Resonant Modes of a Class of Microstrip Rings in a Dielectric Material

A non-Galerkin method based on spline-harmonic basis and testing functions is used to analyze the resonant characteristics (resonant frequency, quality factor, and radiation pattern) of a new class of microstrip rings. Our rings, which we call single harmonic rings, are defined by adding a perturbative single harmonic term to the constant circular ring equation, in the polar coordinates. This definition contains various ring shape geometries including square and triangular rings with smooth corners. It is shown that the application of the spline-harmonic basis and testing functions in the spectral domain leads to integrals with rapidly decaying integrands in the radial spectral direction and provides relatively smooth functions of the angular spectral variable. Therefore, the numerical calculation of the system matrix elements can be performed easily in the polar spectral coordinate system. Mode families are defined based on coupled harmonics, and a mode numbering scheme is introduced. Numerical results are produced for a range of ring parameters, and variations of the resonant characteristics are investigated.