TABLE OF CONTENTS A waveguide normally consists of a hollow conducting pipe of arbitrary cross-section (Figure 6.1). In the ideal case both the conductor and the dielectric filling the waveguide are assumed lossless.
Analysis of the possible field structures within the guide is accomplished by solution of Maxwells equations, which for sinusoidal excitation are
| (6.1) |  |
| (6.2) |  |
(exp( j ?t) dependence assumed) and for a source-free region
| (6.3) |  |
| (6.4) |  |
Taking the curl of (6.1) and substituting (6.2) we obtain
| (6.5) |  |
or
| (6.6) |  |
and from (6.3), for source-free regions, we obtain the Helmholtz equations
| (6.7) |  |
| (6.8) |  |
where
| (6.9) |  |
If we assume that the direction of propagation is along the z axis then the fields can be expressed in terms of the propagation constant ?:
| (6.10) |  |
where for a lossless waveguide ? = ? implies an exponentially decaying or cut-off wave and ? = j ? implies a propagating wave with sinusoidal variation along the z axis. The Helmholtz equations can be expressed as
| (6.11) |  |
| (6.12) |  |
where
| (6.13) |  |
The E and H fields can be obtained by solving (6.11) and (6.12) with the appropriate boundary conditions, which in this case are that the tangential E field should be zero on the surface of the conducting pipe. General expressions for the fields in waveguides of arbitrary cross-section are difficult to obtain. Fortunately most practical waveguides have simple rectangular or circular cross-sections. Initially we...
