# Understanding Attenuation in a Parallel Plate Waveguide

### Key Takeaways

• It’s possible to fabricate waveguide structures on a PCB using traces, planes, and vias.

• A parallel plate waveguide is a simple structure that involves two planes on adjacent layers.

• Attenuation in a parallel plate waveguide can be adjusted by changing the distance between plane layers.

Waveguides are useful structures for directing electromagnetic radiation along a specific direction while also isolating a propagating signal from noise sources. When referring to waveguides, designers are typically describing the large pipes and fittings designed for microwave frequencies or possibly optical fibers. While it’s not very common, larger waveguide structures are sometimes used on a PCB to provide the routing of microwave signals with high isolation.

Among the various waveguiding structures that can be placed on a PCB, one less-common structure is a parallel plate waveguide. The attenuation in a parallel plate waveguide is important to consider, as the size of the waveguide will determine the total attenuation experienced by signals traveling through the waveguide. To see how this works, we need to draw on some basics from electromagnetic theory and we’ll use the eigenmodes of the waveguide system to see how to define attenuation in terms of the system’s excitation frequency and geometry.

## Waveguide Basics in a PCB

Waveguides in a PCB are formed by creating closed structures from plane layers, copper pour, and/or vias as sidewalls. Probably the most common waveguide structure is a coplanar waveguide on the surface layer of a PCB, although this is an open waveguide that has lower isolation than other structures. Other structures like substrate integrated waveguides, parallel plate waveguides, and shielded stripline waveguides can be used to provide higher isolation than routing on the surface layer.

### Parallel Plate Waveguide

Although you get higher isolation with an internal-layer waveguide structure, you have a problem with attenuation, dispersion, copper roughness losses, and other losses that affect the design. It is much easier to modulate the attenuation in a parallel plate waveguide because there is only one geometric parameter that determines the wavenumber and losses.

The image below shows a typical parallel plate waveguide, its wavenumber, and how the electric field distribution relates to the wavenumber. In this structure, an electromagnetic wave travels between the two plates, and the spatial distribution of the field depends on the distance between the two copper regions. The typical arrangement is to have copper pour on one layer and a power or ground plane on the other layer.

A parallel plate waveguide structure

What’s important to note here is that the PCB substrate has some dielectric losses as manifested in the complex dielectric constant. By simply taking the square root of the complex number in the above equation, you’ll have another complex number that defines the wavenumber for the nth waveguide mode. The complex part tells you the attenuation in a parallel plate waveguide.

### What’s Missing From the Above Equation?

There are a few things missing from the above equation that define the wavenumber for the parallel plate waveguide:

1. Skin-effect losses: The skin effect occurs in the upper and lower copper regions, which incurs some resistive and inductive power losses as excited eddy currents.
2. Copper roughness: The roughness of the deposited copper effectively increases the magnitude of losses due to the skin effect.
3. Radiation losses: The above model defining the wavenumber and attenuation in a parallel plate waveguide assumes the lateral length is infinite. This is only valid when the lateral width is much larger than the free-space wavelength of the signal injected in the waveguide.

Therefore, we need to modify the above equation using the definition of wave impedance and transmission line impedance so that skin effect losses and copper roughness losses are included.

### Attenuation in a Parallel Plate Waveguide With Skin Effect Losses

The image below shows the total attenuation (in Nepers/meter) for TEM, TE, and TM modes in a parallel plate waveguide. These equations include the skin resistance per unit area (Rs) in the second term, which will also depend on the wave frequency and the dimensions of the overlapping copper layers.

Attenuation in a parallel plate waveguide

### Parallel Plate Waveguide Pros and Cons

A parallel plate waveguide is the only internal waveguide structure in a PCB that is closed in one direction. Other structures, like a substrate integrated waveguide, are closed in two directions by connecting the two planes with vias, which creates a totally enclosed structure. Therefore, it’s worthwhile to compare a parallel plate waveguide and substrate integrated waveguide.

 Parallel Plate Substrate Integrated Designing Losses Only the layer height can be used to adjust losses, and this value is constrained by stackup requirements. The designer has more freedom, as the height and width of the structure can be adjusted. Cutoff Frequencies Adjusting losses also changes the cutoff frequencies for the structure because there is only one geometric parameter to adjust. A change in one geometric parameter can be compensated by an opposite change in another parameter, so losses can be modified without changing cutoff frequency. Field Distribution Easier to design for multi-mode propagation, as the mode cutoffs are only described with one geometric parameter (substrate thickness). It’s easier to change the mode order by changing the width of the waveguide.

A substrate integrated waveguide will have an additional term in the wavenumber that will determine the cutoff frequency for each mode. These design problems require balancing multiple objectives, but an electromagnetic field solver can help you calculate the field distribution in these structures. This is very important in areas like antenna design and shielding design, but the right tools can help you visualize electromagnetic field distribution in your waveguide structure.

When you need to design and calculate the attenuation in a parallel plate waveguide, make Cadence’s PCB design and analysis software your go-to application for every task in electronics design. You’ll have access to a range of simulation features you can use for pre-layout design evaluation to ensure RF signal integrity, and you can seamlessly move into physical layout with schematic capture features and a complete set of CAD tools.

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