual coupling of two resonators creates resonances centered around fc, we show here by circuit analysis that these natural resonances exist. Since version 15 of HFSS, the Eigenmode solver stored energy is also constant and even user selectable. Eigenmode analysis is not limited to resonant structures.

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A defined field at a given port boundary is applied as excitation for the 3D EM structure and that excitation causes EM fields to build up in the structure and possibly propagate to other ports. Financials Powerful finance and business management for growing and medium-sized businesses with big plans.

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The Eigenmode solver can be set up to show multiple resonances fundamental and higher order and its associated unloaded Q-factors if material with finite conductivity has been defined.

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