Analysis of a TM01 circular to TE10 rectangular waveguide mode converter
Abstract
A TM sub 01 mode is incident in a circular waveguide in which only the TE sub 11 and TM sub 01 modes can propagate. Two apertures in this circular waveguide feed two rectangular waveguides of identical cross section in which only the TE sub 10 dominant mode can propagate. Close each aperture with perfect conductors. Attempting to restore the original tangential electric field on both sides of each of these conductors, the magnetic current M on one side of the conductor and M on the other side of the conductor. Expand M as a linear combination of expansion functions each of which is approximately the magnetic current associated with one of the rectangular waveguide modes. Substituting this M into the equation of continuity of the tangential magnetic field across the apertures and testing, as in Galerkin's method, this equation with the expansion functions for M, one arrives at a matrix equation which determines the coefficients of the expansion functions in the expansion for M. In turn, M determines the field in the waveguides, and, in particular, the amplitudes of the TE sub 10 modes in the rectangular waveguides. Detailed formulas for the matrix elements are given in terms of Bessel functions and roots of Bessel functions. Further work is required to program these formulas in order to obtain numerical results using a digital computer.
 Publication:

Technical Report No. 1
 Pub Date:
 August 1989
 Bibcode:
 1989syra.rept.....M
 Keywords:

 Apertures;
 Circular Waveguides;
 Electromagnetic Fields;
 Method Of Moments;
 Propagation Modes;
 Rectangular Waveguides;
 Traveling Waves;
 Bessel Functions;
 Continuity Equation;
 Digital Computers;
 Tangents;
 Electronics and Electrical Engineering