EM Ports — A Ground Is Out There Somewhere
As a designer, you certainly need to know where the ground of your circuit is. EM simulators work the same way. You should know the ground of each port so that you can properly interpret the results. If different ports have different grounds, don't be surprised if you see some non-intuitive results.
All ports used in EM simulators must have a notion of ground. Why? For argument's sake, let's agree it is because without it, you can't take your data and use it in a circuit simulator. Let's take a closer look at the issues.
As electrical engineers, we all know about ground. Along with voltage and current, it is one of the most fundamental concepts anchoring electrical engineering. But what you may not know is that ground is not used in Maxwell's equations, the physical equations that form the basis of electromagnetics. It is these equations that are numerically solved in EM simulators. Maxwell equations work with electric and magnetic fields, not voltage. Voltage is what is called a derived quantity — if you know the electric field for a problem, you can find the voltage between two points by integrating the electric field along a path between those two points.
Since EM simulators solve Maxwell's equations, and these equations don't use voltage and ground, why should we even worry about it? Indeed, we could create a simulator that calculates S-parameters using purely EM field concepts. First, we would set up our ports using wave concepts. (By the way, this is common in 3D simulators that use wave ports.) Then we could calculate the input and reflected power to the various ports by using the electric and magnetic fields at the port. Finally, we could take ratios of the various powers and determine our S-parameters. Unfortunately, we can't use these S-parameters in a circuit simulator. Circuit simulators work with current and voltage. In order to get our S-parameters into the circuit world, we need to have a notion of the port's impedance. There are many definitions for port impedance, but they all involve some kind of circuit concept: voltage or current or both. That's why we need to know what a port's ground is.
The easiest way to find a port's ground is to determine where the current coming out of the port originates. Every electrical engineer knows (I hope!) that current must flow in continuous loops. Current is flowing out of our port. Where is it coming from? This current is called the port's ground return current; i.e., it is the current flowing back into the port from the local ground. Sometimes this is fairly obvious. Figure 1 shows two types of port grounds for a planar EM simulator. (I am illustrating the concept using AXIEM from AWR.) Port 1 has a ground strap attached that lets current flow from the ground plane below to the port. Clearly, the port's ground reference is the ground plane below. A similar situation exists in EM simulators in a box. The line attaches to the perfectly conducting side wall of the box. The current return is out of the side wall, through the port, and down the line. The side wall is therefore the local ground for the port. However, look at port 2 in Figure 1. There is no ground strap. Where is the ground current return? The answer is that it is coming from infinity! Hopefully, as a practical engineer, this makes you feel uneasy. Infinity is a long way away. Fortunately, the ground plane in this case also goes out to infinity, so maybe that helps. I will discuss more of this concept in future articles.
Figure 1: Explicit and implicit grounding schemes in EM simulators
Figure 2 shows another common type of port. Ports 2 and 3 are edge ports, as we showed inFigure 1. Port 1 is an internal port. It goes by different names in different simulators: internal port, circuit port, series port. The idea is that you cut the line and place the port. The port has a port impedance; let's assume it's 50 ohms for simplicity. Now, where is port 1's ground? It is on the negative side of the port. The laboratory analogy is using a two-point probe. The red probe tip goes on the one side of the port; the black probe tip goes on the other. Local ground is the metal line the black probe tip touches.
Figure 2: Port 1 is an internal port.
The S-parameters generated with this type of port can be confusing. For example, what is S11 at low frequencies for Figure 2, assuming all port impedances are 50 ohms. The answer is S11 = 0.5. See if you can figure out why. For a real challenge, try figuring out S21. It will make you appreciate why port ground and S-parameters can be tricky! Unfortunately, many designers don't appreciate the ports in Figure 2 have different grounds, and completely misuse the S-parameters.
In conclusion, take the time to understand the ports you use in EM simulation. Just like in real circuits, ground can be your friend or cause you grief. The easiest way to think of ground is current return. If you can predict where all the port currents are coming from, you are well on your way to avoiding problems with misinterpreting the results coming out of your EM simulator.
For a more detailed discussion of these issues, please see my white paper Understanding Grounding Concepts in EM Simulators.
About The Author
Dr. John Dunn, a recognized expert in EM modeling and simulation for high-frequency and high-speed circuit applications, is a senior applications engineer at AWR and develops and presents AWR training material to customers world-wide. Before joining AWR, he was head of the interconnect modeling group at Tektronix and a professor of electrical engineering at the University of Colorado, Boulder, where he led a research group in EM simulation and modeling. Dr. Dunn received his Ph.D. and M.S. degrees in applied physics from Harvard University and is a senior member of IEEE. You can contact him at firstname.lastname@example.org.
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