29SAKASAI Makoto et al.

1 Introduction

In accordance with the Radio Law, NICToffers calibration services for loop antennaswith a frequency coverage of 9 kHz to30 MHz, dipole antennas with that of 30 MHzto 1,000 MHz, and horn antennas with that of1 GHz to 18 GHz. Specifically with respect tohorn antennas, in 1993 NICT developed andhas since employed a calibration system basedon the three-antenna method for a bandwidthof 1 GHz to 5 GHz［1］. In 1998, NICT addedthe 5 GHz to 18 GHz bandwidth to the cover-age of calibration based on the same method,and also began evaluation of calibrationuncertainty. The previous calibration systememployed an antenna measurement systemincorporating the use of a microwave receiver.This system made use of an external direction-al coupler and down-converter for a receiver,allowing for compensation of propagation loss

to extended lengths of coaxial cable. Whilethis represented an advantage under the previ-ous system, this feature also presented draw-backs: the IF bandwidth was fixed, so it wasdifficult to ensure a high S/N ratio and thedynamic range was narrow. This measurementsystem was recently replaced by a networkanalyzer offering faster measurement andsecuring a dynamic range of approximately140 dB for the receiver, thus improving therange (measurement environment) by approxi-mately 50 dB compared to the former system.For horn antennas with a frequency coverageof 1 GHz to 18 GHz, NICT currently cali-brates the pyramidal horn antennas used asstandard horn antennas in EMI antenna cali-brations. Additionally, in light of the necessityunder recent international agreements and inview of NICT’s plans to obtain ISO 17025accreditation, we have carried out evaluationof uncertainty in horn antenna calibration.

3-2 Evaluation of Uncertainty of HornAntenna Calibration with the Frequencyrange of 1 GHz to 18 GHz.

SAKASAI Makoto, MASUZAWA Hiroshi, FUJII Katsumi, SUZUKI Akira, KOIKE Kunimasa, and YAMANAKA Yukio

NICT performs an EMI antenna calibration based on the Radio Law. Recently, the uncertain-ty of the EMI antenna measurement was evaluated with the three antenna method with a fre-quency coverage of 1 GHz to 18 GHz. The type of antenna under calibration is a pyramidalstandard gain horn antenna. The main measurement device of the traditional antenna calibrationsystem was a signal generator with a high-power amplifier and a microwave receiver. However,it was changed to a network analyzer providing a high dynamic range. The study about the 14error factors revealed that the expanded uncertainty (k = 2) were ±0.7 dB (1 to 5.85 GHz) and±1.1 dB (5.85 to 18 GHz).

KeywordsStandard Horn antenna, EMI Antenna Calibration, Uncertainty, Antenna gain, Three-antenna method, Mismatch

30 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

Since the degree of uncertainty varies signifi-cantly between low frequencies and high fre-quencies within a broad frequency range of1 GHz to 18 GHz, we evaluated uncertaintyseparately for the frequency range from 1 GHzto 5.85 GHz and the frequency range from5.85 GHz to 18 GHz. It should be noted thatthis evaluation of uncertainty was limited tothe calibration of standard horn antennas.

2 Calibration system

For the calibration of horn antennas, weinstalled transmitting and receiving antennasat the midpoint of the longest side of NICT’slarge six-surface anechoic chamber [insidedimensions: 14 m (width)×18 m (depth)×6.4 m (height)], and positioned the antennasface-to-face at a distance apart of approxi-mately 14.6 m, at a height of 3.5 m from thefloor surface. Using the three-antenna method,we then obtained the antenna gains for threeantennas simultaneously. This calibration sys-tem is illustrated in Fig. 1. For the transmis-sion and reception system in this experiment,we use a network analyzer featuring a widedynamic range. To ensure a high S/N ratio, weuse a low-loss coaxial cable and avoid the useof an amplifier, which could cause higher har-monics and level fluctuation. The antennas aremounted on Bakelite antenna adjustment plat-forms (allowing for adjustment of azimuth,

elevation angle, and height) placed on blocksof foam polystyrol. A 6-dB pad is attached tothe point of the coaxial cable connected to theantennas to reduce error in the reflection coef-ficient.

For axial alignment of the transmitting andreceiving antennas, a laser generator is posi-tioned midway between both antennas, and thelaser beam is used to determine the horizontaland vertical of the antenna adjusting devicesfor optimum positioning. The platforms of theantenna adjusting devices are designed toenable fine adjustment of azimuth, elevationangle, and height. The coaxial cable connect-ing the antennas is routed along the side wallof the anechoic chamber to the backs of theantennas in order to minimize the effect ofreflected waves. The network analyzer isinstalled in an anterior room located outsidethe anechoic chamber, and is connected to aPC via GP-IB. We use measurement softwaredesigned for the three-antenna method to max-imize the efficiency and speed of calibration.The point of the coaxial cable to be connectedto the antenna under calibration is fitted with a6 dB pad to reduce error due to impedancemismatching within the transmission andreception system. The standard horn antennasused in the calibration system cover a frequen-cy range of 1 GHz to 18 GHz, comprised ofthe following eight bands.

Band 1, with a frequency range of 1 GHz

Fig.1 Block diagram of calibration system

31SAKASAI Makoto et al.

to 1.15 GHz; Band 2, from 1.15 GHz to1.7 GHz; Band 3, from 1.7 GHz to 2.6 GHz;Band 4, from 2.6 GHz to 3.95 GHz; Band 5,from 3.95 GHz to 5.85 GHz; Band 6, from5.85 GHz to 8.2 GHz; Band 7, from 8.2 to12.4 GHz; and Band 8, from 12.4 GHz to18 GHz.

In our experiment, we evaluated uncertain-ty in two separate frequency bands: the fre-quency range from 1 GHz to 5.85 GHz (Band1 through Band 5; referred to below as “BandL”) and the frequency range of 5.85 GHz to18 GHz (Band 6 through Band 8; “Band H”).

3 Calibration theory and mea-surement method

A number of EMI antenna calibrationmethods are available, as follows: (1) the ref-erence method, which uses a standard antennaas a reference for the antenna under calibra-tion, (2) the standard field method, whichdetermines field strength at the position of theantenna under calibration, and (3) the three-antenna method, which combines each pair ofthree antennas for calibration. One of the com-mon drawbacks of methods (1) and (2) is thatsignificant error may result if the directivitiesof the antennas are not identical. Method (3),on the other hand, offers an advantage in thatthe three antennas used in the calibration donot necessarily have to be identical; further,this method allows for calibration of anyantenna capable of both transmission andreception.

Measurement of antenna gain［2］by thethree-antenna method is based on the Friistransmission formula［3］. This method mea-sures received power P0 resulting from thedirect connection of the transmission andreception cable and received power Pji (i, j = 1to 3, i≠j) resulting from radio-wave emissionfrom three different combinations of opposingantennas (#1, #2, #3).

Given the received power, Pji (i, j = 1 to 3,i≠j), obtained from the pair of antenna #i as areceiving antenna and antenna #j as a trans-mitting antenna, the antenna gains of antenna

#1, #2, and #3 can be calculated by the follow-ing formulas.

(1)

(2)

(3)

where d is the distance between the trans-mitting and receiving antennas; this distancemust remain the same in the measurementoperations conducted with the three antennacombinations. The validity of the calibrationresults was judged by comparison with previ-ous calibration results for NICT’s two stan-dard horn antennas (other than the antennaunder calibration).

4 Factors contributing to uncer-tainty

According to the ISO Guide dealing withuncertainty, many factors may lead to uncer-tainty, and these factors come into play incomplex ways to produce a variety of effects［4］.These factors include: (1) definition of thequantity to be measured, (2) environmentalconditions, (3) differences in values read bythe individuals conducting measurement, (4)resolution or detection limit of the equipment,(5) inaccuracy of constants and parameters,(6) ambiguity of an approximation or hypothe-sis in the measurement method or procedure,and (7) differences arising in repeated obser-vations of the quantity measured.

Since the system used in our experimentcalibrates antenna gain based on direct-cou-pled measurement and propagation measure-ment using the three-antenna method in theanechoic chamber, measurement errors inher-ent in the three-antenna method contribute touncertainty. The main causes of these errors inthe three-antenna method can be classifiedinto three groups: errors proceeding from themeasurement system, errors proceeding from

32 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

the antenna setup, and measurement errorsinherent in the three-antenna method.4.1.1 Errors proceeding from the mea-

surement systemSuspected errors proceeding from the mea-

surement system are as follows: error due tothe S/N ratio, error due to the coaxial cablearrangement (specifically, bending), error inmeasurement stability (fluctuation over timeof measured values and fluctuation due totemperature changes during measurement),and non-linearity error (i.e., level accuracy) ofthe measurement system.4.1.2 Errors proceeding from the

antenna setupErrors proceeding from the antenna setup

include error in the distance between theopposing transmitting and receiving antennas,error in the far-field condition with the givendistance between antennas, error due to dis-persion in measurement of propagation loss,and error due to deviation in antenna axialalignment in the horizontal/vertical directionand in the azimuth.4.1.3 Measurement errors in the three-

antenna methodMeasurement errors in the three-antenna

method are generated by a number of factors,as follows: error in propagation measurementdue to radio-wave reflection from walls, theceiling, and the floor (even an anechoic cham-ber is not a completely “free” space), error dueto uncertainty in the center of radiation for thehorn antenna under calibration, and errors dueto mismatching among the antenna under cali-bration, the coaxial cable, the pad, the signalsource, and the receiver.

4.2 Errors proceeding from the mea-surement system

4.2.1 Error due to the S/N ratioTwo measurement techniques are employed

in the three-antenna method. Direct-coupledmeasurement is performed by directly con-necting a coaxial cable between the transmit-ting and receiving antennas, whereas propaga-tion measurement is conducted by setting upboth antennas for radio-wave transmission.

Since propagation measurement generatespropagation loss, the level of reception falls20 dB to 40 dB below that obtained in direct-coupled measurement. In addition, the level ofreception decreases even further at higher fre-quencies, since coaxial cable loss is greater athigher frequencies. We measured the S/N ratioover a frequency range covering the eightbands mentioned above. Figure 2 shows anexample of our measurement results. Theseresults indicated an S/N ratio of 50.14 dB forBand L (frequency range of 1 GHz to5.85 GHz); error (La) attributable to this S/Nratio was 0.027 dB. For Band H (frequencyrange of 5.85 GHz to 18 GHz), the S/N ratiowas 37.9 dB and the error due to this ratio was0.11 dB.

Error La is a Type B error unique to eachmeasurement instrument, and uncertainty iscalculated based on a rectangular distribution.

4.2.2 Error due to coaxial cable bendIn our experiment, the coaxial cable is

routed from the network analyzer in the mea-surement room outside the anechoic chamberto the two opposing antennas along the wall ofthe anechoic chamber. The coaxial cable fromthe network analyzer to the antennas is laidout such that each bend had a radius of morethan 50 cm, but the cable is run verticallyfrom the connector at the coaxial waveguideconverter of the antenna toward the floor. Thisresults in a cable bend featuring a radius ofapproximately 10 cm near the antenna connec-tor. To measure the effect of this cable bend,we set up an antenna such that the bending

Fig.2 Error due to S/N ratio (Band 8)

33SAKASAI Makoto et al.

radius was 10 cm in the horizontal direction.Example measurement results are shown inFig. 3. Here, error (Lb) is within 0.01 dB forBand L and within 0.025 dB for Band H. Thisdegree of error has a direct effect on the levelof reception. As indicated in formulas (1)through (3), antenna gain is proportional to thesquare root of received power; therefore, wemultiplied the obtained error value in decibelsby 1/2 and multiplied this product by three,since the same error occurs in all three anten-nas. The error due to coaxial cable bend is aType A error, and uncertainty is calculatedbased on a normal distribution.

In actual measurement, however, it is nec-essary to prevent bends of a radius of less than10 cm from occurring in the cable.

4.2.3 Uncertainty due to factors relat-ed to measurement system sta-bility

4.2.3.1 Error due to fluctuations over timein the measurement system

The three-antenna method requires up toaround 15 minutes to complete direct-coupledmeasurement and propagation measurementsfor the three antennas. To evaluate the stabilityof this measurement system, we connected thecoaxial cable used in the calibration and twopads, each with an attenuation level of 6 dB,to the network analyzer, and connected fixedattenuators that would simulate the actuallevel of propagation loss in place of the trans-mitting and receiving antennas. After fivehours of warm-up operation of the networkanalyzer, level changes were measured for a

duration of 25 minutes. Although the resultsshowed fluctuations of within 0.02 dB, weconservatively determined the error Lc due tofluctuations over time in the measurement sys-tem as 0.05 dB for both Band L and Band H.Error due to fluctuations over time in the mea-surement system is unique to each measure-ment system and is a Type B error. Uncertain-ty is calculated based on rectangular distribu-tion.4.2.3.2 Error due to temperature fluctua-

tions in the measurement systemWe activated the heating/cooling apparatus

in the large anechoic chamber and measure-ment room; after the room temperaturereached approximately 20˚C, we noted tem-perature changes using a temperature recorder.During the 15-minute period necessary formeasurement based on the three-antennamethod, we detected a temperature fluctuationof 0.2˚C. This experiment was conducted on acold day in December. After the measurementinstrument set up for direct-coupled measure-ment had warmed up sufficiently, we turnedon the heating/cooling apparatus in the largeanechoic chamber and measurement room andobserved the change in the indicated valuecaused by the increase in temperature. Theresults of measurement showed that error Lddue to these temperature changes was 0.03 dBat maximum for both Band L and Band H,even if the temperature change was estimatedto be sufficiently large; i.e., ±1˚C. The errordue to temperature fluctuations in the mea-surement system is unique to each measure-ment instrument and is a Type B error. Uncer-tainty is calculated based on a rectangular dis-tribution.4.2.4 Error due to non-linearity in the

receiving systemWe inserted a standard attenuator with a

given value between Port 1 (signal source) andPort 2 (receiving side) of the network analyz-er. We then measured the degree of non-linear-ity in the receiving system while varying theattenuation. We changed the attenuation in10 dB increments and evaluated non-linearitybased on the value indicated on the network

Fig.3 Error due to coaxial cable bend

34 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

analyzer and the accurate attenuation value ofthe standard attenuator. The standard attenua-tor used in this measurement was a standardtransfer attenuator periodically calibrated bythe NMIJ (National Metrology Institute ofJapan) of the AIST (National Institute ofAdvanced Industrial Science and Technology).The error Le resulting from non-linearity inthe receiving system was 0.04 dB for Band Land 0.05 dB for Band H. Error due to non-lin-earity in the receiving system is a Type Berror, and uncertainty is calculated based on arectangular distribution.

4.3 Errors proceeding from the anten-na setup

4.3.1 Error due to the antenna-to-antenna distance setting

In the measurement of antenna gain usingthe three-antenna method, it is important todetermine the distance d between antennaswith accuracy, as seen in formulas (1) through(3). In our experiment, we use a large ane-choic chamber measuring 18 m in insidedepth. The most suitable distance between theantenna apertures in this case is approximately14.6 m, taking convenience into consideration;for example in terms of antenna installation.Since we used a laser range finder to measurethe distance between the apertures of thetransmitting and receiving antennas, highaccuracy (±1 cm) is possible in establishingthe distance between antennas. When anantenna distance of 14.6 m is set with an errorof less than ±1 cm, error Lf in antenna gaincan be maintained within ±0.003 dB for bothBand L and Band H, as indicated by formulas(1) through (3). Error due to the antenna-to-antenna distance setting is a Type A error, anduncertainty is calculated based on a normaldistribution.4.3.2 Error in the far-field condition

When the measuring distance is finite,measurement error results if the amplitude dis-tribution of the surface of the wave reachingthe aperture of the antenna under calibration isnot uniform. When the opposing antennas areregarded as point-wave sources and the maxi-

mum aperture dimension of the test antenna isD, the distance d between the antennas result-ing in measurement error of 0.05 dB or lowercan be expressed by the following formula［5］.

(4)

When the opposing antenna is a hornantenna, the distance d between the antennascan be expressed by formula (5), given thatthe maximum diameters of both test antennaare D1 and D2.

(5)

To suppress error to ≤0.05 dB in measure-ment of a standard horn antenna with a fre-quency coverage of Band 1 to Band 8, theminimum required distance between theantennas is 14.3 m for Band L. This require-ment was satisfied by the large anechoicchamber, which allowed for a distance of upto 14.6 m between antennas. Under these mea-surement conditions, the error Lg in the far-field condition was ±0.048 dB. For Band H,on the other hand, the minimum required dis-tance between the antennas is 18.2 m, and thisrequirement could not be met in measurementusing the large anechoic chamber. Althoughthe required distance could be attained if theantennas were set up in the diagonal directionin the large anechoic chamber, this wouldresult in a greater coaxial cable length andwould also generate a number of other prob-lems, such as a reduced S/N ratio. In view ofthe above, we decided to include the errorresulting from failure to satisfy the far-fieldcondition as a factor contributing to uncertain-ty. The calculation of error Lg in measurementobtained with a distance of 14.6 m betweenthe antennas yielded a value of 0.078 dB［5］.This is a Type A error, and uncertainty is cal-culated based on a normal distribution.4.3.3 Error due to measurement dis-

persionIn the three-antenna method, propagation

loss is measured three times using three differ-ent antenna combinations. We have found that

35SAKASAI Makoto et al.

dispersion in these measurements is notablylarge. To evaluate this dispersion, we mea-sured the propagation loss 22 times, by sweep-ing the frequencies in Band L and Band H inthe large anechoic chamber under conditionsequivalent to those of actual EMI antenna cali-bration, and calculated the standard deviation.Figures 4 and 5 show example results. Sincemeasurement dispersion has a direct effect onthe level of reception, we multiplied theobtained error value in decibels by 1/2 andmultiplied the product by three, since the sameerror occurs in all three antennas, in the samemanner as when calculating uncertaintycaused by error due to a coaxial cable bend.The calculations yielded values of ±0.29 dBfor Band L and ±0.41 dB for Band H.

This dispersion in measurement is evaluat-ed as a Type A error, and uncertainty is calcu-lated based on a normal distribution.4.3.4 Error in axial alignment4.3.4.1 Error in the horizontal-direction

settingFor the alignment of the antenna axes, we

set up a laser generator at the midpointbetween the opposing antennas in the largeanechoic chamber, and adjusted the positionsof the antenna platforms such that the laserbeam was aligned with the marks at the bot-tom of the apertures of the antennas. The lasergenerator featured a built-in level for automat-ic adjustment of horizontal and vertical posi-tions, and produced a laser beam correspond-ing to the X-Y axis. To measure error in thehorizontal-direction setting, we varied theposition of the receiving antenna by a distanceof 1 cm at a time (up to ±4 cm) in the horizon-tal direction and measured the resultant levelof reception. The results of this measurementare shown in Fig. 6. The antenna axis wasadjustable within a range of ±1 cm in the hori-zontal direction. Error resulting from a shift of±1 cm in the right or left direction was0.05 dB for Band L and 0.17 dB for Band H.While measurement dispersion has a directeffect on the level of reception, the antennagain is proportional to the square root of thereception level; thus we estimated error inaxial alignment in the horizontal direction bymultiplying the obtained error value (convert-ed to decibels) by 1/2 and multiplied the prod-uct by three, since this measurement was con-ducted three times. According to our calcula-tion results, the error Li in the horizontal-direction axial setting was ±0.08 dB for BandL and ±0.26 dB for Band H. As the error dueto the horizontal-direction setting is unique toeach measurement instrument, it is a Type Berror, and uncertainty is calculated based on arectangular distribution.Fig.4 Measurement dispersion (Band 5)

Fig.5 Measurement dispersion (Band 8)Fig.6 Example results of horizontal anten-

na axis alignment measurement

36 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

4.3.4.2 Error in the vertical-direction set-ting

To measure error in the vertical-directionsetting, we irradiated a laser beam from thelaser generator in the direction perpendicularto the aperture of the antenna, and varied thereceiving antenna height at increments of 1 cmfrom the center (up to ±4 cm) in the verticaldirection, and measured the resultant level ofreception. The measurement results are shownin Fig. 7. The antenna axis was adjustablewithin a range of ±1 cm in the vertical direc-tion. Error resulting from a shift of ±1 cm was±0.09 dB for Band L and 0.24 dB for Band H.In the same manner as calculation of error inthe horizontal-direction setting, we multipliedthe obtained error value (converted to deci-bels) by 3/2. According to our calculationresults, the error Lj in the vertical-directionaxial setting was ±0.14 dB for Band L and±0.36 dB for Band H. Error due to the verti-cal-direction setting is a Type B error, anduncertainty is calculated based on a rectangu-lar distribution.

4.3.4.3 Error due to the azimuth settingUsing the beam from a laser generator, we

set up the antenna platforms such that theouter shapes of the transmitting and receivingantennas were centered. In this process, eachantenna was held in place by inserting theantenna into a dedicated slit so that theazimuth could be adjusted within ±1˚. Weevaluated the error in the azimuth by first

measuring the directional characteristic of theantenna and then obtaining the differencebetween the level obtained when the antennaswere facing precisely in accordance with thestipulated characteristic (0˚) and the levelsobtained when there was a deviation of ±1˚ to3˚. The results of measurement yielded valuesof ±0.04 dB for Band L and ±0.24 dB forBand H. Since error in the azimuth setting hasa direct effect on the level of reception, wemultiplied the obtained error value (in deci-bels) by 3/2. According to our calculationresults, the error Lk in the axial azimuth set-ting was ±0.06 dB for Band L and ±0.36 dBfor Band H. Error due to the axial azimuth set-ting is a Type B error, and uncertainty was cal-culated based on a rectangular distribution.

4.4 Error in measurement based onthe three-antenna method

4.4.1 Error due to ambient reflectionsin the anechoic chamber

The three-antenna method conducted in afree space is designed to evaluate measure-ment only of the direct radio wave that isemitted from the transmitting antenna andreaches the receiving antenna. Therefore, errorresults when the radio wave is reflected by thefloor, ceiling, wall, or antenna mounting basein the anechoic chamber, and these reflectedwaves are superimposed on the direct radiowave to form standing waves. To measure theeffect of these reflected waves, we measuredthe level of reception by moving the receivingantenna tower for a total distance of approxi-mately 50 cm. Figure 8 shows the results of18-GHz measurement in this case, indicatingerror of ±0.05 dB for Band L and ±0.09 dB forBand H. In the same manner as for other typesof error, the obtained error value (in decibels)was multiplied by 3/2. According to our calcu-lation results, error Ll due to ambient reflec-tions in the anechoic chamber was ±0.07 dBfor Band L and ±0.14 dB for Band H. Sincethe error due to ambient reflections in the ane-choic chamber represents reproducible values,it is a Type A error, and uncertainty is calcu-lated based on a normal distribution.

Fig.7 Example results for vertical antennaaxis alignment measurement

37SAKASAI Makoto et al.

4.4.2 Error in the antenna center ofradiation

In the three-antenna method, gain is calcu-lated as a function of the distance between thecenters of radiation of a radio wave transmit-ted and received by opposing antennas. How-ever, this value is usually defined based on thedistance between horn apertures, which areeasier to measure. Therefore, we estimateduncertainty in this case by considering the areabetween the feed section and antenna aperture,where the center of radiation is located. Asshown in Fig. 9, in the three-antenna method,the distance between the transmitting antennaaperture and the receiving antenna aperture isindicated as R, and the distance between thehorn aperture and the feed point is indicated asL. Although the distance d between the anten-nas used in the calculation should beexpressed as d = R + 2∆, which includes thedistance from the radiation center of the trans-mitting antenna to the radiation center of thereceiving antenna, we considered the arearange containing the center of radiation as an

uncertainty factor, since the exact radiationcenter positions were unknown.

Since the center of radiation is usuallylocated between the antenna aperture and thefeed section (the apex of the horn), the value dis within the range R ≤ d ≤ R + 2L. Assumingthe worst case, in which the center of radiationis located on the aperture plane, we performedour calculations based on the condition d = R.However, we believe that the true center ofradiation is located at the farthest point behindthe antenna and that the use of “d = R + 2L” isappropriate. When “d = R + 2L” is substitutedin formula (1), the gain G1 of antenna #1 isexpressed by the following formula.

(6)

The expression in braces represents thegenerated error. This is the worst value for theuncertainty resulting from the indeterminacyof the location of the center of radiation. Thefollowing formula expresses this error factor.

(7)

According to this formula, the longer the dis-tance R between the antennas, the less signifi-cant the antenna length L becomes, and“10 log(1 + 2L/R)” eventually converges to 0.In other words, if the distance R between theantennas is sufficiently large in relation toantenna dimension L, the error caused bydeviation in the center of radiation becomesminimal. Figure 10 shows the results of calcu-lations we performed using formula (7) for ourstudy of the required distance. The horizontalaxis on the graph indicates the distance Rbetween the antenna apertures, and the verticalaxis represents ∆G in formula (7).

As indicated on the graph, when R is10 m, for example, the worst value for uncer-tainty is approximately 0.2 dB even if antennalength L is 25 cm (the length of the double-ridged guide antenna, or DRGA). In practice,

Fig.8 Propagation characteristic (18 GHz)

Fig.9 Measurement distance and centerof radiation used in three-antennamethod

38 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

we measured the characteristic of fieldstrength distance by varying the distancebetween the antennas, obtained a regressionline based on the measured characteristic, andestimated the center of radiation using theconventional method［1］(i.e., using a lineextended from the regression line to estimatethe center of radiation within the aperture).According to our results, error due to the devi-ation in the center of radiation was ±0.29 dBfor Band L and ±0.28 dB for Band H. Thesevalues are significantly smaller than thoseshown in Fig. 10, and represent appropriateresults. This is a Type B error, and uncertaintyis calculated based on a rectangular distribu-tion.

4.4.3 Error proceeding from mismatch-ing

Using the three-antenna method, gains G1,G2, and G3 of antennas #1, #2, and #3 can becalculated using formulas (1) through (3). Letus now examine the measurement of propaga-tion loss between the transmitting and receiv-ing antennas using antennas #1 and #2 select-ed from the three antennas (#1, #2, and #3).Figure 11 shows a schematic diagram of thistest method. Diagram (a) shows the setup inwhich received power P21 is measured with thetwo connected antennas. Diagram (b) illus-trates a setup in which the received power P0

is measured with antennas that are directlyconnected via an adaptor. The received powerP21 obtained as shown in Fig. 11 (a) isexpressed as follows when mismatching at theantenna terminal and the SG terminal aretaken into consideration, in addition to losscaused by the pad and cable.

(8)

Received power P0 in Fig. 11 (b) is as follows.

Fig.10 Results of calculation for center ofradiation

Fig.11 Measurement system for three-antenna method

39SAKASAI Makoto et al.

(9)

Whereas,Pg : Signal source output powerΓg : Signal source output reflection

coefficientΓL : Receiver input reflection coeffi-

cientΓT : Reflection coefficient when signal

source side is viewed from trans-mitting antenna connector

ΓR : Reflection coefficient when receiv-er side is viewed from receivingantenna connector

[CT] : S matrix for combination of cableon transmitting side and pad

[CR] : S matrix for combination of cableon receiving side and pad

[SD] : S matrix for direct-coupling con-nector

[S(ji)A] : S matrix between two antennas (#i→ #j)

Received power was obtained for othercombinations of antennas in the same manner,and these values were substituted in formula(1), yielding the following formula.

(10)

In formula (10), the expression in bracesindicates the factor that produces uncertaintyin the calibration result. Here, five approxima-tions are given.• When antennas are connected and measure-

ment is conducted, SA21 and SA12 are suffi-ciently smaller than 1 and multiple reflec-tions can be ignored.

• S =S (SA11 for transmitting antenna #3(23)A11

(13)A11

remains unchanged even if the receivingantenna is changed)

• S =S (SA22 for receiving antenna #2remains unchanged even if the transmittingantenna is changed)

• SD11 and SD22 for the through-adaptor areextremely small values.

• SD21 and SD12 for the through-adaptor caneach be assumed to equal 1.

Based on the above conditions, formula (10)can be rewritten as follows:

(11)

Whereas,(1-S ΓT) : Multiple reflections at the con-

nection of antenna #1 and cableon transmitting side

(1-S ΓR) : Multiple reflections at the con-nection of antenna #1 and cableon receiving side

(1-S ΓT) : Multiple reflections at the con-nection of adaptor and cable ontransmitting side

(1-S ΓR) : Multiple reflections at the con-nection of adaptor and cable onreceiving side

(1-ΓTΓR) : Multiple reflections betweencable on transmitting side, adap-tor, and cable on receiving side

Each factor in the braces in formula (11)represents the uncertainty of a U-shaped dis-tribution. Therefore, by actually measuring thevolume of each reflection coefficient, it is pos-sible to determine uncertainty attributable tomismatching. Figure 12 shows an example ofcalculation of this uncertainty. It should benoted that Fig. 12 shows the results of calcula-tion performed for each frequency. Since thiserror is a Type B error, uncertainty is calculat-ed based on a U-shaped distribution.

To calculate uncertainty Umismatch due toactual mismatching, we used the worst-casevalues in each band based on a U-shaped dis-tribution, as shown below.

D22

D11

(13)A22

(21)A11

(23)A22

(21)A22

40 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

(12)

5 Uncertainty budget

We evaluated uncertainty in the EMIantenna calibration of horn antennas with afrequency range of 1 GHz to 18 GHz using thethree-antenna method. Since the antennaunder calibration covered a frequency range of1 GHz to 18 GHz in eight bands, this frequen-cy range was divided at 5.85 GHz into Band Land Band H. Table 1 shows the uncertaintybudget. Based on these results, we determinedthat the expanded uncertainty (coverage factor

k = 2) was ±0.7 dB for Band L and ±1.1 dBfor Band H.

6 Conclusions

We examined 14 error factors that wouldresult in uncertainty in EMI antenna calibra-tion of a pyramidal standard gain horn antennawith a frequency coverage of 1 GHz to18 GHz. The results of our study showedexpanded uncertainty (coverage factor k = 2)of ±0.7 dB for Band L (1 GHz to 5.85 GHz)and ±1.1 dB for Band H (5.85 GHz to18 GHz).

Prior to our evaluation of uncertainty,NICT switched from its conventional antennacalibration system, which had incorporated amicrowave receiver, to a new measurementsystem using a network analyzer. This net-work analyzer provides a wide dynamic rangeeliminating the need for the previously useddirectional coupler, down-converter, poweramplifier, and other components; the newsetup also simplified the calibration system forgreater ease of use. The simplified system alsoenabled us to realize the concept we presently

Fig.12 Error due to mismatching (Band 8)

Table 1 Uncertainty budget for 1-GHz to 18-GHz horn antenna calibration

41SAKASAI Makoto et al.

apply to the evaluation of mismatch problemsin high-frequency attenuators; thus, we wereable to indicate the uncertainty due to mis-matching clearly, using actual measurements.

Further, we focused on error in the hornantenna center of radiation and error due tomismatching. For error in the center of radia-tion, we varied the distance between theopposing antenna apertures by approximately4 m and measured the propagation distancecharacteristic (field strength). Based on thedistance characteristic, we obtained the regres-sion line, extended that line, and estimated thecenter of radiation inside the aperture. Thismethod simplified the estimation of the centerof radiation based on antenna dimensions.Comparison of the results obtained by the twomethods indicated that these values were veryclose.

The following describes precautions to beobserved in EMI antenna calibration of hornantennas with a frequency coverage of 1 GHzto 18 GHz.(1) To minimize uncertainty in EMI antenna

calibration due to inaccuracy in the centerof radiation, determine the distancebetween antennas by estimating the centerof radiation through measurement of thefield strength distance characteristic or byassuming a center of radiation at the mid-point between the aperture of the antennaunder calibration and the feed point.

(2) Our study was limited to EMI antenna cal-

ibration of standard gain horn antennas.For other types of antennas of differentshapes and characteristics (such as double-ridged guide antennas), it is necessary toreevaluate uncertainty by measuring direc-tional characteristics and reflection coeffi-cients in advance.

(3) The characteristics of an anechoic chambercan change over time due to the aging ofthe wave-absorbing material used. There-fore, it is necessary to measure site attenu-ation periodically in order to confirm thecharacteristics of the anechoic chamber.

(4) In order to minimize dispersion in mea-surement, it is important to handle careful-ly and regularly check the coaxial cableand the connecting pads used with the cali-bration system.We are currently developing an EMI

antenna calibration system for horn antennaswith a frequency coverage of 18 GHz to40 GHz. When this is complete, we plan toevaluate uncertainty using the methoddescribed in this paper.

Acknowledgements

We would like to express our appreciationto Professor Akira Sugiura at Tohoku Univer-sity for his kind guidance regarding EMIantenna calibration and its improvements inaccuracy.

References01 H. Masuzawa, et. al., “Calibration System for 1-5 GHz-band Field Strength Meters”, Review of CRL, pp.

73-81, June 1993.(in Japanese)

02 E.B. Larsen, R, L. Ehret D. G. Gamell, and G. H. Koepke, “Calibration of Antenna Factor at a Ground

Screen Field site using an Automatic Network Analyzer”, 1989, IEEE International Symp. on EMC, pp.

19-24, 1989-5.

03 Y. Mushiake, “Antennas and Radio Propagation”, CORONA PUBLISHING, pp. 120-122, 1961. (in

Japanese)

04 K. Iizuka, “Guide to the Expression of Uncertainty in Measurement”, Japanese Standards Association,

pp. 26-27, 1996. (in Japanese)

05 IECE , Antenna Engineering Handbook, OHMSHA, pp. 440, 1980. (in Japanese)

42 Journal of the National Institute of Information and Communications Technology Vol.53 No.1 2006

SAKASAI Makoto

Researcher, EMC Measurement Group,Wireless Communications Department

Electromagnetic Compatibility

FUJII Katsumi, Dr. Eng.

Researcher, EMC Measurement Group,Wireless Communications Department

Electromagnetic Compatibility

MASUZAWA Hiroshi

Radio Engineering & Electronics Asso-ciation

Calibration

SUZUKI Akira

Senior Researcher, EMC MeasurementGroup, Wireless CommunicationsDepartment

Calibration

YAMANAKA Yukio

Group Leader, EMC MeasurementGroup, Wireless CommunicationsDepartment

EMC Measurement

KOIKE Kunimasa Telecom Engineering Center Calibration