32nd URSI GASS, Montreal, 19–26 August 2017

Antenna Measurements through Planar Near Field Apparatus: An Educational Paradigm LinkingElectromagnetic Theory, Sampling Techniques, and FFT

Yahya Rahmat-Samii and Joshua M. Kovitz(1) Electrical Engineering Department, University of California Los Angeles

Los Angeles, CA, USA http://www.antlab.ee.ucla.edu

AbstractIntegrating antenna pattern measurements in the class-room offers many captivating insights about electromag-netic fields that is visually appealing to young scientistsand students. In particular, the planar near-field measure-ment techniques allow instructors to connect to fundamen-tal knowledge about antennas. Challenging concepts be-come immediately a hands-on discussion while providingstudents an important application of fundamental electri-cal engineering and electromagnetic theories. Our table-top bipolar apparatus also brings out a discussion on thechallenges of measurements at high frequencies, such asmmWaves, where cable movement and flexing can causesignificant errors. This paper suggests planar near-fieldmeasurements as an educational paradigm linking electro-magnetic theory, sampling techniques, and FFT.

1 Introduction

Antenna pattern measurements is an exciting area to aidwith student teaching and inspiration. Among various an-tena pattern measurement techniques, near-field measure-ments have everything that an instructor would hope toinclude in a stimulating educational experience. A com-plete experience with near-fields would engage studentswith deep electromagnetic theories, tradeoff studies, en-gineering practice, design principles, and a little glamourfrom the robotics, laser positioning metrology, and visuallyappealing absorber. Among the three spherical, cylindrical,and planar near-field techniques, the class of planar tech-niques make for a complete and easy-to-access discussionin a lecture. The advantage is that planar near-field tech-niques can employ the Fast Fourier Transform (FFT) basedon the Fourier transform relationship between planar near-fields and antenna far-fields. The Fourier transform is oftenmore accessible for undergraduate and graduate students tovisualize, and even students interested in signal processingcan get a strong feeling about electromagnetic fields.

In this paper, our hope is to encourage readers, instructors(future and current), and mentors that planar near-field mea-surements can provide a holistic educational experience forstudents. We will focus on our bipolar near-field cham-ber that was developed as a tabletop anechoic chamber formmWave measurements at UCLA [1, 2], but these experi-ences can be easily applicable for plane-polar and plane-

AUT Radiates

Measure Fields ina Bipolar Grid(Both Magnitude and Phase)

Use OSI toInterpolate to Recatangular Grid

Use FFT to Compute Far Field Patterns

OptimalSamplingInterpolation (OSI)

Fast Fourier Transform (FFT)

Key Steps in Measurement

RF laboratory engineering practices

and antenna design

Shannon's Sampling Theorem

applied to radiated fields

Numerical techniques

for effective interpolation

Education Value

Fundamentals of FFT, surface

equivalence, and far-field relationship to

near-fields

Figure 1. Illustration of the steps used to measure an an-tenna far-field pattern with a planar bipolar near-field cham-ber. The corresponding educational component for eachkey step in the measurement process is also illustrated.

rectangular chambers as well. By integrating this materialinto regular classroom lectures, potentially more studentscan get excited about antenna radiation metrology, whichinvolves expertise beyond electromagnetics. We also pro-vide an example where we show the step-by-step imple-mentation being executed for a measurement.

2 Relating Pattern Measurements to theFundamentals

Antenna metrology is an interesting area because it involvesfundamentals from many areas within electrical engineer-ing. Figure 1 highlights the educational component thateach step within an antenna near-field measurement pro-vides in the context of a bipolar chamber [1, 2]. In this sec-tion we walk step-by-step through each major educationalcomponent and discuss how instructors can relate the mea-surement experience with an application of electrical engi-neering and electromagnetics fundamentals.

2.1 AUT Positioning and Good Lab Practice

The first step in conducting a near-field measurement is thephysical set up. This is possibly the most important andchallenging step within the entire measurement process.

Open Ended Waveguide

(OEWG) Probe

Antenna Under Test

(AUT)

(a)

(b)

Figure 2. (a) Tabletop bipolar anechoic chamber to helpstudents visualize and understand radiated electromagneticfields from a variety of antennas like horns, arrays, etc.(b) Magnified view of an example antenna under test(AUT), which is a spline-profiled horn antenna from [3].

Poor alignment and positioning errors can lead to notice-able phase errors in the near-field, resulting in dramatic er-rors in the far-field. This step provides an opportunity forinstructors to discuss the operation of robotics equipmentand stepper motors. It also provides an opportunity for stu-dents to get creative when developing brackets and posi-tioning equipment. For our particular example in Figure 2,the students opted to 3D print the bracket. While plastic 3Dprinting methods do not provide the best resolution, it madefor a nice educational moment where students satisfied theircuriosity in fabricating important engineering designs using3D printers.

Another learning component in this step is the proper us-age of sensitive RF equipment. At this point, instructorscan incorporate good RF engineering practices into the labdiscussion, where proper handling of coaxial cable, connec-

tors, antenna probes, and connector mating can be stronglyemphasized. Students also get a chance to learn how to usevaluable equipment such as spectral analyzers, RF powermeters, and vector network analyzers (VNA’s). In near-field

Figure 3. Near-field chambers require both magnitude andphase values, necessitating the use of high-performanceVNA measurements.

measurements, VNA’s are employed because both magni-tude and phase information is needed to perform the near-field to far-field transformations in post-processing. Ourtabletop bipolar anechoic chamber is connected to an Agi-lent PNA-X 5247A, as shown in Fig. 3, which can measurewell into the mmWave bands with this configuration.

2.2 Shannon’s Theorem and Radiated Fields

With the physical measurement setup complete, the nextimportant question is in the sampling locations for the elec-tric fields. The bipolar configuration uses two rotationalstages to position the probe. In Figure 4, we illustrate thesampling locations with respect to the bipolar coordinates(β ,α), where the AUT rotation determines α and the bipo-lar arm rotation determines β [1, 2].

(a) (b)

Figure 4. (a) The bipolar measurement configuration usestwo rotational stages to position the probe, where α is con-trolled by rotating the AUT, β is controlled by rotating thebipolar arm. (b) Illustration of the bipolar coordinates β

and α . The sample intervals ∆β and ∆α are important todetermine for proper sampling. Figures adapted from [1].

Ultimately, we are sampling the electric field (magnitudeand phase) in discrete points in space, with the hope to as-certain all pertinent information about those fields. Shan-non’s theorem tells us that perfect reconstruction from a

sampled function can only occur when the original func-tion is bandlimited. In this respect, there are two importantconsiderations to be understood. First, the far-field radia-tion patterns are computed from a Fourier Transform of thenear-field data, allowing the use of the FFT operation. Us-ing currently available, efficient FFT techniques means thatwe must provide the data in a rectilinear grid. Assumingthat no evanescent spectral components exist in the mea-surement plane (this is a good assumption if we are in theradiating near-field zone of the antenna), then the maximumspatial variation observed in the near-field is k0, the free-space wave number. Analgous to signal processing, thismeans that our sampling spacing for this rectilinear gridmust be [4]

∆x,∆y≤ π

k0=

λ0

2(1)

where λ0 is the free-space wavelength. This is analogous tothe time sample intervals ∆t = 1/2 fmax = π/ωmax, wherefmax and ωmax are the maximum frequency and angular fre-quency components of the time-varying signal.

The second important consideration is that the bipolar griddata must be interpolated to a rectilinear grid. In the earlydays of planar near-field measurements, the general con-sensus was to choose sample spacings such that the arcbetween adjacent points was roughly λ0/2 [5]. However,studies in [6] revealed that the near-field distributions couldbe even more bandlimited if the proper mathematical mod-ification to the fields could be made. These potential mod-ifications to the fields (spherical phase cancellations) arediscussed in the next section. These studies ultimately de-termine the sampling intervals ∆β , ∆α , with respect to thebipolar coordinate system, that ensures the proper intervals[1, 2]. This proper spacing allows us to interpolate the dataonto a rectilinear grid with intervals λ0/2 or less.

2.3 Interpolation

Once the fields have been sampled in their respective grid,the fields must be interpolated into a rectilinear grid. Wedo the interpolation so that we can apply the FFT operationonto the near-field data. The very large amount of inter-polant data makes the interpolation very cumbersome andtime-consuming. As previously mentioned, studies haveshown that the radiated fields from a given AUT could

Bipolar Grid Rectilinear Grid

Figure 5. Interpolation from a bipolar grid to a rectilineargrid. Note that values outside the circle are set to zero.

be made bandlimited by cancelling the spherical phaseexp(− jkr). This removes the rapid oscillations of the near-fields observed from the exp(− jkr) factor. After remov-ing these oscillations, an interpolation called Optimal Sam-pling Interpolation (OSI) can be employed, which interpo-lates along β with the sinc(·) function and along α withthe Dirichlet function [6, 7]. The interpolation between thebipolar grid and rectilinear grid is illustrated in Figure 5.

2.4 Surface Equivalence

The surface equivalence theorem provides the theoreticalbasis for all of near-field measurements, and it is often achallenging theorem to grasp without the help of measure-ments [1]. Fundamentally, the surface equivalence theoremstates that we can enclose a radiator with a fictitious surfaceand create equivalent electric and magnetic currents that areimpressed tangentially along this surface outside the vol-ume. By “equivalent”, we mean that the radiation fromthese equivalent currents will be identical to the originalradiator inside the surface. This is illustrated in Figure 6,

PEC I II

S

I II

S

Fictitious Surface

Antenna

Equivalent Scenarios

Figure 6. Illustration of Love’s equivalence theorem,which justifies near-field measurements using Maxwell’sequations [1]. Introducing PEC allows the usage of theequivalent magnetic current, simplifying the measurementby only using an electric field probe (OEWG in Fig. 2).

where a radiator was enclosed by a fictitious surface and re-placed by an equivalent magnetic surface current Ms. Themajor breakthrough from this principle is that knowledgeof the radiated fields is completely known when we samplethe tangential fields on a closed surface around the antenna,even in the near-field. Furthermore, we only have to samplethe electric field, which can be used to create the fictitiousmagnetic surface current Ms. This is one of the excitinglinks between near-field measurements and electromagnetictheory, and it very clearly demonstrates the importance ofunderstanding these fundamental theorems.

3 Fourier Transforms and the FFT

At this point, we have the data on a plane (ideally ex-tended to infinity), which effectively creates a closed sur-face around the AUT. After the OSI interpolation, we would

-10 -5 0 5 10-10

-5

0

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10 0

-5

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-40

x/λ

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(a)

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(d)Figure 7. Measured near field aperture distributions afterOSI interpolation at 35.75 GHz (a) Copol amplitude dis-tribution, (b) Copol phase distribution. (c) Xpol amplitudedistribution. (d) Xpol phase distribution.

(a) (b)

Figure 8. Resulting far field pattern for the AUT at35.75 GHz. These patterns were generated using the FFToperation. (a) E-plane pattern. (b) H-plane pattern.

have data that appears as shown in Figure 7, which are theso-called near-field plots of the magnitude/phase values forEx and Ey. This near-field data can then be used to obtainthe far-field patterns of the AUT. Since the near-fields areon a plane, the far-fields share a Fourier transform relation-ship with the near-fields. This is a direct result of the vectorpotential integration of the equivalent magnetic surface cur-rent Ms by

E f f (kx,ky) ∝

∫∫∞

−∞

En f (x,y,0)× n̂e jkxx′+ jkyy′dx′dy′ (2)

where E f f is the far-field electric field, En f is the near-fieldelectric field, and n̂ is the normal to the measurement plane.Note that this integral is often truncated when the near-fieldlevels drop below a given threshold, usually below -40 dB.The final far-field patterns are shown in Figure 8, wherea nice beam radiating from the horn antenna is measured.Clearly other steps such as probe pattern compensation arealso required to get highly accurate far field pattern at wideangles [1]. Instructors can use several examples of differentAUT measurements to illustrate this 2D Fourier relation-

ship between the near-fields and far-fields.

4 Concluding Remarks and Discussion

In our experience, the planar near-field antenna measure-ment techniques makes a nice, complete example for stu-dents to grapple with electromagnetic and electrical engi-neering principles. Our tabletop bipolar near-field appara-tus represents the embodiment and application of many fun-damental electrical engineering and electromagnetic princi-ples. This hands-on approach with teaching is invaluable tostudents, where students can better visualize fields, sam-pling techniques, and electromagnetic theory. At the sametime, students are also exposed to the fun world of antennametrology, where engineers can readily get hands-on expe-rience in a number of related fields such as robotics, pro-gramming, and laser positioning systems. There are ample,relevant references in [1] for further reading and details.

5 Acknowledgements

The authors would like to thank Vignesh Manohar for help-ful discussions.

References

[1] Y. Rahmat-Samii, L. Williams, and R. Yaccarino, “Theucla bi-polar planar-near-field antenna-measurementand diagnostics range,” IEEE Anten. Prop. Mag., 37,6, pp. 16–35, 1995.

[2] T. Brockett and Y. Rahmat-Samii, “A novel portablebipolar near-field system for millimeter-wave antennas:construction, development, and verification,” IEEE An-ten. Prop. Mag., 50, 5, pp. 121–130, 2008.

[3] J. Kovitz, V. Manohar, and Y. Rahmat-Samii, “Aspline-profiled horn antenna assembly optimized fordeployable Ka-band offset reflectors in CubeSats,” inIEEE Int. Symp. Anten. Prop., 2016, pp. 1535–36.

[4] J. M. Kovitz and Y. Rahmat-Samii, “Novelties of spec-tral domain analysis in antenna characterizations: Con-cept, formulation, and applications,” in Advanced Com-putational Electromagnetic Methods, W. Yu, W. Li,A. Elsherbeni, and Y. Rahmat-Samii, Eds. ArtechHouse Publishers, 2015, ch. 1, pp. 1–82.

[5] M. Gatti and Y. Rahmat-Samii, “FFT applications toplane-polar near-field antenna measurements,” IEEETrans. Anten. Prop., 36, 6, pp. 781–791, 1988.

[6] O. M. Bucci, C. Gennarelli, and C. Savarese, “Fastand accurate near-field-far-field transformation bysampling interpolation of plane-polar measurements,”IEEE Trans. Anten. Prop., 39, 1, pp. 48–55, 1991.

[7] S. Razavi and Y. Rahmat-Samii, “A new look at phase-less planar near-field measurements: limitations, sim-ulations, measurements, and a hybrid solution,” IEEEAnten. Prop. Mag., 49, 2, pp. 170–178, 2007.