Dispersion Diagram I: Parallel Plate

The parallel plate waveguide is one of the most common waveguides studied in electromagnetics textbooks. A parallel plate waveguide consists of two metallic plates separated by air or a dielectric substrate. The plates are considered to be infinite in extent, but in reality this is not possible and microwave absorber/matched terminations are used at the outer perimeter of the waveguide. Since the parallel plate waveguide consists of two separate metals, a fundamental TEM mode is supported. In this tutorial, the dispersion diagram of a parallel plate waveguide (dielectric substrate permittivity of 10.2 and height of 2.54 mm) is generated using HFSS's eigenmode solver. The following topics are covered:
Dispersion Diagram Basics
Model Setup
Periodic Boundary Conditions
Analysis/Optometrics Setup
Plotting Results


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Dispersion Diagram Basics
We want to use HFSS to obtain a dispersion diagram for the first mode for a parallel plate waveguide. A dispersion diagram is a plot of propagation constant versus frequency; a dispersion diagram basically tells you how much phase shift a material has at a given frequency. Since a parallel plate waveguide allows for waves to travel in two-dimensions, its propagation constant can be written as a vector quantity, β = xkx + yky. In order to generate the dispersion diagram, a unit-cell has to be defined and the appropriate periodic boundary conditions (PBCs) have to be applied. For the sake of simplicity and that a parallel plate waveguide can be treated as a periodic structure, a symmetric unit-cell (square of size p x p mm2) is defined as shown in Fig. 1.