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2 years ago in Electrical Engineering By Simanghi

Can conformal mapping techniques provide useful analytical insight into the surface current distribution on complex UWB patch shapes (like elliptical or tapered slots)?

 I'm analyzing current densities on a UWB elliptical patch antenna from my full-wave simulation. The results are complex. I recall conformal mapping is used in transmission line analysis to transform complex geometries into simpler ones. Could this technique be applied to map, for example, an elliptical patch boundary to a rectangular coordinate system to approximate its fundamental mode current distribution analytically? Is this a viable path to derive closed-form expressions for input impedance or resonant frequencies of such shapes, or is it purely of academic interest given the dominance of numerical solvers?

EMSimulation AnalyticalModeling LaplaceEquation

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By Meghna R Answered 1 year ago

Conformal mapping is powerful for canonical problems with known boundaries (like coplanar strips or coaxial lines) but becomes intractably complex for radiating structures like an arbitrary UWB patch. The primary obstacle is that the radiation condition (open boundary) cannot be easily mapped. You could map the metal boundary of an elliptical patch to a circle, but this doesn't solve for the currents—it only transforms the geometry. The resulting wave equation in the new coordinates is often no simpler. In my experience, for UWB antennas where currents are broadband and complex, the technique offers limited practical design insight compared to moments-method or FEM solvers. Its value today is mainly in teaching fundamental principles of fringing fields and capacitance, not for designing modern, optimized UWB radiators.

 

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