Propagation in the Parallel Plate Waveguide TEM Mode
The simple structure of parallel plate waveguides allows TE, TM, and TEM modes in a single structure.
The lowest order mode in a parallel plate waveguide is the TEM mode.
The TEM mode can be visualized in terms of plane wave propagation along the waveguide axis, but eventually, the TEM mode is cutoff and a TE/TM mode will dominate.
These flanges can interface with a waveguide-based slot antenna, printed antenna, or edge emitter on a PCB
Many microwave systems make use of waveguiding, even if you’re unaware that it happens. Waveguiding refers to the use of a structure that directs the propagation of electromagnetic waves with a specific spatial distribution of the electromagnetic field. This natural tendency for an electromagnetic wave to travel through a bounded medium along a specific direction is the basis for many applications in microwave electronics, and printed circuit engineers have come up with many interesting waveguide structures to drive wave propagation in RF devices.
Whenever you’re designing a waveguide, the question of mode excitation arises. By making the spatial distribution of the excitation pulse at the input of the waveguide orthogonal to specific eigenmodes, you can engineer the mode structure of the propagating wave to produce a desired electromagnetic field distribution. This can be done in optical fibers with spatial light modulators, but it is rather infeasible in microwave interconnects. However, designers can take advantage of the cutoff frequency in a waveguide to excite a small set of modes. In this article, we will focus our discussion on propagation in the parallel plate waveguide TEM mode.
TEM-Only Propagation in Parallel Plate Waveguides
Parallel plate waveguides have a simple structure composed of a parallel pair of conducting planes separated by some distance H, as shown in the image below. The structure supports some set of eigenmodes, each with a specific spatial frequency and angular frequency related by a dispersion relation. The only system parameters that determine the eigenmode frequencies are:
- The dielectric permeability of the filler material between the plane layers.
- The magnetic susceptibility of the filler material between the plane layers.
- The value of H (distance between planes).
The typical parallel plate waveguide structure and the eigenmodes are shown below.
Typical parallel plate waveguide structure and the eigenmodes
In the above equation for the waveguide mode, the eigenmode function simply tells us how the electric field (TE modes) or magnetic field (TM modes) is distributed in space. The magnetic field eigenmode can be calculated using Faraday’s law. Finally, the eigenvalue kn is the important factor that tells us which modes can be excited in the structure for a given frequency.
Exciting the TEM Mode
The TEM mode is simple to excite in a parallel plate waveguide, as it is the lowest-order eigenmode in the system, i.e., the eigenmode with n = 0. To excite the TEM mode, the system is simply driven with a harmonic source at the input end. As long as the source frequency is below the first cutoff frequency, then only the TEM mode will be excited in the structure. In reality, all other modes can be excited below the cutoff frequency, but they decay quickly because the eigenvalue kn will be imaginary and the wave will attenuate quickly.
To summarize, we only have TEM mode propagation when the following condition on the driving source is satisfied:
Cutoff frequency for the parallel plate waveguide TEM mode
If the structure is excited in this range, the TEM mode is the only mode that is active in the structure, and we can observe plane wave propagation. Above the upper range, the cross-sectional electromagnetic field distribution is more complex, as multiple modes are excited and propagate.
The Electromagnetic Field in the Parallel Plate Waveguide TEM Mode
The electromagnetic field in a parallel plate waveguide TEM mode has no variation along the cross-section of the waveguide. When a TE/TM mode is excited, the cross-section has some variation in the electromagnetic field as you move along the vertical direction along the waveguide. The field distributions in the TE01 mode are shown below as an example. Along the width of the waveguide, there is no variation in the field distribution due to the infinite extent of the waveguide.
Field distributions in the TE01 mode
Can We Excite the Parallel Plate Waveguide TEM Mode When N > 0?
The answer is yes, the TEM mode will always be excited when n > 0. This is because the TEM mode is the lowest order mode indexed by n = 0. Any frequency that excites electromagnetic wave propagation in the structure will always excite the TEM mode. However, when exciting the structure above a higher order cutoff frequency, additional modes may be excited, and these higher order modes propagate along the waveguide to the output.
Exciting only the TEM at much higher frequencies than the first cutoff is only possible in two ways:
- Engineering the current density distribution used to excite the structure such that it is orthogonal to all TE and TM eigenmodes.
- Make the waveguide thinner to push the cutoff frequencies to higher values.
The 2nd option is simple and is normally used if a designer wants to use a parallel plate waveguide or similar waveguide to transmit an RF signal through a PCB. The first option is well-known to antenna theorists, although it is not yet a practical option for PCB designers. However, research into unique emitters and the coupling structures that can be used to interface with substrate-defined waveguide structures continues. Designers can investigate and evaluate these designs with a field solver application that takes PCB layout data direct from design tools.
Cadence’s PCB design and analysis software is ideal for creating an RF PCB layout with unique interconnect structures. You can evaluate propagation in the parallel plate waveguide TEM mode and calculate other important performance metrics in 3D with a complete set of analysis tools. When you use Cadence’s software suite, you’ll also have access to a range of simulation features you can use in signal integrity analysis, giving you everything you need to evaluate your system’s functionality.
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