Simple EMC Modelling

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Quite often, simple models are appropriate for design and investigative purposes. For situations where simple modelling is not appropriate, please refer to limitations of simple modelling. Some simple modelling approaches for both application scenarios are now reviewed.

Simple Modelling: EMC Test Scenario

An isotropic antenna radiates power equally in all directions. If the antenna can be assumed to be in free space, then at a distance r from the antenna, the transmitted power is evenly distributed over a sphere of radius r. The surface area of a sphere is given by the formula 4πr². Hence the power density in Watts/m² at a distance r from the antenna is given by the formula:

Pd = Pt/4πr² Equation (1)

where Pt is the transmitted power.

Usually, purpose designed antennas focus the transmitted power into one direction to give an antenna main beam. The focusing of the power gives the antenna gain with respect to an isotrope; the gain is therefore normally expressed in dBi (dB with respect to an isotrope). Equation (1) is therefore normally modified to take account of the gain:

Pd = PtG/4πr² Equation (2)

For EMC purposes field strength is normally expressed in Volts/m for immunity tests or dBµV/m (dB with respect to 1µV/m) for radiated tests. Consequently it is often useful to be able to convert Pd to electric field strength in V/m. Free space has a wave impedance of 120π Ω ≈ 377 Ω. Ohm’s law therefore gives us the relationship:

Pd = E²/120π Equation (3)

where E is the field strength in Volts/m. Substituting equation (3) into equation (1) gives the useful equation:

E = 1/r √(30Pt G) Equation (4)

Equation (4) is of great utility for assessing the threat to electronic equipment and human safety from intentional transmitters of known power and antenna design.

Simple Modelling: Cross-talk

Cross-talk can occur due to mutual inductance Lm, mutual capacitance Cm, or common impedance Zc, as indicated below in Figure 1. Common impedance coupling only occurs when common conductors are used: Zc is an impedance common to both circuits. Any volt drop that occurs in Zc, due to current flow in the culprit circuit, is seen as a driving voltage in the victim circuit.

Figure 1: Lumped parameter circuit cross-talk model

Assuming common impedance is not a problem Lm (the inductive coupling) and Cm (the capacitive coupling) can be modelled using the equivalent circuit shown in Figure 2. The circuit shows that the inductive coupling produces a series noise voltage in the victim circuit whereas the capacitive coupling produces a parallel noise voltage. The signs on the generators show that at the near end capacitive and inductive components add whereas at the far end they cancel.

Figure 2: Cross-talk equivalent circuit

Where:

Determining the mutual inductance and capacitance can be problematic. The mutual inductance, particularly in railway power feed coupling problems is often greatly under-estimated. Mis-calculations of this kind at design stage normally lead to significant problems at commissioning.

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Last Updated: 2004-Oct-21

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