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Matrix methods are applied to static microstrip problems and used to deduce the approximate propagation characteristics of the dominant, quasi-TEM mode. Three basically different techniques are employed, in conjunction with the matrix methods. The first uses a free space Green's function, the second uses multiple imaging to obtain a Green's function for single substrate microstrip, and the third uses Fourier integral methods to obtain the Green's function for multilayered and/or covered microstrip. Several classes of problems are treated. The capacitance matrix, propagation constant, and characteristic impedance are obtained for two-dimensional (transmission line) problems. In addition, a general method for treating capacitive discontinuities in microstrip is developed and applied to typical three-dimensional discontinuity problems such as an open circuit, a gap in microstrip, and a sudden change in width of microstrip. Finally, multilayered and covered microstrip propagation is analyzed by a Fourier integral method.