There are many applications where modeling applied during the design phase of a project enhances product quality and time to market. Unfortunately, the technology of modeling has not advanced to the point where calculations are performed to give you instant EMI/EMC pass-fail results.
This type of technology may never exist because the number of uncertainties and dependencies are too great. But there is much information that modeling can provide without the need to include extra complexity.
What Can EMI/EMC Modeling Do?
EMI/EMC modeling is routinely used to help predict all aspects of a system’s EMI/EMC performance, including radiated emissions, radiated immunity, conducted emissions, conducted immunity and ESD. The models can be as simple as determining the shielding effectiveness of a set of air vents with a wire passing close by or as complicated as the coupling between a printed circuit board (PCB) and cable connectors which provide a path for common-mode currents to external cables.
In all cases, it is important for you to think clearly about where the source of the EMI/EMC disturbance might be, where the actual radiator is, and what is the coupling path between them. If these three areas are not clear, then more than one model may be required to help identify the major source.
EMI Modeling Techniques
Three major techniques are used for EMI/EMC full-wave modeling:
Finite-Difference Time-Domain (FDTD).
Method of Moments (MoM).
Finite Element Method (FEM).
Each of these techniques has different strengths and weaknesses, and no one technique will provide efficient and accurate modeling of all potential problems. As a result, more than one technique is required to model all the likely problems that will come up, and you must know when to use which technique for a particular problem.
These modeling techniques are all full-wave solvers; that is, they satisfy Maxwell’s Equations and can solve for both electric and magnetic fields in both the near field and the far field.
Finite-Difference Time-Domain
FDTD is a volume-based solution to Maxwell’s differential equations. Maxwell’s equations are converted to central difference equations and solved directly in the time domain.
The entire volume of space surrounding the object to be modeled must be gridded, usually into square or rectangular grids, small compared to the shortest wavelength of interest. Then each grid location must be identified as metal, air or whatever material desired.
Figure 1 shows an example of a two-dimensional grid (or a cut-away view of a three-dimensional grid). Once the grid parameters are established, the electric and magnetic fields are determined throughout the grid at a particular time. Time is advanced one step and the fields are determined again.
As a result, the electric and magnetic fields are determined at each time step based upon the previous values of the electric and magnetic fields. Although this example shows a set of slots in a shielded enclosure, it could have been used to model traces on a PCB, to model ground straps or for many other applications.
Once the fields have propagated throughout the gridded domain, the FDTD simulation is complete and the broadband frequency response of the model is determined by performing a Fourier Transform of the time-domain results at the specified monitor points. FDTD is a time-domain solution, so the entire frequency-domain result is available from a single simulation when the source signal is a pulse.
Since FDTD is a volume-based solution, the edges of the grid must be controlled to provide the proper radiation response. The edges are modeled with an absorbing boundary condition (ABC).
There are many ABCs, mostly named after their inventors. In nearly all cases, the ABC must be remote from the source so that the far-field assumption of the ABC holds true. Typically, a good ABC for FDTD will provide a reflection of less than -60 dB.
FDTD is well suited for modeling entities containing enclosed volumes with metal, dielectrics and air as well as for modeling emissions through apertures. FDTD is not well suited to modeling long, thin structures since the computational area overhead increases very rapidly with this type of structure.
When evaluating FDTD modeling tools, consider:
The ease of creating the model.
The capability to monitor both electric and magnetic fields.
The capability to observe the results in both the time and the frequency domains.
The capability to observe time-domain animations of the fields as they propagate through the computational domain.
Method of Moments
The MoM is not a volume-based technique because only the metal surfaces must be modeled. The structure to be modeled is converted into a series of metal plates and wires. Often a solid structure is converted into a wire- frame model, eliminating the metal plates.
Once the structure is defined, the wires are broken into segments (short compared to a wavelength) and the plates are divided into patches (small compared to a wavelength). From this structure, a set of linear equations is created.
The solution to this set of linear equations is the RF currents on each wire segment and surface patch. Once the RF current is known for each segment and patch, the electric field at any point in space can be determined by solving for each segment/patch and performing the vector summation.
There is no need for an ABC in MoM since there are no boundaries of the computational space. The currents on all conductors are determined, and the remaining space is assumed to be air. MoM is very efficient for solving problems with long, thin structures such as external wires or cables.
Since MoM finds the currents on the conductors, it models metals and air very efficiently. However, dielectrics and other materials are difficult to model in MoM with standard codes.
MoM is a frequency-domain solution technique. If the solution is needed at more than one frequency, the simulation must be run for each frequency. This is often required since the source signals within the typical computer have fast rise times and wideband harmonic content.
MoM is very useful for finding the fields when the device to be modeled has long wires or requires lumped circuit elements. MoM can easily find the electric or magnetic fields anywhere in space, even 10 meters away from the modeled device. MoM is not well suited for models with shielding effectiveness (any model where the current on one side of a metal plate is different from that of the other side of the plate) or models with dielectrics.
When evaluating MoM modeling tools, consider:
The ease of creating the model.
The capability to monitor both electric and magnetic fields.
The capability to observe the results of interest; for example, scanning the receive antenna throughout 360° and 1 to 4 meters height, then reporting only the maximum field.
The capability to use lumped circuit elements.
Finite Element Method
FEM is another volume-based solution technique. The solution space is split into small elements—usually tetrahedral shaped—which is referred to as the finite element mesh.
The field in each element is approximated by low-order polynomials with unknown coefficients. These approximate functions are substituted into a variational expression derived from Maxwell’s equations and the resulting system of equations is solved to determine the coefficients. Once these coefficients are calculated, the fields are known, in an approximate sense, within each element.
Since FEM is a volume-based solution technique, it must have some boundary condition at the edge of the computational space. Typically, FEM boundaries must be a few wavelengths away from the structure being analyzed and must be spherical in shape. This restriction results in a heavy overhead burden since the number of unknowns increases dramatically over other computational techniques. Recent technical literature describes new ABCs which may be implemented after careful analysis.
FEM is well suited to applications where the computational space is bounded by metal, as in waveguide problems, and to problems with nonrectangular elements such as curves. It is not well suited to applications consisting of long, thin structures such as long wires, since the computational area overhead increases very rapidly with this type of structure.
When evaluating FEM modeling tools, consider:
The ease of creating the model.
The capability to monitor both electric and magnetic fields.
The ease of wide-frequency range modeling.
The accuracy of the absorbing boundary condition.
Modeling Real-World Applications
It is important to reduce the overall design problem to something that can be modeled yielding a result in a reasonable amount of time; that is, to decrease the overall problem to the components that will make the biggest effect on the EMI/EMC performance. For example, if the sizes of the air vents are a concern, then modeling all the traces on the PCB is not required.
Another example is the coupling from a high-speed net on a PCB to a nearby cable connector. Again, not all the details of every trace on the PCB are important. The major (first-order effect) traces, serving as fortuitous conductors, should be used without every via and minor trace. Each major area can be modeled separately so you can determine which of these areas will make a significant difference in the overall EMI/EMC performance of the product.
Models cannot ignore some parts of the overall problem just because they are difficult to design. For example, emissions from a product will be greatly affected by the long wires and cables that must be attached for testing. If a model is developed that correctly models the product itself, but without including the long cables, then the result will be wrong.
To overcome the problems of modeling both the long cables and the product itself, multiple stage models are often required. Multiple-stage models use the result of one model to serve as the input to the next modeling stage.
When using multistage models, be sure that all the important features are included in all stages. However, the use of multistage models does allow some products to be modeled that could never have been modeled otherwise.
Evaluating Modeling Software
There are many sources for EMI/EMC modeling software. There are a number of software vendors, some universities provide free software, and there is some free software originally developed by the government.
Carefully evaluate the different sources, keeping in mind how flexible the software is (multiple modeling techniques supports), the ease of use to develop models (complicated CAD functionality vs easy-to-use interface), and the level of ongoing support by the provider.
Recent articles suggest a set of standard EMI modeling problems. These proposed problems allow you to evaluate different software packages while using a real-world style set of problems.
Summary
Modeling EMI problems is not a solution to replacing the knowledge gained by experience, nor will it eliminate the need for you to work closely with the design engineer. But because of the high-speed, high-frequency nature of the circuits involved, often there is no other way to predict the effect of emission control features. Old rules of thumb and out-of-context equations/graphs are not useful in these cases because they provide the wrong answer without any warning.
No one modeling technique will accomplish all modeling tasks effectively and accurately. A toolbox approach, where you select the appropriate technique for the specific modeling task, is the only way to ensure success. Reducing cost and time to market and eliminating trial-and-error redesign loops are the main reasons to employ the modeling techniques.
About the Author
Bruce Archambeault, the Director of Research and Development at SETH, has more than 20 years experience in the EMI/EMC profession. He has presented many technical papers and chaired various sessions at symposia and other professional gatherings. While completing his Ph.D. in electromagnetic modeling techniques, Mr. Archambeault performed research on modeling techniques. SETH, 117 Allenbill Dr., Johnstown, PA 15904, (814) 255-4417.
Copyright 1996 Nelson Publishing Inc.
August 1996
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