When an alternating voltage generates an alternating current through a network of conductors, an electromagnetic (EM) wave is generated which propagates away from the source as a combination of E and H fields. Near to the radiating source the geometry and strength of the fields depend on the characteristics of the source (dominant current in a loop, or dominant voltage across a dipole); further away only the orthogonal components of the two field types remain.

Any typical electrical product consists of a collection of radiating current loops and voltage dipoles; near to these structures we find a complex field distribution made up of many different E and H fields. This is the near field. As the observation point moves away from the source, so these decay at different rates, and the total field eventually resolves itself in the far field into the “plane wave”, so called because its E and H field vectors lie in a plane which is at right angles to the direction of propagation. The laws which govern the field structure in this way are given by Maxwell’s field equations.

Field strength due to a radiating antenna

A simple equation to derive the field strength at a distance d metres in free space due to an antenna of gain G relative to an isotropic radiator radiating a power P watts is

E             =          √(30 · P · G)/d  volts per metre          (1)

Imagine that the power being radiated from an antenna spreads out equally in all directions (isotropically) into a sphere around it. Then the power density at any given distance from the antenna will be spread out over the sphere’s surface. Thus the power density will be inversely proportional to the surface area of the sphere, which is in turn proportional to the square of the distance. The field strength is proportional to the square root of the power density, so it must be inversely proportional to distance.

Since a real antenna is not isotropic, the gain of the antenna is included to allow for concentration of power in a particular direction. The equation above assumes that the field is measured in the direction of maximum radiation from the antenna.

The wave impedance

The ratio of the electric to magnetic field strengths (E/H) is called the wave impedance. In the far field, d > λ/2π, the wave is known as a plane wave and its impedance is equal to the impedance of free space given by

Z₀  =  √(μ₀/ε₀)   =    120π          =      377Ω
where μ₀ is 4π . 10^-7 H/m
and ε₀ is 8.85 . 10^-12 F/m

In the near field, d < λ/2π, the wave impedance is determined by the characteristics of the source. A low current, high voltage radiator (such as an open-ended rod or monopole) will generate mainly an electric (E) field of high impedance, while a high current, low voltage radiator (such as a loop) will generate mainly a magnetic (H) field of low impedance. Measurements made in the near field can observe either E or H fields, but do not accurately represent the total interfering capability of a product. This is the main reason why near-field probing, although useful for diagnostics, does not predict the compliance of a product.

The region around λ/2π, or approximately one sixth of a wavelength, is the transition region between near and far fields.

As well as affecting the outcome of field measurements, the wave impedance is important for another reason: it affects the shielding effectiveness of a conducting barrier, since the shielding effectiveness is partly determined by the ratio of barrier impedance to the impedance of the impinging wave.

Rayleigh near field

There is another definition of the transition between near and far fields, determined by the Rayleigh range. This has to do not with the field structure according to Maxwell’s equations, but with the nature of the radiation pattern from any physical antenna (or equipment under test) which is too large to be a point source. For the far field assumption to hold, the phase difference between the field components radiated from the extremities of the antenna must be small and therefore the path differences to these extremities must also be small in comparison to a wavelength. This produces a criterion that relates the wavelength and the maximum dimension of the antenna (or EUT) to the distance from it. Using the Rayleigh criterion, the far field is defined as beyond a distance:

d          >          2D²/λ

where D is the maximum dimension of the test object (d, D and λ in the same units).

The figure shows a comparison of the distances for the two criteria for the near field/far field transition for various EUT dimensions and across frequencies. Note how for typical EUT dimensions the Rayleigh range determines the far field condition above 100–200MHz.

Try your own calculation for field strength from a radiating antenna, based on equation (1):

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