There are a number of electromagnetic modelling techniques which can be used to perform the EMC full wave modelling.

Generally, boundaries to the problem space must be set and all techniques require some form of discretisation, either of the whole problem space, or for some techniques just the bodies in the problem.

Discretisation means that the problem geometry is broken into many small cubes, rectangles or
some other convenient shape, normally referred to as nodes. If small complex geometries are in
the problem then the discretisation will be very fine to capture the shape of the object. Also, as
the frequency of interest increases then the discretisation must become correspondingly fine. The maximum
discretisation mesh pitch must be kept electrically short. The mesh pitch is electrically short providing
it is not greater than λ/10, where λ is the wavelength, and
λ = c/f, where c is the speed of light (3×10^{8}m/s) and f
is the maximum frequency of interest in the model.

As the discretisation becomes finer (more nodes in the problem), the time taken for the computer to achieve a solution increases. This leads to a significant practical problem: on the one hand fine detail and high frequency solutions are required leading to discretisations of typically just a few mm pitch; on the other hand problem spaces must have dimensions in excess of 10m to accommodate typical EMC test distances. Most methods require a reasonably cuboid problem space (ie long tubular problem spaces solve incorrectly). Consequently, a compact problem space might be 10m×10m×5m; if this is then discretised using a 5mm mesh (quite large for many problems) then the problem space is broken into 4 billion nodes. This is far too many for contemporary computers to solve in a practical amount of time.

To overcome these problems, packages with the appropriate level of sophistication have only become available in the last couple of years. The package used by YES is Flo/EMC [5]. Flo/EMC has many work-around features to overcome the discretisation problem. One major feature of the package is variable meshing; this allows areas of the problem space consisting of free space only to be discretised with a much coarser pitch than areas which require a fine pitch.

An example of the application of variable meshing is shown in Figures 3 and 4. Figure 3 shows a balise antenna (in pink) attached to a bogie on the underside of a train body. The mesh in the region of the antenna must be very fine. Figure 4 shows how the variable meshing creates a fine mesh in the region of the antenna, a much coarser mesh is used elsewhere.

The second major method used by Flo/EMC, to overcome the discretisation problem, is the use of equivalent circuit currents. Using this approach the whole problem space is no longer discretised, instead only the portion of the problem space immediately around the equipment under investigation. In this way, both the total number of nodes in the problem and hence the solution time are greatly reduced. An example of the application of the equivalent circuit currents feature is given in Figures 5, 6 & 7. Figure 5 shows a 0.6m cube designed to investigate emissions patterns from equipment at frequencies above 1GHz. The maximum emission frequency of the EUT (Equipment Under Test) was 6GHz. To model an EUT at 6GHz is a difficult problem because the maximum dimension of the mesh pitch for the discretisation must be kept electrically short. At 6GHz the maximum dimension is therefore 5mm, consequently the variable mesh pitch approach described in the previous balise antenna example is of little use.

Figure 6 shows the portion of the problem space that was discretised when using the equivalent circuit currents approach. The light blue line shows the outer dimensions of the 0.6m cube EUT, the dark blue lines show internal detail and the light brown line shows the volume that was discretised. It can be appreciated that the discretised cube, delimited by the brown line is only a few centimetres larger than the 0.6m cube EUT shown by the light blue line.

The equivalent circuit current method allows the field strengths at a defined distance to be calculated from the currents flowing at the boundary of discretisation. Shown in Figure 7 are the field strengths at 6GHz, calculated over a 3m radius cylinder of 1m height, emitted by the 0.6m cube EUT.

When transmission lines are electrically long, the lumped circuit model must be broken into electrically short
sections. This makes a distributed or per unit length model. The modelling is then normally referred to
as **Multi-Conductor Transmission Line** modelling. The techniques are well documented and
require the solution of systems of matrix equations. This is achieved at YES by using MATLAB [6]. The techniques are broadly the same for any system of coupled transmission lines. A good
general coverage of the subject is given by Paul [7][8].
The techniques are widely used in the railway industry and a good railway specific coverage of the subject is given
in a series of guidelines produced by the CCITT [9][10][11];
these include information on how booster and auto transformers should be included in the model.

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- , www.floemc.com [back]
- MATLAB, www.mathworks.com [back]
- Clayton R Paul, “Introduction to Electromagnetic Compatibility”, Wiley (ISBN: 0471549274) [back]
- Clayton R Paul, “Analysis of Multiconductor Transmission Lines” Wiley (ISBN: 047102080X) [back]
- CCITT Directives Vol II, “Calculating Induced voltages and currents in practical cases” [back]
- CCITT Directives Vol III, “Capacitive, Inductive and Conductive Coupling: physical theory and calculation methods” [back]
- CCITT Directives Vol IV, “Inducing-currents and voltages in electrified railway systems” [back]

Last Updated: 2004-Oct-21