Two-dimensional equations for the analysis of microstrip line dispersion and step discontinuities

Abstract

It is shown how the two-dimensional equations for microwave planar circuits, which are in fact a generalization of the one-dimensional telegraphists' equations, can be derived through a rigorous theory based on Maxwell's equations. These equations are used in the thesis to calculate the dispersion of the fundamental and of the higher-order modes of propagation on microstrip lines, the losses on microstrip lines, and the components of the equivalent circuit for symmetric, asymmetric, and cascaded microstrip lines. The quasistatic parameters, necessary in the calculation of the modal dispersion, are determined using a new hybrid analytical-numerical approach. Four methods were developed, two of them being variational methods, together with theorems for the lower and upper bound of capacitance. Thus, the error in calculating the quasi-static parameters can be controlled. The results obtained in calculating the dispersion are within the error of measurement range for experimental data. The proposed dispersion model permits also the inclusion of losses in the initial formulation. Thus, the attenuation and the phase constants can be obtained simultaneously. Using the same model, the dispersion of the higher-order modes of propagation is obtained with an error of less than 1% when compared to the more accurate full-wave solution. For symmetric and asymmetric step discontinuities, simple formulas for the components of the equivalent circuit are obtained. The results are in good agreement with those from the fullwave solution, the error being less then 1.5%. In the case of cascaded microstrip lines, the proposed method reduces drastically the computation time while giving acceptable accuracy. The two-dimensional equations can be successfully used up to the cutoff frequency of the first 'TM' mode, well within the operation range of the microstrip lines.