Back-of-the-Envelope EMI Modeling for Design and Training

Easy-to-use tools for computational electromagnetics modeling make the EMC engineer an essential and effective member of the product design team.

The concept of EMI modeling often produces thoughts of large computers solving complex problems by means of sophisticated mathematical methods applied to Maxwell's equations.¹ While this is sometimes the case, a large number of EMI problems can be addressed directly using fairly simple models. Simple models can also be used to provide the EMC engineer with greater insight into the electromagnetic behavior of a particular system.

Another misapprehension is that problems must be large and complex before modeling can be useful. Similarly there are no requirements that modeling tools be expensive. A number of computational electromagnetics tools are available cost free from the Internet, and some of these are very powerful indeed. Significant models can be run on today's personal computers. This flexibility makes possible rapid response to the many hypothetical questions that can arise in development meetings. Computational electromagnetics thus serves to update the engineer's favorite design medium: the back-of-the-envelope calculation.

EMC and the Design Team

The ability to produce early, effective, and accurate analysis is what makes an EMC engineer a useful part of a product design team. EMC engineering used to be considered primarily a support function in product design. The EMC engineer would be asked what he or she would like to see in the product for control of EMI, and then the design team would take it from there, perhaps with further consultation but often without. The next time the EMC engineer would see the product was when it appeared at the EMI test site, at which time the process of diagnosing the emissions and fixing them would begin.

With today's more densely packaged products and significantly shorter times to market, this is not a cost-effective way to work. The EMC engineer should become an integral part of the design team, being a necessary contributor of detailed design inputs based on specific aspects of each product. Computational modeling has been in common use for thermal and mechanical design but is fairly new for EMC. Product benefits can be enormous, as many design requirements can be combined in the early stages of the development cycle. Component and assembly cost savings are often significant.

The case of an actual system posing several divergent problems at once provides a practical example of an efficient design process. Thermal modeling indicated a need for air ducting to ensure cooling of critical system circuitry. Structural analysis called for stiffening of the enclosure. And serious EMI concerns were raised regarding coupling between a series of strong EMI sources and some low-speed interface connections that typically provided little high-frequency attenuation. In this case, the EMC need was critical and had to be addressed.

An array of modeling efforts drove the design of this particular system. By dealing with all three problem areas in one modeling enterprise, the design team created a simplified and much lower cost design. This synergy could have been achieved without EMI modeling, provided the EMC engineer had been able to convince the rest of the design team that he knew what was needed. But it was accomplished much more easily when clear results from the EMI models could be presented that compared the behavior of each of the options being considered. EMC design should be a science, not just expert opinion that cannot be backed up with proof of its validity.

The Basic Approach to EMC Modeling

The first steps in developing a computer model for EMI/ EMC design or analysis are to define the problem and to determine what data can be usefully obtained by means of computational electromagnetics modeling tools. In defining the problem, it is always best to establish the fundamental elements of the situation and then let the model fill in the details. EMI/EMC engineers usually second-guess the physics of a problem. When using computational models, it is more important to provide solid starting data and know what needs to be generated from those data. Also necessary is a good understanding of how available modeling tools can best address the problem.

A few basic questions need to be addressed before creating a model for any EMC problem. These are what is wanted, what is known, and how can the available tools be used to solve the problem.

What Is Wanted from the Model? In considering the application of computer modeling to EMI problems, it is important to begin with realistic goals. EMI modeling cannot solve all problems. The easiest way to begin is to focus on specific questions. Approaches to modeling can be relative or absolute. The relative approach answers questions of the form, How much better is option A than option B? The absolute approach answers questions such as, What is the radiated field strength when I have a 100-mV RF source at this location? When the absolute approach is taken, details such as source impedance and feed geometry are needed for the acquisition of accurate answers. Such details are not usually needed when the relative approach is used. When two or more similar cases are compared, small omissions or even simple errors tend to cancel. Therefore, determining what is wanted by employing the relative approach can simplify the modeling task.

Most people have an idea of what they want from an EMI model, but they may not pick the best of several different means to achieve that goal. For example, in many cases the first thing looked for is a calculation of the electric field strength at a given distance, perhaps comparable to the test geometry expected. What may actually be needed is only an equivalent measure of the field strength.

Equivalent measures of the field strength can be determined as circuit or field values. Circuit values, such as the current on a conductor, the voltage between one conductor and another, or the feed point impedance, can be obtained when a structure is modeled as an antenna. Antenna models can also provide close-in electric- or magnetic-field values; however, these are not as easily used to estimate far field strength as the circuit values. The local electric or magnetic fields are of greater importance when coupling from the source structure to other nearby conductors is being considered.

What Is Known about the Problem? The data obtained from any model can be no more accurate than the fundamental data from which the model is built. The first requirement for solving any kind of problem is to gather together all known information. The more that is known about a problem at the beginning, the better positioned the engineer will be to understand the problem and find solutions. Assembling prior knowledge also helps to highlight what information is missing. EMC design is very much the study of parasitics and other stray effects, so it is essential to have a good description of the physical objects involved in the model.

How Can Available Tools Be Used to Solve the Problem? Before commencing construction of a model, it is prudent to consider how the available modeling tools address the problem. The fullest benefits of modeling are obtained when, of several fundamental approaches to using modeling tools, the one most appropriate for a given problem is used. While generic field solvers are available, most tools were developed for specific applications. All tools can be stretched to tackle a wide range of problems, but using each as intended minimizes the risk of getting spurious results.

The focus of this article is back-of-the-envelope calculations, which require fast evaluations of EMI phenomena. The Numerical Electromagnetics Code (NEC)² is an ideal tool for such work and is used here for demonstration. NEC models can be created and run very easily on a portable PC. (More-detailed analyses of the various numerical techniques are provided in the book EMI/EMC Computational Modeling Handbook.)³

EMC Modeling with NEC

The Numerical Electromagnetics Code utilizes the boundary element method, better known as the method of moments (MoM). Developed specifically for antenna analysis, NEC works by solving for the current distribution over a structure. Once the current distribution is known, many separate parameters can be determined. These include the feed point impedance of the antenna, field strength at any point in space, and radiation patterns. For the EMC engineer, the current distribution and input impedance are of particular value.

To create a wire frame antenna model with NEC requires the following steps:

• Define each wire used to represent the problem geometry.
• Define the ground plane, if present.
• Define the frequency range of interest.
• Add the source(s) and any loads.

Problem Geometry. The first step in creating an EMI/EMC model with NEC consists of defining and entering the problem geometry. Surfaces may be modeled as surface patches or wire frames. In general, a wire frame model can be solved in less time than its surface patch equivalent, at a small sacrifice of accuracy. Wire frame models are used almost exclusively for EMI problems because they are easily constructed and provide more than adequate results.

When a wire frame model is constructed, the framework created has to have sufficient detail to allow an accurate representation of the current distribution. In the case of a complex structure, a rectangular wire frame mesh having a density of at least one-tenth wavelength for the highest frequency of interest would need to be used. On the other hand, long wires could be used in place of the mesh to represent attached cables or elements where the current is traveling in only one direction. These long wires must even then be segmented finely to ensure that the current distribution along them can be fully represented.

Ground Plane. The presence of a ground plane is very common in EMI/ EMC measurements and is an important detail that must be included in practical emission models. In studying smaller problems, a perfect, infinite ground plane can be used in place of a module reference plane. This simplifies the model by eliminating the need for adding a wire mesh to represent the module reference plane. The ground plane is readily implemented in NEC and, through the use of symmetry, does not significantly add to the solution time.

Frequency Range. It is important to know the complete range of frequencies for which an NEC model is to be solved. The wire segment size will be defined by the highest frequency of interest; therefore, the same model can be used for perhaps as much as two decades below this frequency. This is often enough for a practical EMI/EMC problem of 30 MHz to 3 GHz. However, wider frequency ranges will call for the use of more than one version of the model so that the optimal combination of required resolution and desired solution time can be achieved.

Sources. In NEC, adding the source or sources is accomplished by replacing one or more of the wire segments with a voltage or current source. Since the MoM technique used in NEC solves for the current distribution on all the segments, it is easy to include lumped circuit values within the model, whether they are sources or loads (R, L, and C).

A Basic Example: Modeling Heat Sinks with NEC

Probably the most common questions needing to be addressed by an EMC engineer during the development of a new product are the type that ask, How much better is A than B? Answers are often based upon previous experience. But there are occasions when further work is needed to enable the implications of problems to be more clearly understood.

One such question concerns variations in EMI behavior among several heat sink options. It was understood that increasing the height made for a better antenna and thus a worse EMI situation. But at what dimensions did this relationship really become a concern? This was an ideal situation for back-of-the-envelope modeling. A highly detailed model was not required. What was needed instead was a baseline understanding of how several heat sinks with different geometries compared over a one-decade frequency range.

Four heat sinks with approximately the same cooling capacity were compared with respect to their antenna characteristics. The heat sinks were all square and had heights adjusted to achieve roughly equal cooling capabilities. Their sizes were 50 x 50 x 100 mm, 60 x 60 x 70 mm, 76 x 76 x 45 mm, and 100 x 100 x 25 mm. The heat sinks were quickly modeled by means of NEC. In order that simple models could be constructed, the physics of the problem had to be thought through and the implications of all necessary assumptions understood.

For this work it was assumed that the RF source was located at the center of the heat sink, that the fins would have little effect, and that the printed circuit module was large in comparison with the heat sink so that a perfect infinite ground plane could be used in the heat sink antenna model. Each of these assumptions could be tested with further models, if necessary. If one or more of the assumptions were found to be false, then the model would have to be upgraded to include the detail missing from the simplest case.

The goal is to have as simple a model as can provide the basic information needed. Unnecessary complexity not only increases the computation time but also makes the model harder to construct. The experience of the EMC engineer is key in producing small, efficient models.

 

Figure 1a. Physical heat sink over a ground plane. Figure 1b. Wire heat sink model.

The actual geometry of the heat sink was approximated by the use of only nine wire elements. Figure 1 shows the simplified model geometry. The NEC input file for one of the heat sink models is shown in Figure 2. It is expected that with such a minimal model the calculated values would not be precise. However, it will be shown that this basic model is acceptable to provide sufficient guidance for heat sink selection.

CM	Heat sink example 100 x 100 x 25 mm
CE
GW	1,3, 0,0,0 0,0.006, .001
GW	2,6, 0,0,.006, -.05,-.05,.006, .001
GW	3,6, 0,0,.006, -;.05,.05,.006, .001
GW	4,6, 0,0,.006, .05,.05,.006, .001
GW	5,6, 0,0,.006, .05,-.05,.006, .001
GW	6,6, -.05,-.05,.006, -.05,-.05,.031, .001
GW	7,6, -.05,.05,.006, -.05,.05,.031, .001
GW	8,6, .05,.05,.006, .05,.05,.031, .001
GW	9,6, .05,-.05,.006, .05,-.05,.031, .001
GS	0 0 1
GE	1
GN	1
FR	0 180 0 0 100 5
EX	0 1 2 01 1.0 0.0
XQ	0
EN
Figure 2. NEC input file for a heat sink model.

The time required to create the first model is perhaps 10 minutes for someone familiar with NEC. Each additional model can be a simple edit to the input file and can be produced even more quickly. The run time for each heat sink model on a 400-MHz Pentium II PC was under 20 seconds.

Other information was acquired from detailed signal-integrity modeling of the VLSI device package. This provided both the magnitude and the impedance of the EMI source that wouldbe driving the heat sink antenna. While the simple model discussed here enabled comparisons between the various heat sink options to be made rapidly, the source data were later combined with a more-detailed heat sink model to more accurately predict the radiation from the heat sink.

A second set of models was created to study the effect of heat sink height alone. In this case, the cross section was maintained at 100 x 100 mm, and heights of 25, 50, 75, and 100 mm were modeled. Since only one parameter, height, was variable, the model provided a much clearer understanding of the effects seen in the previous models where both height and cross section were varied. The same simplified geometry was used as in the previous example.

Results of this modeling are shown in Figures 3 through 6. The resonant frequency of the heat sinks can be seen at the zero crossing on the reactance plots. The higher the radiation resistance at resonance, the more likely a structure is to be an efficient antenna, and to be a source of radiated EMI. Clearly, the tallest heat sink is not only a much better antenna than the other options, but it also becomes a more-efficient radiator under 600 MHz than they are. The importance of this depends upon the spectrum of energy from the EMI source. In this particular example, heat sink height has a much greater impact on emissions than do width and height. Therefore, emissions can be reduced significantly through use of a shorter heat sink.

 

Figure 3. Reactance versus frequency for various sizes of heat sinks.

Figure 4. Radiation resistance versus frequency for various sizes of heat sinks.

Figure 5. Reactance versus frequency for heat sinks of fixed size at various heights.

 

Figure 6. Radiation resistance versus frequency for heat sinks of fixed size at various heights.

A simple spreadsheet set up to perform circuit analysis was loaded with the feed point impedance data along with the source impedance, frequency, and heat sink geometry. This allowed rapid comparison of many parameter combinations. The key parameter required from this spreadsheet was the power dissipated in the radiation resistance, which equates to the total power radiated. Naturally, the goal is to minimize this quantity.

A Real-World Heat Sink Modeling Experience

The basic heat sink example above is based on an actual product design effort involving one of the authors in the early 1990s. EMI concerns arose because the system clock frequency was 400 MHz and a number of large heat sinks were being contemplated. During the project's early stages many suggestions were made and evaluated, including using one very large heat sink for multiple devices and bonding the heat sink to the module reference plane. NEC models were created to address all the suggestions in order to achieve the best synergy of EMC and thermal design.

The real-world heat sink case was more complex than the basic model. The RF source from the VLSI device was not placed symmetrically, and the heat sink and the module reference plane were physically connected. As a result the heat sink did not behave only as a short fat monopole as in the above example, but rather at some frequency it behaved more as a loop antenna with very different characteristics. The modeling done in this case provided a range of heat sink sizes that would not unacceptably increase emissions from the system. Despite the additional complexity of this real situation, a total of perhaps 25 small NEC models provided 90% of the information the design team needed. A couple of more-detailed NEC models were also constructed to verify that the simple models were on the right track.

Conclusion

NEC is a very powerful tool and, in its original IBM punched card/Fortran form, is freely available on the Internet. Also available are several shareware and commercial codes that utilize the NEC core but that also provide graphical user interfaces of various levels of complexity. NEC was written for the purpose of modeling antennas. Since EMC engineers are trying to minimize antenna effects, the match is obvious.

Other low-cost electromagnetic tools available use different numerical techniques, such as the finite difference time domain and the finite element method. These tools often complement NEC, providing a broad range of modeling options.

The availability of inexpensive yet sophisticated modeling tools enables EMC problems to be examined at levels of detail not previously possible. By focusing on small, specific tasks, the EMC engineer can respond rapidly and confidently to the numerous design and "what if" questions raised during product development. With design cycles ever shortening, the importance of products being compliant with regulatory limits on the first pass is increasing. Back-of-the-envelope EMI modeling can be a great tool for achieving this goal.

References