| A rigorous method for solving problems in Corrugated Waveguides is presented that offers a simple structure suitable for implementation on computers, and which results are traceable to Maxwell's Equations and the boundary and continuity conditions. This technique, based on the Modal Matching procedure, does not require the tracking of repeated scattering of individual waves.; The case of a single step discontinuity in a Parallel Plate Transmission Line is treated first. By equating the two series expansions of the electromagnetic fields at the discontinuity and imposing the boundary conditions at the step wall, a large, but finite set of simultaneous equations are obtained that can be solved by matrix methods. The convergence of the series coefficients is then verified without performing a matrix inversion. Then, a memory efficient method that requires smaller matrices is studied. A truncated set of equations is solved by Gaussian Elimination and numerical results are provided in graphical form. Solutions for Rectangular Waveguides are given as an extension of the theory.; The problem of a Parallel Plate Transmission Line which contains a transverse groove is later analyzed. By equating the series expansions at each discontinuity and establishing a link between the fields in the groove region, a solvable set of simultaneous equations is obtained. A modification is introduced that reduces the system of equations to be solved in half. Then, numerical results are obtained through Gaussian Elimination and plotted.; A solvable system of simultaneous equations is developed for Corrugated Parallel Plate Transmission Lines by a generalization of the single groove case. The theory is later extended for application to Rectangular Waveguides.; The source of electromagnetic energy is rotated {dollar}piover 2{dollar} radians about an axial line to effect incident Transverse Electric waves. Solutions are then obtained for all cases analyzed with the original source configuration.; Numerical results of a Parallel Plate Transmission Line containing a single discontinuity and a single groove are compared against known behavior: (A) The Shunt Capacitance of a step discontinuity is verified in the electrostatic limit with the aid of an exact method. (B) Circuit Theory models of waveguide grooves are developed, however, electromagnetic results differ due to tunneling of energy by evanescent waves. (C) Phase Velocities inside Rectangular Waveguides containing a cavity (groove) show regions of slow and fast waves. |
