The World of the Near Field

by Tom Lecklider, Senior Technical Editor

When Scotty is beaming up, he’s working in the very far field.

Distinguishing between near field and far field conditions is especially important in EMC testing. Published antenna factors and related calibration data generally are intended for use in far field measurements.

The far field corresponds to an RF source-to-measurement antenna distance (r) great enough that energy radiates from the source only in a radial direction. The E and H fields are mutually perpendicular to that direction and each other, and their ratio is 377 Ω, the impedance of free space.

There is no unique distance beyond which the far field exists and within which near field considerations apply. In general, the equations are complicated that describe how the E and H fields vary radially and angularly with respect to an RF source. However, because the equations include 1/r, 1/r², and 1/r³ terms, it’s possible to ignore those terms that become small for certain ranges of r.

For example, small fractional values of r cause the 1/r³ term to become large. Conversely, for large values of r, the 1/r term may be orders of magnitude bigger than the others. This kind of reasoning results in the definition of three regions: the reactive near field, the radiating near field, and the far field.

In the reactive near field, energy is stored in the electric and magnetic fields very close to the source but not radiated from them. Instead, energy is exchanged between the signal source and the fields. Should a device capable of coupling energy from the fields be nearby, a received signal will be developed by that device. This is the mechanism behind near field radio frequency identification (RFID) tag coupling, for example. A resonant circuit in the tag is tuned to the frequency being transmitted by a nearby antenna and absorbs power from it.

The approximate outer edge of the reactive near field is given by

r = λ/2π                                    (1)

which works well for antennas electrically small compared to a wavelength λ. For electrically large antennas, the reactive near field boundary is better described by

                      (2)¹

where D is the largest dimension of the antenna.

As shown in Figure 1, these two definitions have very different implications. For example, at relatively low frequencies, much larger values of r are associated with equation 1 than with equation 2. On the other hand, for EMC test purposes, transmitting antennas are seldom more than two or three meters in size so in comparison to a wavelength can be considered electrically small up to about 30 MHz.

At the near field RFID 13.56-MHz operating frequency, a wavelength is about 22 m. The antennas you pass at a store entrance are physically large but electrically small compared to 22 m. From Figure 1, the near field extends for approximately 3.5 m. Stores with several entry doors often have a number of RFID antennas spaced across the entry area to give complete coverage because the field intensity falls rapidly with distance from the antenna.²

In the radiating near field, the angular field distribution depends on distance from the RF source unlike in the far field where it does not. Energy is radiated as well as exchanged between the source and a reactive near field. Equation 3 defines the outer boundary of this region for an electrically large antenna:

r = 2D²/λ                                (3)

Figure 1 includes this equation. For electrically small antennas, the radiating near field is minimal if it exists at all. So, the behavior of these antennas can be adequately described by two regions where electrically large antennas may require three.

Above 50 to 100 MHz, the boundary of the near field for electrically small antennas occurs at a smaller distance than for an electrically large antenna. For example, the AR Worldwide Model AT5026 Log Periodic Antenna is designed for frequencies from 26 MHz to 5 GHz and measures 279 × 54 × 202 cm. It can handle input power of 1 kW at 1 GHz.

Compared to the 6-m wavelength of a 50-MHz signal, this antenna cannot be considered electrically small. At 50 MHz, equation 2 gives 2.6 m as the extent of the reactive near field, and equation 3 yields a value of 1.2 m.

As the frequency increases, this antenna will exhibit larger values for the reactive near field distance. This is equivalent to saying that a larger source-to-measuring-antenna distance is required at higher frequencies to obtain far field conditions. At some point, working in the near field may be the only practical solution to EMC testing.

In fact, many antennas are designed to develop very high E fields within the reactive near field distance. For example, the Model HBA-2030 1.37-m Biconical TDK RF Solutions Antenna at 30 MHz and r = 1 m operates in this way. The antenna dimension-to-wavelength ratio is only 0.137, so it behaves like a small dipole with a large electric field. This particular antenna is used to develop very high electric fields and can handle 3.5 kW continuously from 20 to 300 MHz.

Ultrawideband
Conforming to Effective Isotropic Radiated Power Levels
On the right-hand side of Figure 1, the extent of the radiating near field for electrically large antennas is shown for three antenna dimensions: 5, 10, and 20 cm. At frequencies in the 10-GHz region, an antenna would need to be no more than a few millimeters long to be considered electrically small. At the frequencies used in ultrawideband (UWB) transmissions, antennas usually are treated as electrically large with their far field boundary following equation 3.

Also, because of recent FCC regulations that severely limit the effective isotropic radiated power (EIRP) per unit bandwidth of a UWB DUT, the available power in the far field is small. In Testing UWB, an article in the May and June 2005 issues of EE-Evaluation Engineering, the author discussed the difficulties associated with making a UWB measurement at 1 GHz.

The received signal from a DUT with an emission limit of -63.3-dBm EIRP is equivalent to 32 dBµV/m at 3 m, the ANSI C63.4-2003 measurement distance. At 1 GHz and with a 1-MHz resolution bandwidth, a good spectrum analyzer may have a noise floor of approximately 17 dBµV. A 10-dB margin above the noise floor cannot be achieved for this signal without using a preamplifier with a gain of about 30 dB.

The detection limit is given by the sum of the noise floor, the antenna factor, cable losses, and the 10-dB margin. In this case, the limit = 17 dBµV + 27.3 dB/m + 2 dB + 10 dB = 56.3 dBµV. Obviously, this situation won’t work because the 10-dB detection level is 24 dB higher than the actual signal, hence, the need for the preamp.³

A commercial antenna that covers the 200-MHz to 2-GHz range is the ETS-Lindgren Model 3106 Double Ridged Waveguide Horn Antenna with an antenna factor of about 23 dB (1/m) at 1 GHz rising to over 30 near 2.0 GHz. So-called standard gain horn antennas are available from several manufacturers and feature a lower antenna factor, meaning they have increased gain compared to a wideband horn antenna but over a much narrower band. However, in the UWB EIRP example, even if the antenna factor were 15 rather than 27.3, a 20-dB gain preamp still would be required.

For comparison, the A. H. Systems Model SAS-580 Standard Gain Horn Antenna covers the frequency range from 1.12 GHz to 1.70 GHz and has a constant antenna factor of 18.2 dB (1/m). Its gain varies from 13 to 15 dB while the wideband Model 3106 gain is between 8 and 10 dB.

The 18.2 dB (1/m) notation and that used in the UWB EIRP discussion, 27.3 dB/m, both relate to field strength measured per meter. For example, the FCC has provided a formula to convert from field strength at a 3-m measurement distance to dBm EIRP: dBm EIRP = dBµV/m – 95.2. Because the antenna factor is referenced to a per meter field measurement, the four logarithmic terms added to obtain the overall 56.3-dBµV-signal level really are dimensionally consistent.

At higher frequencies, even adding a preamp may not make 3-m measurements possible because of unavoidable receiver noise levels. In a paper titled “On Measurements for EIRP Compliance of UWB Devices,” the authors examined the measurements necessary to prove EIRP compliance of UWB devices above 10 GHz. They concluded that for a DUT of any practical size, measurements must be made in the near field.

The relationships among DUT size, allowed EIRP power level, the near/far field demarcation, and frequency are shown in Figure 2. Considering the 20-cm, EIRP = -61.3 dB line, at 10 GHz it has a value greater than 1 on the vertical axis. This means that the measurement distance Rmeas can be greater than the far field distance RFF and still detect the signal 6 dB above the theoretical noise floor of a perfect receiver. From Figure 1, it can be seen that for a 20-cm maximum source dimension at 10 GHz the far field begins 2.7 m away.

Conversely, following the same 20-cm line in Figure 2, at 20 GHz, accounting for only the theoretical receiver noise level, the EIRP signal level cannot be detected in the far field. From Figure 1, the far field begins at 5.3 m. This measurement and any others that fall below the R_meas/R_FF = 1 line must be made in the near field.

An interesting question related to near field operation is “how fast is the electric field attenuated in the near field?” The authors described an experiment in which the E field associated with several different types of antennas was measured at distances from a few centimeters to 3 m. The results are found in Figure 3.

These curves show that near field measurements made on DUT sources resembling any of the four types of tested antennas can assume a 20-dB/decade rate of attenuation with distance up to about R_meas/R_FF = 0.6. A patch antenna deviates considerably for closer source-to-measurement antenna distances, followed by a standard gain horn and open-ended waveguide. The goal of the investigation was to determine an upper attenuation rate, and it’s clear that none of the simulated source configurations falls off faster than 20 dB/decade up to about R_meas/R_FF = 0.3.

As the authors commented, “This means that a reasonable estimate for the EIRP of a known radiator can be formulated. However, a general near field attenuation rate for an unknown radiator does not exist, and thus direct determination of DUT EIRP cannot be guaranteed…the field attenuation rate within [the near field] is a strong function of radiator type. While application of measured field attenuation rates can be performed for devices with a known radiating structure, the question still remains as to which near field attenuation rate should be required for use when computing the EIRP of an unknown DUT.”⁴

UWB Antenna Development
As part of a cancer detection system, an array of small UWB antennas is used to sequentially transmit low-power pulses. The backscatter signals from the patient’s body are processed to produce an image of backscattered energy as a function of location. Different tissue densities alter the image.

Key to this project was development of a low-cost miniature UWB antenna, which was undertaken by students in the University of Wisconsin Department of Electrical and Computer Engineering. They elected to perform both computer simulations and physical experiments on a modified version of a wideband double-ridged horn antenna.

One of the ridges was replaced by a curved, tapered metal plane terminated by two 100-Ω resistors. While the remaining ridge is electrically part of the outer, grounded pyramidal shell, the curved plane is isolated from the shell. Driven directly from a 50-Ω coaxial feed, the antenna design eliminates the need for a balun. In addition, the outer shell acts as a ground plane, confining the main beam of the radiation pattern to the opening of the horn.

Intended to cover the 1- to 11-GHz frequency range, the diminutive horn antenna is shown in Figure 4. Both numerical characterization of a finite-difference time-domain (FDTD) antenna model and physical tests on actual metal models indicated that the voltage standing wave ratio (VSWR) was less than 1.5:1 over the entire frequency range. In addition, the antenna’s fidelity, defined as the maximum magnitude of the cross correlation between the observed and ideal responses, ranged from 0.92 to 0.96 over a 180° angular span centered on the boresight.

To determine radiation patterns, two antennas were placed 300 mm apart, one attached to a 6-GHz RF source and the other to a measuring receiver. Referring to Figure 1, the 2.5-cm dimension of the antenna corresponds to a far field distance of 4.2 mm at 1 GHz or 42 mm at 10 GHz. In either case, the 300-mm measurement distance is indeed in the far field.⁵

In this scanning application, the antenna dimensions were constrained by the need to fit several antennas within a limited size array. In this case, the antenna aperture is much less than a quarter wavelength at 1 GHz, so you would expect the efficiency to be low.

Summary
For many EMC test situations, the demarcation between the far field and near field is clear. In these cases, testing is relatively straightforward. Where it’s possible to obtain far field conditions, it makes sense to do so.

On the other hand, understanding how the reactive and radiated near field and the far field antenna behaviors differ can only help ensure accurate measurements. Should test results appear inconsistent, it may be that near field effects are manifesting themselves. And, in some immunity tests involving extremely high fields, it is intended that the DUT be positioned in the near field.

UWB testing is problematic because of the low signal levels and wide bandwidths involved. A narrowband signal of similar amplitude would be relatively easy to work with because the receiver noise within a small bandwidth is much smaller than in the cited 1-MHz example. This is an area that no doubt will see refinements in test methods and equipment as UWB applications are further developed.

References
1. McLean, J., et al, Interpreting Antenna Performance Parameters for EMC Applications, TDK RF Solutions, www.tdkrfsolutions.com/antennas.htm
2. Tutorial Overview of Inductively Coupled RFID Systems, UPM Rafsec, 2003, www.rafsec.com/rfidsystems.pdf
3. Gubish, R., “Testing Ultrawideband,” EE-Evaluation Engineering, May, pp. 60-69, and June, pp. 58-61, 2005.
4. Brunett, J. D., et al, “On Measurements for EIRP Compliance of UWB Devices,” Proceedings of the 2005 IEEE International Symposium on Electromagnetic Compatibility.
5. Li, X., et al, “Numerical and Experimental Investigation of an Untrawideband Ridged Pyramidal Horn Antenna With Curved Launching Plane for Pulse Radiation,” IEEE Antennas and Wireless Propagation Letters, Vol. 2, 2003, www.engr.wisc.edu/ece/faculty/hagness_susan/li_IEEEAWPL_03.pdf

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