A fast and accurate analysis of high Q patch resonators

Abstract

With the advent of high-temperature superconductivity, it is now possible to construct very high Q patch resonators. Because of their light weight, small volume and low expenses, they are widely used for satellite communications.

In high Q filters, say Q > 100, one in fact requires accurate analysis, with an error of less than 1%. Such accuracy is normally not attainable by regular numerical methods, such as moment method, for most arbitrarily shaped patches. Such accuracy is attainable by two-dimensional (2D) methods, like modal or contour integral, where a magnetic wall is considered at the edge of the structure.

This research starts with a fast 2D method, and analyzes a patch considering a magnetic wall at the edge. Then the magnetic wall assumption is removed to include the fringing field effect. This new formulation is three dimensional (3D), and is based on a variational expression which guarantees the accuracy. Our modeling is based on adding a correction term in the form of a line integral to a 2D method. This new hybrid (2D/3D) method has the speed of computation for 2D methods and the higher accuracy of regular numerical 3D methods.

To reduce the effect of circuit connection on the performance, gap coupling is used in most high Q filters. In this work gap coupling is analyzed, and for a special kind of gap structure a novel model is presented. This model is then added to our hybrid method to analyze gap coupled patch resonators.

The new hybrid method is then extended to analysis of coupling between different patches. Compared with conventional numerical methods, our formulation is more accurate and faster. Using this analysis, we are able to analyze high order filters such as Chebyshev.