Intermediate Level Modelling for EMC : Principles

Here we outline some of the principles of intermediate level modelling. Examples of results are shown in the "examples" frame following.

An Enclosure with an Aperture

Enclosure with an Aperture

The Figure above shows a typical shielding problem - a box with an aperture. It can be considered as a waveguide (red), terminated at one end with a short circuit (the back of the box - green) and at the other with an aperture (blue). As far as the incident field (orange) is concerned we use a Thévenin equivalent circuit with an impedance corresponding to the intrinsic impedance of free space (377 ohm). The modelling of the slot is more problematic. We reason that an incident field will induce signals, which propagate along the length of the slot in a manner similar to propagation on a transmission line. The parameters of this line are those of a coplanar strip transmission line. Thus the slot in this model is simply a transmission line shorted at both ends (the ends of the slot).

To find the electric field shielding we need to compare the incident voltage to the voltage at the desired location inside the waveguide (or equivalently along the TL). The magnetic field shielding can be similarly obtained by comparing currents at the corresponding locations. By adding some loss to the waveguide propagation (i.e. specifying the Q-factor of the enclosure) we can represent the effect of the loss due to the contents of the enclosure. The equivalent circuit model is shown below.

Equivalent circuit of enclosure with aperture
Equivalent circuit of an enclosure with an aperture illuminated by a plane wave

Try our online shielding calculator which demonstrates the above model!
 
Considering Enclosure Contents

Enclosure contents can be considered by extending the simple circuit model. Small Loops, such as those on printed circuit boards, and in wiring looms, can be considered as inductances coupled to the transmission line model. For larger loops such as those represented by longer PCB tracks and looms, we must also consider the capacitive coupling and the fact that the coupling is distributed in nature, so the probem becomes one of coupled transmission lines. The inductances and capacitances can be calculated using simple closed form expressions.
The effect of whole PCBs with, or without  ground planes can also be considered but the cacluation of equivalent circuit elements requires further work.

Enclosure with loops

Enclosure with two loops

Equivalent circuit of box with loops
Equivalent circuit for enclosure with two loops

Wire Penetrations

A simple equivalent circuit for monopole and dipole antennas gives good results for wires, inside and outside an enclosure beyond their quarter-wavelength resonance.

Improving Accuracy

The accuracy of the models can be improved by including higher order waveguide modes.

Equivalent circuit for monopole
Monopole/Dipole equivalent circuit

Applied Electromagnetics and Electron Optics Research, Department of Electronics, University of YorkResearch in the Department of Electronics, University of YorkThe University of YorkThe University of York