# (Re)Discovering the Lost Science of Near-Field Measurements, Part 3

This is the third part of our article “(Re)Discovering the Lost Science of Near Field Measurements.” Part 1 of this article (see In Compliance Magazine, July 2023) explained what near and far field measurements entail, and that one-meter measurements are very much near field. Part 2 (In Compliance Magazine, August 2023) explained the evolution of the earlier 12” and present-day one-meter separation measurements, considerations in antenna selection, the difference between antenna-induced and field strength limits, and the evolution from one to the other. This third part investigates practical problems arising from the misapplication of field intensity and far-field concepts to near-field phenomena.

## Practical Problems Arising from the Use of Field Intensity Limits in the Extreme Near Field23

The term “extreme near field” has a specific quantitative meaning in this context. It means that the transmit-receive antenna separation is of the same magnitude as its physical aperture, or less. In the case of radiated emission measurements made one meter away from a test sample with 1.5 m or longer attached cables, not even the Hertzian dipole equations suffice to describe the near field. The Hertzian dipole field equations only apply when the separation distance is much larger than the radiating structure dimensions.24

SAE ARP-958 uses the physical model of two identical antennas in each other’s far field (Friis equation) to calculate an “effective” gain at one-meter separation. This is an effective gain because the antennas are in each other’s extreme near field. Therefore, the antenna factor so derived is only valid for measuring the field at that distance, and the standard of value is that antenna’s response to its own field at that distance. There is no particular value to comparing the “field intensity” measured by (for example) a biconical to the field intensity that biconical would see from another biconical a meter away. In fact, it is quite harmful in that there is an unspoken (and incorrect) assumption on the part of many EMC engineers that the field intensity measured at one-meter separation is scalable in some prescribed manner so as to be able to predict what the measured field intensity would be at another distance.

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### A Dash of Maxwell’s: A Maxwell’s Equations Primer – Part One

Solving Maxwell’s Equations for real-life situations, like predicting the RF emissions from a cell tower, requires more mathematical horsepower than any individual mind can muster. These equations don’t give the scientist or engineer just insight, they are literally the answer to everything RF.

Figure 8 presents data gleaned from an old EMCO catalog. The same sort of information may be found on the ETS‑Lindgren website antenna page.25 If one-meter “field intensity” measurements were scalable, the antenna factors would be identical. Now proponents of field intensity measurements and one-meter antenna factors will rebut the use of such data, saying that one- and three-meter antenna factors are measured differently. And this is true, but it is not fundamental.

What is fundamental is that the assumption that extreme near-field intensity measurements are scalable violates one of the most fundamental laws of physics, namely the conservation of energy or power. And only some high school physics and algebra is necessary to comprehend this.

Based on the diagram of Figure 9, the Friis equation may be written as:

PR/PT = GT GRλ2 / (4πr)2

The Friis equation assumes that the separation distance places the antennas in the far field. In that asymptotic condition, the gain values are independent of separation, which is what makes far-field antenna calibration useful. But two elementary observations are apparent:

The left-hand side ratio is bounded by unity, and in practice will always be less than unity, or 0 dB; and

The right-hand side increases without bound as the separation decreases unless the gain values decrease commensurately.

The inescapable conclusion is that in close, gain is in fact a function of antenna separation. While gain or antenna factor asymptotically approaches a fixed far field value, this means nothing when the antennas are closer in than that.

Assuming half-wave dipoles (far field gain = 1.64 numeric, 2.15 dBi), one may solve the Friis equation for the distance at which the left-hand side ratio is unity, or 0 dB.

r = 0.13λ, or

r = D/4

where D is the half-wave dipole length

This is a purely theoretical construct that just says the gain must roll off at closer separations than this. Of course, the gain begins to roll off well before this calculated separation. The measured received power levels plotted in Figure 10 were taken using the set-up of Figure 9, with separation “r” variable between 2 meters and 30 cm. Two different frequencies were evaluated: 400 MHz (λ = 75 cm, D = 37.5 cm) and 1 GHz ((λ = 30 cm, D = 15 cm). Figure 10 shows measured vs. theoretical far field PR/PT ratios as a function of separation distance and wavelength. An inspection of Figure 10 shows that long before the far field calculation of received power shows it equal to transmit power, the response has rolled off.

There are complicating factors involved in the close placement of two wire-type antennas, which include dipoles and biconicals. In very close proximity, there is capacitive coupling with which to contend and, above a ground plane, inductive coupling. Further, the direction of energy flow away from the antenna is different close to the antenna than farther away. Schelkunoff and Friis pointed this out long ago.26 Figure 11a is copied from Reference 26 and shows the direction of energy flow (Poynting vector) away from the antenna element as a function of distance along the quarter-wave long antenna element itself and as a function of distance from the antenna. While the mathematics behind Figure 11a are complex, the notional Figure 11b drawing of the electric and magnetic fields from such an antenna provides an intuitive grasp.

The exact same effect is seen with higher gain antennas: gain derates rapidly from the far field values at separations less than a tenth of the far field distance (2D2/λ).27 Figure 12 is copied from Reference 27 and shows gain derating for both dish and horn aperture-type antennas. Figure 12 is used in the following manner.

Power density or equivalent field intensity is calculated using the far field gain at the 2D2/λ far-field boundary. Then the appropriate curve is followed inward to the Fresnel zone distance of interest. Here there are no complicating near-field effects from capacitive or inductive coupling, and the quasi-static and inductive regions are contained well within the antenna feed point or phase center. They do not propagate down the waveguide to reach the antenna aperture itself.

The Reference 27 handbook citation is not the origin for this work. It goes back over sixty years and is hardly new.28

The fourth and final installment of this article will list theoretical misunderstandings arising from the erroneous substitution of field intensity for antenna-induced concepts and show the serious practical results of these theoretical mistakes.

## Endnotes

1. One prominent physicist refers to what the author terms the “extreme near field” as “inside the dipole.”
2. A complete mathematical treatment may be found in a companion article in this magazine issue, entitled “Journey To The Center Of The Dipole.”
3. https://www.ets-lindgren.com/products/antennas?page=Products-Landing-Page
4. Schelkunoff, S.A. & Friis, H.T. Antennas, Theory and Practice, John Wiley & Sons, Inc. 1952.
5. NAWCAD TP 8347, Electronic Warfare and Radar Systems Handbook, October 2013
6. Hansen, R.C., and Bailin, L.L., “A New Method of Near Field Analysis,” IRE Transactions on Antennas and Propagation, December 1959.

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