332 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009

Performances of UWB Wheeler Cap andReverberation Chamber to Carry Out Efficiency

Measurements of Narrowband AntennasGwenn Le Fur, Christophe Lemoine, Philippe Besnier, Member, IEEE, and Ala Sharaiha, Member, IEEE

Abstract—This letter deals with using ultrawideband (UWB)Wheeler Cap (UWB WCap) and reverberation chamber (RC) tomeasure efficiencies of narrowband antennas. This first testbeddesigned for very broadband systems can also be accurate fornarrowband antennas. The second one, first designed for electro-magnetic compatibility (EMC) measurements, offers advantagesto measure antenna efficiency. Results are given to assess uncer-tainty and accuracy of both measurement means.

Index Terms—Antennas efficiency measurement, ultrawidebandWheeler Cap (UWB WCap), reverberation chamber (RC), nar-rowband antennas.

I. INTRODUCTION

R ADIATION efficiency is a classical antenna performanceparameter very convenient in characterizing antennas for

mobile and wireless terminals that operate in complex multipathenvironments. It is defined as the ratio of the total power radi-ated by the antenna to the net power accepted by the antennaat its terminals during the radiation process [1]. The conven-tional method of measuring antenna efficiency is to determinethe ratio of power gain in any specified direction to the di-rectivity in that same direction in an anechoic chamber.This measurement is often difficult, especially for low-gain an-tennas, and results are often inaccurate. A variety of techniqueshave been proposed over the years for the measurement of an-tenna efficiencies. In 1959, Wheeler introduced a measurementconcept that uses a conducting shell named “radiansphere” [2](well known as the “Wheeler Cap” (WCap) method). This ra-diansphere is a theoretical sphere with a radius that corre-sponds to the boundary between the near-field and the far-fieldof a small antenna. The scattering parameters of the antennaare measured in free space, and inside the closed conductingshell or WCap. Some variants were developed such as applyingthe powers method to WCap [3] or using other shapes of res-onant cavity like waveguide [4]. These processes are all nar-rowband and, consequently, each sphere or resonant cavity isdesigned for only one resonance frequency. Recently, Schantzproposed an adaptation of the WCap method to ultrawideband

Manuscript received July 04, 2008; revised August 29, 2008. First publishedSeptember 19, 2008; current version published May 15, 2009.

The authors are with the Institute of Electronics and Telecommunicationsof Rennes (IETR), University of Rennes 1, 35065 Rennes Cedex, France, andINSA of Rennes, 35043 Rennes, France (e-mail: Gwenn.lefur@univ-rennes1.fr).

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LAWP.2008.2006072

(UWB) antenna measurements named “UWB Wheeler Cap”(UWB WCap) [5].

[6] and [7] introduce antenna efficiency measurements in thereverberation chamber (RC). This testbed offers the advantageof being useful for many antenna geometries. Indeed, there areno volume and symmetry restrictions in RC. In this letter, wepresent developments on both methods to measure narrowbandantenna efficiency. Results are presented to show advantagesand uncertainties of each method. Among these results, wepresent the measured efficiencies of two different antennas. Thefirst one is a compact planar inverted-F antenna (PIFA) witha double-band behavior for GSM/DCS bands [8]. The secondone is a small helix antenna centered at 1600 MHz.

II. UWB WHEELER CAP

Recently, a new method has been developed for evaluatingUWB antenna efficiency [5]. Instead of a closed spherical shellof radius at the frequency of interest like in the clas-sical WCap method [2], the “UWB WCap” method uses a muchlarger spherical shell (Fig. 4). The antenna is centered at theorigin of the conducting shell.

Rather than inhibiting radiation from the antenna, the UWBWCap allows the antenna to radiate freely. Due to the sphericalnature of the radiation and the test setup, the radiated energy re-flects to the sphere boundary and is radiated back to the antenna.

As demonstrated by Schantz [5], the various reflections thatoccur inside the cap can be represented by power fractions. As-suming that all the transmitted power is available at the receiveantenna thanks to the negligible loss due to the cap, reflectionsinside the sphere can be explained as follows [9] (Fig. 1): first,at time , a normalized power of 1 W is applied to antennainput. A fraction of this power reflects back to the gener-ator due to the mismatching and the remaining fractionpasses through the antenna port. This fraction is radiated withradiation efficiency , so is the radiated power frac-tion. At (the time needed by the wave to go back andforth to the antenna), the antenna receives the backward travel-ling wave with the same efficiency. Due to the mismatch at theport, part of this received signal is retransmitted with a fractionof , and the other part is absorbed with an efficiency andan impedance mismatch . At the input port,is thus received, and the reradiated wave of is trav-eling again in the sphere volume and so on.

Using scattering parameters (S parameters) and consideringthe reflected signal with negligible structural scattering of the

1536-1225/$25.00 © 2009 IEEE

LE FUR et al.: EFFICIENCY MEASUREMENTS OF NARROWBAND ANTENNAS 333

Fig. 1. Evolution of the power fractions in a UWB Wheeler Cap.

shell , the reflection coefficient inside the UWBWCap can be expressed as follows:

(1)

Radiation efficiency is therefore deduced [9] substitutingby

(2)

This method has two main assets besides the fact that it is fast.First, only the reflection coefficient in free space andinside the WCap ) are needed. Second, it doesn’t re-quire any calibration with a reference antenna whose efficiencyis known. Nevertheless, the diffraction is neglected in this ap-proach, and this can introduce a small uncertainty on the totalefficiency measurement, which can be ignored. Now, if the an-tenna is perfectly matched , and this is seldom thecase since antenna under test (AUT) are usually not, (2) willno longer be valid.

III. REVERBERATION CHAMBER MEASUREMENTS

RCs have been proposed in [6] and [7] to perform antennacharacterization such as radiation efficiency measurements.These chambers offer intrinsically wideband environmentsfor testing any type of antenna, alone or embedded, withoutpositioning constraints.

Either for electromagnetic compatibility (EMC) or antennameasurements, test protocols in RC are based on the stochasticbehavior of fields, created using various stirring or tuningmethods. In the case of mechanical stirring, this behavior isobtained using the rotation of a mechanical mode stirrer, whichaims to change the boundary conditions for the electromagnetic

Fig. 2. Photograph of the PIFA.

field. Therefore, correctly selecting each location of the stirrercreates an independent field distribution. As far as frequency(or electronic) stirring is concerned, the principle consists insweeping the frequency. The sweeping range is containedwithin the antenna bandwidth and its rate of change is adaptedin order to have access to independent measurements. Thestochastic nature of fields in RCs was theoretically understoodand experimentally validated [10]–[12]. One of the key issuesfor performing accurate measurements, such as those requiredfor antenna characteristics, is to ensure a sufficient collection ofstatistically independent measurements. Therefore, the qualityof measurements in a RC depends on the total number ofindependent measurements, and the measurement uncertaintyis directly related to the central limit theorem [13].

The radiation efficiency of an antenna under test in a RCmay be obtained through the evaluation of the following ratioof two antenna radiation efficiencies [14]:

(3)

The letter “r” denotes the reference antenna whose radiation ef-ficiency is known, and the letter “a” denotes the antenna undertest. Moreover, parameters are scattering parameters mag-nitude measured with a vectorial network analyzer at a two-portsystem. Port 1 is the input of a fixed transmitting antenna, andport 2 is associated with the receiving antenna. The notationstands for expected values of the different involved scatteringparameters. These measured parameters are indeed consideredas specific realizations of a random variable.

Measurements are performed in two steps. First, it consists inevaluating (r) scattering parameters when the reference antennais in place. Second, the antenna under test is substituted for thereference antenna, and measurements are achieved identicallyto determine (a) scattering parameters.

The three following properties underlie such a measurement.First, expected values of (and ) parameters convergeto reflection coefficients of the transmitting and receiving an-tennas, respectively, as if they were measured in free space.Second, expected value of converges to a value that is pro-portional to antenna efficiencies and inversely proportional tochamber losses. Finally, it is assumed that chamber losses re-main constant when the antenna under test is substituted for thereference antenna.

IV. MEASUREMENTS RESULTS

1) Antennas Under Test: Two narrowband antennas are in-vestigated. The first one is a PIFA [8] working on a double band(GSM/DCS). The antenna dimensions are 37 22 9 mmmounted on a printed circuit board (PCB) of dimensions104 39 mm (Fig. 2). The second one is a homemade helix

334 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009

Fig. 3. Photograph of the helix antenna.

Fig. 4. The IETR UWB Wheeler Cap.

Fig. 5. The dimensions of the IETR reverberation chamber.

antenna working at 1600 MHz. It is made from metal wire witha diameter of 0.8 mm and peripherally fed. The total lengthof the helix is 25.8 mm, the number of turns is 2.6, and itsradius is equal to 2.4 mm. Dimensions of the ground plane are70 70 mm . The global size of the antenna is around ,which constitutes a small antenna compared to the wavelength(Fig. 3).

2) Measurements Setup: All experiments are carried out inthe IETR RC and in the IETR UWB WCap. RC dimensions are2.9 3.7 8.7 m (Fig. 5). The inside sphere of the UWB Capthat we built has a diameter of 30 cm (Fig. 4).

In the RC, the lowest usable frequency is established around250 MHz. The test volume shown in Fig. 5 is far enough fromwalls and from the stirrer since the distance is at least . Thetransmitting antenna is a horn antenna (ETS-Lindgren Model3115) with a radiation efficiency of 95%. It is placed in a corner,out of the test volume, and directed through the corner. The re-ceiving antenna, either the reference antenna or antenna undertest, is placed in the test volume of the cavity. In order to esti-mate precisely scattering parameters and the radiation efficiency

Fig. 6. (a) PIFA total measured efficiencies versus frequency (b) in GSM bandand (c) in DCS band.

of the antenna under test, we select a large amount of inde-pendent measurements, using mechanical and frequency stir-ring. For a helix antenna, measurements of the radiation effi-ciency are performed every 10 MHz from 1400 to 1900 MHz.In each 10-MHz frequency band, we select 100 frequencies, andwe estimate that at least 50% of those frequencies are indepen-dent [13]. Moreover, 30 independent mechanical stirrer loca-tions are added to collect scattering parameters for one 10-MHzfrequency band. Therefore, it leads to select 1500 independentmeasurements of scattering parameters per 10-MHz frequencyband. The same setup is applied for the reference antenna. Fromprevious experiments leading to 400 evaluations of , fol-lowing this protocol for both helix and PIFA antennas, the ratio

is evaluated with % uncertainty using a 95% confi-dence interval.

Measurements in UWB WCap are realized all over the bandwith a frequency step of 100 kHz thanks to the rapidity of thismethod. In the RC, the measure is performed at selected bandsonly since this technique is time-consuming.

3) Efficiency Measurements Results: In Figs. 6 and 7, wepresent the total efficiency measured for the PIFA and the helixantenna, respectively, using the two previous methods. Both ofthem provide the radiated efficiency . Then, the total efficiency

is computed through the following expression by takinginto account the mismatching losses:

(4)

We obtain for the helix antenna a total efficiency of dBat 1.58 GHz in UWB WCap and dB for RC measurement.For the PIFA, total efficiencies are about dB at 920 MHz

LE FUR et al.: EFFICIENCY MEASUREMENTS OF NARROWBAND ANTENNAS 335

Fig. 7. Helix antenna total measured efficiency versus frequency.

Fig. 8. � of the helix antenna deduced in RC compared to the measured �in free space.

Fig. 9. � of the PIFA deduced in RC compared to the measured � in freespace (a) in GSM band and (b) DCS band.

[GSM band Fig. 6(b)] in UWB WCap and dB in RC.For the DCS band, total efficiencies are dB at 1.8 GHz inUWB WCap and dB in RC [Fig. 6(c)].

4) Discussion: Some differences are observed between thetwo methods for helix efficiency measurements. The evaluationof is particularly important for efficiency measurements.Two measurements of this parameter were achieved, one in freespace using an anechoic chamber and another in a RC [15]. Forthe helix antenna, we observe some gaps between both thesemeasurements (Fig. 8). This can explain the differences men-tioned above besides the uncertainties. However, UWB WCapmethod is consistent with the IE3D simulation and in quite goodagreement with results in the RC.

For the PIFA, despite the uncertainty over RC measurements,the two parameters are in good agreement, as shown in

Fig. 9. Moreover, efficiencies in UWB WCap are consistent withRC measurements for the two bandwidths.

V. CONCLUSION

The capability of the UWB Wheeler Cap and reverberationchamber methods to measure narrowband antenna efficiencywas presented through the characterization of two different nar-rowband antennas. Through a cross comparison, the efficienciesmeasured are in good agreement and are also consistent. Theseresults show the accuracy level of both measurement methods.The UWB Wheeler Cap method offers two main assets, namelythe measurement’s speed and the use of one sphere for manyantenna resonant frequencies. The reverberation chamber mea-surement allows characterization of voluminous or integratedantennas and the control of measurement uncertainties.

ACKNOWLEDGMENT

The authors would like to thank C. Luxey from the Labora-tory of Electronics, Antennas and Telecomunications (LEAT),University of Nice-Sophia Antipolis, France, for the providedPIFA and S. Jaffredo from the IETR for the UWB Wheeler Capmanufacture.

REFERENCES

[1] IEEE Standard Definitions of Terms for Antennas, IEEE Std 145-1993,1993, E-ISBN: 0-7381-0555-4.

[2] H. A. Wheeler, “The radiansphere around a small antenna,” Proc. IRE,pp. 1325–1331, 1959.

[3] S. Agahi and W. Domino, “Efficiency measurements of portable-handset antennas using the Wheeler Cap,” Appl. Microw. Wireless,vol. 12, pp. 34–42, 2000.

[4] R. Johnston and J. McRory, “An improved small antenna radiation-efficiency measurement method,” IEEE Antennas Propag. Mag., vol.40, no. 5, pp. 40–48, Oct. 1998.

[5] H. Schantz, The Art and Science of UWB Antennas. Norwood, MA:Artech House, 2005, ISBN: 1-58053-88-6, .

[6] K. Rosengren, P.-S. Kildal, C. Carlsson, and J. Carlsson, “Charac-terization of antennas for mobile and wireless terminals in reverbera-tion chambers: Improved accuracy by platform stirring,” Microw. Opt.Technol. Lett., vol. 30, pp. 391–397, Sep. 2001.

[7] P.-S. Kildal, K. Rosengren, J. Byun, and J. Lee, “Definition of effec-tive diversity gain and how to measure it in a reverberation chamber,”Microw. Opt. Technol. Lett., vol. 34, pp. 56–59, Jul. 2002.

[8] P. Ciais, R. Staraj, G. Kossiavas, and C. Luxey, “Compact internalmultiband antenna for mobile phone and wlan standards,” Electron.Lett., vol. 40, no. 15, pp. 920–921, Jul. 2004.

[9] M. Huynh, “Wideband compact antennas for wireless communicationapplications,” Ph.D. Dissertation, Virginia Polytechnic Instit. and StateUniv., Blacksburg, VA, 2004.

[10] D. A. Hill, “Plane wave integral representation for fields in reverbera-tion chambers,” IEEE Trans. Electromagn. Compat., vol. 40, no. 3, pp.209–217, Aug. 1998.

[11] P. Corona, G. Ferrara, and M. Migliaccio, “Reverberating chambersas sources of stochastic electromagnetic fields,” IEEE Trans. Electro-magn. Compat., vol. 38, no. 3, pp. 348–356, Aug. 1996.

[12] C. Lemoine, P. Besnier, and M. Drissi, “Investigation of reverberationchamber measurements through high power goodness of fit tests,” IEEETrans. Electromagn. Compat., vol. 49, no. 4, pp. 745–755, Nov. 2007.

[13] C. Lemoine, P. Besnier, and M. Drissi, “Advanced method for esti-mating number of independent samples available with stirrer in rever-beration chamber,” Electron. Lett., vol. 43, no. 16, pp. 861–862, Aug.2007.

[14] K. Rosengren and P.-S. Kildal, “Radiation efficiency, correlation,diversity gain and capacity of a six-monopole antenna array for aMIMO system: Theory, simulation and measurement in reverberationchamber,” IEE Proc. Microw. Antennas Propag., vol. 152, pp. 7–16,Feb. 2005.

[15] P.-S. Kildal, C. Carlsson, and J. Yang, “Measurement of free space im-pedances of small antennas in reverberation chambers,” Microw. Opt.Technol. Lett., vol. 32, no. 2, pp. 112–115, Jan. 2002.