Microwave Engineering Europe - December 2008 - (Page 12) 12 EM MODELING Finding ground in an EM simulator… and learning how to use it By Dr. John Dunn, AWR, www.awrcorp.com T he concept of “ground” is the foundation of all aspects of electrical engineering. Once it has been defined, you can describe the voltage at a point in a circuit with a single number. However elemental this may appear, it can be confusing in practice. We’re all familiar with what happens when we don’t have a “good” ground. For example, when there is too much resistance or inductance in a ground plane, different points in the ground network may be at different voltages. However, EM simulators do not even appear to have the semblance of ground. So you might wonder how the circuit simulator puts in a ground in order to perform a circuit simulation Circuit simulators require an unambiguous, universal ground node that is usually referred to as “node 0,” which is necessary because simulators solve for voltages, and a unique voltage is required at all nodes. To sort out the concept of ground as it applies to EM simulators, we will look at ports and see how they implicitly use ground when the resulting S-parameters are transferred to the circuit simulator. We will examine imperfect ground return within EM simulation and how to model it, and we’ll use three examples to illustrate the concept of ground in EM simulation. Figure 1: Exposing ground nodes using transformers. Ports in EM simulators and ground EM simulators essentially solve Maxwell’s equations for electric and magnetic fields. Voltage (and thus ground) is not an EM field concept but is derived from the electric field by integrating it along a chosen path [1]. If we work entirely within the realm of EM simulation, there is actually no need to discuss ground, and only when the results are sent to a circuit simulator, usually in the form of an S-parameter file, do we need to consider ground or “node 0”. Although S-parameters can be defined entirely by the concepts of power, modes, and modal impedance, and we don’t need a voltage definition [2], it is not possible to export them to a circuit simulator without such a definition. Let’s consider two types of simulators. The first group directly solves for the electric field throughout the entire region of the problem, and either the finite element method (FEM) or finite difference time-domain method (FDTD) is typically used. This type of simulator can use a so-called “wave port,” in which an area normal to the signal line (the port) is defined and the electric field patterns of the relevant modes are calculated. Once we know the mode pattern, power is injected into the mode, and the reflected and transmitted powers to the various ports are calculated. S-parameters can be derived by looking at the power and either the current or voltage on the signal line. You need to define an impedance line over which the electric field is integrated to get the voltage. The conductor on which the line starts is the ground for the port. That is, it is the reference point for the voltage. However, different ports can have completely different reference conductors, which can be confusing to say the least. The second group of simulators solves for the currents on the conductors using method-ofmoments (MoM). The conductors are meshed and the currents in each cell interact with every other cell through electric (capacitive) and magnetic (inductive) coupling, as defined by an object known as Green’s function. This results in a dense matrix equation that must be solved for the unknown currents on the meshes. It is analogous to the “wave port” mentioned above, in this case called the “edge port,” which is either placed at the end of the signal line or at the edge of the simulation box. MoM simulators differ in this regard. Some exist in an electrical box and some are in open space. The port is excited, the incident and reflected currents are measured, and the Sparameters are determined. The calculation assumes the currents are operating in a transmission line mode and that there is a local ground return. But where is it? In the case of a boxed MoM simulator (closed boundary) it is the sidewall, and the voltage excitation is across a small gap between the signal line and the sidewall. In the unboxed simulator (open boundary), either a ground plane (microstrip and striplines) or side grounds (coplanar lines) are assumed. The grounds can be different at the various edge ports, which can lead to problems with interpreting the S-parameters. Fortunately, in the boxed simulator, the sidewalls represent a fairly good “ideal” ground. The bottom ground plane usually does the same for the microstip and stripline cases unless it is extremely lossy. Ultimately, you must determine if the grounds at the various ports can be called the “same.” So in summary, EM simulators use ports to get Sparameters, and those ports make an assumption of a local ground in some way. The local grounds at the various ports should all be electrically about at the same voltage or the circuit simulator may incorrectly interpret the S-parameter file. AWR details port issues in simulators in several webinars [3]. Modeling an imperfect ground If the grounding structure used in the EM simulation is “less than ideal”, it must be modeled in some way. Designers often incorrectly assume that imperfect ground properties can be observed by looking at the exposed node (for example, the loss of the ground plane). The exposed ground approximation assumes the ports’ local grounds are the same but imperfect ground properties would make the ports’ local grounds different voltages. There is even greater confusion with multi-port S-parameter files in which differential ports or local grounds are requested. For example, a two-port S-parameter file will now have four ports, with Port 3 corresponding to Port 1’s “ground” and Port 4 corresponding to Port 2’s “ground.” Microwave Engineering Europe ● December 2008 ● www.mwee.com http://www.awrcorp.com http://www.mwee.com
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