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.

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:

Equation (1)

where P_{t} 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:

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 P_{d} 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:

Equation (3)

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

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.

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

Assuming common impedance is not a problem L_{m} (the inductive coupling) and C_{m}
(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.

Where:

- L
_{m}= per unit length mutual inductance of circuits (µH/m) - L = coupled length of circuit (m)
- C
_{m}= per unit length mutual capacitance (pF/m) - ω = radians per second, ie 2πf
- I = current in culprit circuit
- V = voltage between conductors in culprit circuit
- R
_{NE}= Near End load resistance - R
_{FE}= Far End load resistance - V
_{NE}= Near End noise voltage - V
_{FE}= Far End noise voltage

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