For conformance and compliance, electromagnetic compatibility (EMC) and antenna performance testing, it is crucial to know the nuances of electromagnetic (EM) radiation from an antenna at given distances from the antenna aperture. This is important because the EM signal from an antenna behaves differently at various distances from the antenna, and if not properly accounted for, can result in substantial measurement errors. This is because there are three main regions where the EM radiation behaves differently as a function of distances away from an antenna: the reactive near-field, the radiating near-field/Fresnel Region and the far-field/Fraunhofer Region.
The majority of specifications are designed and written for testing an antenna in the far field, which requires a test engineer to know how far away from a given antenna the test antenna must be placed. Additionally, the different antenna types and sizes require different calculations to determine the boundary between these regions. Different applications present different methods of calculating when the far-field begins.
This paper aims to educate those new to the concepts of antenna field regions and help readers to understand the calculations involved in determining the boundaries between the various regions.
It is important to note that the transitions between the three regions are not distinct but are instead gradual. Hence, determining the field region’ boundaries has resulted in several different methods, mainly the electric dipole/elemental magnetic loop, wave impedance, antenna characterization method and wave’s phase front method.
There are a wide range of near-field to far-field transformation approaches and theories, which are beyond the scope of this paper.
Where I is the current in the wire, l is the length of the wire in meters, Beta is the electrical length of the dipole per meter of wavelength, ⍵ is the angular frequency as radians per second, 𝜺_0 is the permittivity of free space, 𝜇_0 is the permeability of free space, Θ is the angle between the axis of the zenith wire and the point of observation, f is the frequency in hertz, c is the speed of light in free space, r is the distance between the source and observation point in meters, 𝜼_0 is the free-space impedance, and j is the complex number imaginary term designator commonly used by electrical engineers.
Similarly, the element magnetic loop can be derived as (SK Schelkunoff method):
The definitions of the terms are the same as from Equations 1, 2 and 3. It can be observed that the terms in the above equations include 1/r, 1/r^2, and 1/r^3. From this, it can be concluded that while r<1 the 1/r^2 and 1/r^3 terms dominate, but as β*r exceeds 1, the value of these terms rapidly declines. Hence, in the near-field the 1/r^2 and 1/r^3 terms dominate in the field equations; however, the 1/r term is still present. This term then dominates the further away the observation point is from the radiator, for instance the far-field.
Hence, a boundary between the near-field and the far-field could be designated at points at which the 1/r^2 term and 1/r term are equal, noting that the 1/r term will be dominant at every distance further than this point.
results in , which is a commonly used definition for the near-field and far-field boundary. However, this is only one method of which several others exist for their utility in various applications.
To calculate this, the ratio of Equation 1 to Equation 2 can be derived as:
And the ratio of Equation 4 to Equation 5 can be derived as:
From these equations it can be observed that the two boundaries and three regions can be estimated. Therefore, these regions can roughly be designated as:
However, the boundaries between these regions may change based on the designer’s preferences and the demands of a given application.
By omitting the 1/r^2 and 1/r^3 terms, then Equation 3 can be rewritten as: FORMULA Where r’ is FORMULA for the close case, and FORMULA for the far away case. In the far-field, the term r’-zcos(theta) reduces to ~r, which results in a simplification of the preceding equation, with the exception of the r’ term in the exponent, which represents the phase effect — very sensitive to small variations in separation distance. Choosing a phase difference that produces acceptable errors, sometimes given as pi/8 of the wavelength results in: FORMULA and FORMULA Choosing the boundary definition in this case depends on the chosen references, or even MIL-SPEC — MIL-STD-449 and MILSTD- 462, specifically.
Using Figure 1, the following equations can be derived from a triangle with hypotenuse = r+𝚫*r, adjacent side = r, and opposite side = z/2, where z = one half the antenna length of the receiving antenna, l.
𝚫r is typically chosen in terms of a fraction of a wavelength that produces phase errors at the minimum tolerance level for a given application. If a path difference of less than ⅛ the wavelength at a given frequency is chosen, or the highest applicable frequency as that would result in the lowest phase error, then the previous equation reduces to approximately the length of the receiving antenna divided by the wavelength. Using the Rayleigh Criterion for 𝚫r results in an r term approximated as two times the length of the receiving antenna divided by the wavelength, which is as derived previously in the antenna characteristics method.
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