Take a look at any respectable development board, high frequency analog board, radar board, or other RF system, and you’ll see unique waveguide structures embedded directly in the PCB layout. Among the various RF waveguide structures used from high frequency layout and routing, coplanar waveguide design is probably the most common. There are some particular reasons for this, many of which stem from its ease of placement on the surface layer of a PCB.

Coplanar waveguide designs are easy to route in an RF PCB layout, and they are normally used for controlled impedance routing. This is quite important for RF applications, where a signal often needs to be routed to an amplifier, mixer, antenna, or other RF component. In this brief guide, I’ve compiled the important coplanar waveguide equations you’ll need when designing for controlled impedance in your PCB layout.

All coplanar waveguides come in two varieties: standard coplanar waveguide and grounded coplanar waveguide. The standard coplanar waveguide can be placed above a ground plane, or it can be placed without ground (i.e., on top of a 2-layer of a PCB with no internal ground). Both are designed for routing on the surface layer, although you can create variations that operate in an internal layer.

There are some advantages to using a coplanar waveguide design over a standard microstrip or stripline design:

**High isolation.**This is probably the most common reason for using a coplanar waveguide design. Although the waveguide is routed on the surface layer, it will have some lateral isolation thanks to the surrounding ground planes. This is the same reason ground pour is used to fill in the surface layer routed with low speed traces: it provides additional EMI shielding and terminates field lines emanating from the trace.**Lower loss than striplines.**A stripline and some other waveguides, such as substrate integrated waveguides, confine the field entirely to the substrate, so the wave sees entirely a lossy PCB substrate. In a coplanar waveguide, much of the field lines pass through the region above the dielectric, so they will not experience as much loss.**Tunable bandwidth.**The bandwidth of the structure can be tuned by adjusting the geometry. Coplanar waveguides used at ~5 GHz can be quite large, but the bandwidth can be confined to just the frequency range needed for single-mode propagation.**Single mode propagation.**The fact that the bandwidth is tunable means that we can limit the bandwidth to just the value needed for a single mode (normally TE-mode in fenced waveguides).**Compatible with existing PCB manufacturing processes.**These structures do not need special manufacturing processes for production. Current manufacturing processes are useful for fabricating coplanar waveguide designs with carrier frequencies up to ~100 GHz and higher.

*The three standard coplanar waveguide geometries.*

As part of coplanar waveguide design, there are two primary quantities that need to be calculated: impedance and effective dielectric constant (this has basically the same meaning as that for microstrip traces). The primary mathematical tool used for these calculations is the elliptical integral of the first kind, which arises due to the use of conformal mapping for deriving wave impedance in these structures. Let’s look a bit more closely at each type of structure to see how these calculations are performed.

There is a long set of equations needed here involving elliptical integrals. Rather than repeat this list of equations here, interested readers should look at Brian C. Waddel’s *Transmission Line Design Handbook*, pages 73-74. This excellent resource provides closed-form design equations for a huge range of RF structures and should be required reading for any RF designer.

This structure is something of a transition from a microstrip to a true coplanar waveguide. In the limit of substrate height *h* approximately equal to *b*, we now have approximately microstrip behavior. Otherwise, we can use the above coplanar waveguide equations with reasonable accuracy.

Here, the field lines are confined between the central conductor and the nearby ground on the surface layer, although field lines can now terminate at the lower ground. The effective dielectric constant is approximately independent of the waveguide’s geometry and is approximately the average of the dielectric constants of air and the substrate. For the impedance, we need to use the elliptical integral K(k) shown below.

In this equation, *a* is the width of the central trace and *b* is the distance between the edges of the ground plane. There are many calculators online and some open source tools that will handle the above calculation for you. See also Waddel’s textbook, page 79.

Here, we have a simple structure that adds vias for mode selection and greater suppression of radiation (i.e., higher isolation). This structure is used on a PCB as an alternative to a microstrip line. The gaps between the strip and ground must be less than the signal’s carrier frequency, but greater than the thickness of the substrate, so the field is contained between the strip and the lower ground plane. Finally, TEM propagation is ensured when the via gap is less than half the signal’s carrier wavelength.

To date, I have not seen closed form equations for grounded coplanar waveguide design impedance. The calculators you’ll find online use curve fitting results that are only valid within a certain parameter range. Outside this range, these curve fitting approximations fail. A field solver that uses method of moments will provide a highly accurate solution for the impedance, propagation constant, and effective dielectric constant.

There are other waveguide geometries that can be used for high frequency routing. These waveguides can provide TE-mode propagation and can provide isolation thanks to the nearby ground shielding. These other waveguide routing styles can be found in another article on our blog. These other routing styles can also be fabricated with standard processes, making them easy to include in your next RF PCB.

Just like a coplanar waveguide design, these other routing styles do not provide TEM mode propagation. They also provide the same advantages of high isolation, tunable bandwidth, and single-mode propagation. In addition, by selecting the appropriate termination, a standing mode can form in the structure, which is useful for coupling to an antenna or other passive RF component on the PCB. If you have access to a program like Mathematica, you can calculate the elliptical integrals listed above with high precision and determine the electromagnetic behavior of your coplanar waveguide design. More complex structures may need a field solver to get an accurate description of wave propagation in the device.

Currently, the most advanced high speed and high frequency routing standards involve broadband design, where the network parameters and dispersion in the system are considered throughout the signal bandwidth. To learn more about this important area of RF design, take a look at one of my recent technical presentations from the 2020 IEEE EPEPS conference. By looking at the wave impedance in the waveguide, the structure can be designed with desired impedance *throughout the signal bandwidth*. Upcoming high speed digital standards (e.g., USB 4.0) are taking this approach to interconnect design, and RF designers can do the same to eliminate signal distortion in their waveguide designs.

**The experienced PCB design and layout team at NWES can help you create your next advanced RF PCB layout with any of the coplanar waveguide design types shown in this article. We help private clients, aerospace companies, and the US military 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.**