## Waveguide Cavity Design in Your RF PCB Layout

By ZM Peterson • Sep 22, 2020Working with RF signals requires careful routing and confinement of waves to interconnects. The goal in these layouts is to ensure low-loss/low-dispersion propagation where possible, as well as isolation between RF interconnects and other portions of your system. A waveguide cavity is a great way to route sensitive RF signals around a board as it provides natural isolation and mode selection.

In reality, many structures can be used to form a waveguide cavity, and we often don’t refer to typical transmission line structures in a PCB as waveguides. Even traditional stripline and microstrip structures exhibit waveguiding properties at high frequencies, including excitation of higher order modes and dispersion due to the geometry of the system. If you want to use a waveguide cavity in your RF PCB layout, here are some points to consider when designing a waveguide and ensuring your design can be reliably fabricated at scale.

## Waveguide Cavity Geometries in PCBs

Waveguides come in all shapes and sizes, but only certain types of waveguides can be reliably fabricated on a PCB using standard manufacturing processes. DFM requirements limit the geometry of your PCB, which in turn limits the available interconnect geometries you can place in a PCB layout. The one exception is 3D printing, which allows you to fabricate nearly any waveguide cavity geometry you can imagine.

If you’re like most designers, you need to work within traditional fabrication processes. The image below shows some common waveguide geometries that can be fabricated with standard planar processes.

*Common waveguide cavity geometries used in RF PCBs.*

What makes these waveguide cavity geometries quite different from microstrips and striplines is their dimensions in comparison to the wavelength of the analog signal traveling on the line. For a digital signal, we like to work with microstrips and striplines because they allow TEM wave propagation along the line, and leaky waveguiding effects are not seen until very high frequencies. As such, microstrips and striplines used in practical PCBs and ICs have very high bandwidth. This is especially true as PCBs become denser and more advanced, which pushes their TEM cutoff frequencies to very high values.

All these waveguides have some particular characteristics that make them unique from typical microstrip and stripline traces:

**Mode selection.**Electromagnetic waveguides, according to the formal definition, do not allow TEM modes. The TEM mode is a trivial solution to the wave equation, thus it has zero amplitude. In contrast to striplines and microstrips, waveguides have a cutoff frequency beyond which the first mode can begin propagating in the structure.**Tunable bandwidth.**The bandwidth of a single-mode waveguide is defined by its frequency difference between the lowest order mode and the next higher order mode. By adjusting the geometry of the waveguide, you can tune the bandwidth of the structure.**Engineered field distribution.**Although this is not typically used in waveguides built for signal propagation, the electromagnetic field distribution within the waveguide can be chosen by exciting a certain mode in the waveguide. Most waveguides operate in the TE10 mode simply due to the match between frequency and waveguide size, but other modes could be selected. Applications like THz sensing and imaging, and waveguide coupling, can benefit from selecting a specific field distribution in the waveguide.

Despite these unique characteristics, signals injected into waveguides experience losses and dispersion, just like signals on standard planar interconnects. In addition, dispersion in a waveguide depends on the geometry, just like in a typical transmission line. The important point in designing a waveguide cavity is to tune the geometry to provide the desired cutoff and bandwidth.

## Analyzing Waveguide Cavity Designs

All waveguides are something of a cross between a typical transmission line and a resonant structure. They act like transmission lines in that they can be described in the language of parasitic circuit elements, but they also act like resonators in that they have a mode structure with specific cutoff frequencies. As was mentioned above, only certain modes are allowed to form a particular spatial distribution of electric and magnetic fields.

### Modal Frequencies

The modal frequencies for a closed waveguide (e.g., substrate integrated waveguide (SIW)) are functions of the cavity geometry (width *W* and height *H*) and can be found with a simple equation, which is shown below:

*Waveguide modal frequencies for rectangular geometries.*

For the waveguides shown above, you need to use an effective width along the guide to determine the cutoff frequency and modal frequencies. The effective width for these waveguides varies, but you can find a number of closed-form equations in Brian C. Wadell's *Transmission Line Design Handbook*. Dealing with dispersive systems and lossy systems uses standard techniques you’ll find in any partial differential equations textbook.

### Input Impedance

The input impedance of a waveguide can be described using the standard input impedance equation for a transmission line. As long as you know the wave impedance for the waveguide, you can calculate the input impedance, which typically uses a shorted load. The wave impedance for a homogeneous rectangular waveguide cavity is defined below:

*Waveguide cavity impedance above the cutoff frequency*

For a homogeneous rectangular waveguide, you can then use this in the standard input impedance equation for transmission lines. Together with the modal frequencies, you can examine how the field in different excited waveguide cavity modes will behave. One other point to consider is coupling structures to other waveguides or transmission lines, which I’ll discuss in more depth in an upcoming article.

**The experienced PCB design and layout team at NWES can help you create your next advanced RF PCB layout and create the waveguide cavity designs you need to ensure RF signal integrity. We help our clients stay at the cutting edge with advanced PCB design and layout services. We've also partnered directly with EDA companies and advanced PCB manufacturers, and we'll make sure your next design is fully manufacturable at scale. Contact NWES for a consultation.**