Transverse Resonance Technique for Analysis of Symmetrical Stub in Microstrip Transmission Line
Keywords:Open stub, Transverse resonance method, Resonance frequencies, Scattering matrix, Microstrip line
Open or short-circuit stubs in a strip (microstrip) transmission line are one of the most common elements of planar circuits used in numerous devices in the microwave frequency range: various types of filters, couplers, power amplifiers, antennas, sensors, wireless energy transfer systems, etc. Modern planar circuits in the microwave frequency range already contain stubs of a complex shape and a complex pattern inside the microstrip line. Therefore, an urgent problem is to develop an analyzing method for discontinuities in form of the closed or open stub in a microstrip transmission line at frequencies at which the transmission line theory already has significant errors and high-frequency effects must be considered.
In paper a technique of scattering characteristics calculating on a symmetrical microstrip open stub by transverse resonance method is presented. Boundary value problems for a rectangular volume resonator based on a microstrip transmission line with a symmetric open stub are solved for three different boundary conditions in the plane of symmetry and on the longitudinal boundaries. To algebraize the boundary value problems for the resonator’s eigen frequencies with discontinuity, the corresponding two-dimensional functions of the magnetic potential are constructed, through which the components of the current density on the strip are calculated. The magnetic potential functions were written by decomposing them into series by orthogonal Chebyshev polynomials, which consider the behavior of the field on a thin edge and ensure fast convergence of the series and the algorithm. The developed algorithms were tested by calculating the scattering characteristics of a microstrip open stub using the transverse resonance method on the example of open stub in a microstrip transmission line with a resonant frequency of about 3.0 GHz. In addition, the method was tested on the example of numerical calculations of the dependence of resonant reflection frequencies of an open stub on its width.
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