Wheeler Method for Evaluation of Antennas Submerged in Lossy Media

applied sciences

Article Wheeler Method for Evaluation of Antennas Submerged in Lossy Media

Yerim Oh, Dongkwon Choi , Jae-Yeong Lee and Wonbin Hong *

Department of Electrical Engineering, Pohang University of Science and Technology, Pohang 37673, Korea; [email protected] (Y.O.); [email protected] (D.C.); [email protected] (J.-Y.L.) * Correspondence: [email protected]; Tel.: +82-54-279-5935

Abstract: A Wheeler method for the evaluation of the radiation efficiency of submerged antennas within lossy media is presented and demonstrated for the first time in the literature. Extensive investigations have been devised by empirical and simulation methods. Normal-mode helical antenna (NMHA) was first designed and fabricated to exemplify a real-life application at the UHF band (0.3 to 3 GHz). The antenna under test (AUT) was evaluated within an artificial lossy material using a series of Wheeler caps featuring different radii to study the validity of this method. The error between the experimental and simulation radiation efficiency is below 3% near the theoretical radian length. The presented measurement method of radiation efficiency without any essential measurement facilities or accessories could be a promising candidate for fast and accurate evaluation for any wire-type antenna submerged within lossy media.

Keywords: radiation efﬁciency evaluation; radiation resistance measurement; Wheeler method; lossy media; submerged antennas

Citation: Oh, Y.; Choi, D.; Lee, J.-Y.; Hong, W. Wheeler Method for Evaluation of Antennas Submerged 1. Introduction in Lossy Media. Appl. Sci. 2021, 11, Antenna radiation efficiency is an important parameter for calculating the wireless 1862. https://doi.org/10.3390/ link budget and optimizing antenna structures. This can be controlled and improved app11041862 by modifying the antenna topology in the case of the constant antenna volume [1–4]. Currently, various methods such as pattern integration method, the Wheeler method [5–8], Academic Editors: Costantino radiometric method [9], and the Q–factor method [10] have been reported for measuring De Angelis and Hosung Choo radiation efficiency in free-space. For some applications, such as in underwater, underground, and in-body scenarios, Received: 18 January 2021 wireless signals propagate through lossy media [11–15]. These usually have short-range Accepted: 18 February 2021 Published: 20 February 2021 communication systems due to the high attenuation of electromagnetic (EM) waves in the lossy medium. Meanwhile, the antenna characteristics are significantly different from those

Publisher’s Note: MDPI stays neutral in free space. In this respect, antennas submerged in lossy media has been analytically with regard to jurisdictional claims in and numerically studied using ideal dipole antennas. These studies include modified published maps and institutional affil- parameters such as radiation efficiency, directivity, gain and effective area [16,17], and the iations. effects of the insulation layer of submerged antennas and the equivalent circuit model of uninsulated antenna [18,19]. Since the conventional radiation efficiency [20] is only useful for lossless media, studies of radiation efficiency in lossy media have been in demand. The radiation characteristics of submerged antennas in lossy media have been mostly measured using the gain comparison Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. method which employs standard gain reference antennas [21–24]. The recently reported This article is an open access article measurement technology using a reverberation chamber was conducted to measure the distributed under the terms and radiation efficiency in consideration of the spurious radiation effect of the feed cable [25]. conditions of the Creative Commons However, the attenuation area is different depending on the conditions of the lossy medium, Attribution (CC BY) license (https:// such as shape, size, and antenna location [21]. In addition, it is difficult to apply this creativecommons.org/licenses/by/ approach for applications such as establishing a wireless link between implanted devices. 4.0/). To resolve these drawbacks, a modified radiation efficiency is introduced based on the

Appl. Sci. 2021, 11, 1862. https://doi.org/10.3390/app11041862 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x 2 of 10

Appl. Sci. 2021, 11, 1862 2 of 10 to apply this approach for applications such as establishing a wireless link between implanted devices. To resolve these drawbacks, a modified radiation efficiency is introduced based on the total power of the radiated field through the spherical surface with a radius total power of the radiated field through the spherical surface with a radius of propagation of propagation distance [16,17,26,27]. However, the modified radiation efficiency method distance [16,17,26,27]. However, the modified radiation efficiency method still exhibits an stillinverse exhibits proportion an inverse between proportion measurement between datameasurement accuracy anddata testingaccuracy time and to testing obtain time total toradiated obtain total power radiated in all spherical power in surfaces. all spherical surfaces. ThisThis paper paper introduces introduces and and demonstrates demonstrates an an efficient efficient evaluation evaluation method method for for the the radi- ra- ationdiation efficiency efficiency of ofsubmerged submerged antennas antennas in inlossy lossy media media by by using using the the Wheeler Wheeler method. method. WithoutWithout the the required required measurement measurement facilities facilities or or e essentialssential accessories accessories to to obtain obtain electric electric field field intensityintensity or or power power density, density, the the presented presented Whee Wheelerler cap cap method method has has been been devised devised featuring featuring aa short short testing testing time and high accuracy usingusing onlyonly thethe Wheeler Wheeler metallic metallic cavity. cavity. This This paper paper is isorganized organized as as follows: follows: Section Section2 introduces 2 introduces the the antenna antenna radiation radiation efficiency efficiency for for lossy lossy media; media;in Section in Section3, the 3, evaluation the evaluation method method of radiation of radiation efficiency efficiency in media in media with variouswith various dielectric die- lectricconstant constant and loss and tangent loss tangent has been has demonstrated been demonstrated by using by the using Wheeler the Wheeler method, method, and the andmeasured the measured efficiency efficiency of a wire of antenna a wire antenna within the wi artificialthin the artificial lossy material lossy material [28] at the [28] UHF at theband UHF (0.3 band to 3 GHz)(0.3 to is 3 concluded GHz) is concluded to be in good to be agreement in good agreement with the measured with the efficiencies; measured efficiencies;Section4 concludes Section 4 the concludes paper. the paper.

2.2. Antenna Antenna Radiation Radiation Efficiency Efficiency for for Lossy Lossy Media Media MeasurementMeasurement using using the the gain gain comparison comparison meth methodod in lossy in lossy media media is presented is presented in Fig- in ureFigure 1. The1 . Thepropagation propagation region region between between Tx and Tx Rx and is Rxdivided is divided into two into physical two physical layers: layers: lossy mediumlossy medium and air. and Inevitably, air. Inevitably, the radiated the radiated field is field scattered is scattered at the atboundary. the boundary. Attenuation Atten- regionuation R1 region is different R1 is different depending depending on the cond on theitions conditions of the lossy of the medium lossy medium such as suchshape, as size,shape, and size, antenna and antenna location. location. In this case, In this the case, radiation the radiation efficiency efficiency based basedon combining on combining radi- atedradiated power power in all in directions all directions cannot cannot be specified be specified [21]. [21].

FigureFigure 1. 1. IllustrationIllustration of of conventional conventional gain comparisoncomparison methodmethod whichwhich evaluatesevaluates radiation radiation characteris- charac- teristicstics for antennafor antenna in lossy in lossy media. media.

AA modified modified radiation radiation efficiency efficiency 𝜂ηMR ofof the the antenna antenna for for lossy lossy media media is defined is defined as fol- as lows:follows: 2 ηMR(dr) = Prad(dr)/Pacc = Prad(dr)/ Pin 1 − |S11| , (1) 𝜂𝑑𝑃𝑑/𝑃 𝑃𝑑/𝑃1|𝑆| , (1) where P is the total radiated power related to the propagation distance due to the where 𝑃rad is the total radiated power related to the propagation distance due to the path path loss in the lossy media (Figure2), P is the incident power, and P is the power loss in the lossy media (Figure 2), 𝑃 is thein incident power, and 𝑃 is radthe power inci- incident to the antenna terminals. It is calculated by integrating the power flow normal dent to the antenna terminals. It is calculated by integrating the power flow normal to the to the virtual sphere surface according to the radial distance from the antenna center [4]. virtualHowever, sphere all previouslysurface according reported to works the radial related distance to the from modified the antenna radiation center efficiency [4]. How- have ever,been all demonstrated previously reported and verified works without related experimental to the modified results radiation [16,17, 26efficiency,27]. have been demonstrated and verified without experimental results [16,17,26,27]. Appl. Sci. 2021, 11, 1862 3 of 10 Appl. Sci. 2021, 11, x 3 of 10

Appl. Sci. 2021, 11, x 3 of 10

Figure 2. Simulation setup for calculation of radiated power.power.

The Wheeler method is used to assess the efficiency efficiency η𝜂MR of of thethe insulatedinsulated antennaantenna inin lossylossy media (Figure 33a).a). WhenWhen d𝑑r is is equal equal to to the the radius radius of of the the WheelerWheeler cap,cap, thethe modifiedmodified radiation efficiencyefficiency cancan bebe brieflybriefly obtainedobtained usingusing thethe WheelerWheeler method.method. WhenWhen thethe metallicmetallic cap with Figure a a radius radius2. Simulation of of radian radian setup forlength lengthcalculation is covered, is of covered, radiated the power. the radiation radiation resistance resistance can be can removed be removed with withan equivalent an equivalent circuit, circuit, as shown as shown in Figure in Figure 3b. 3Theb. The radiation radiation efficiency efficiency 𝜂ηWR is obtainedis obtained as asfollows: follows: The Wheeler method is used to assess the efficiency 𝜂 of the insulated antenna in lossy media (Figure 3a). When 𝑑 is equalRe{Z toin }the− radiusRe{Z WCof the} Wheeler cap, the modified radiation efficiency can be brieflyηWR =obtained using the Wheeler ,method. When the metallic (2) 𝜂 Re{Zin} , (2) cap with a radius of radian length is covered, the radiation resistance can be removed with where Z is the antenna input impedance, Z is the input impedance𝜂 by enclosing the wherean 𝑍 inequivalent is the antenna circuit, as input shown impedance, in Figure 3b. 𝑍TheWC radiation is the input efficiency impedance is obtained by enclosing as the antennafollows: with a radiation shield [8]. The radius of the radiation shield is equal to the radian antenna with a radiation shield [8]. The radius of the radiation shield is equal to the radian length, where the far-field and near-field have the same intensity. The radian length rl in length, where the far-field and near-field𝜂 have the same, intensity. The radian length(2) 𝑟 in free space is as follows: free space is as follows: where 𝑍 is the antenna input impedance,λg 𝑍 isλ the0 input impedance by enclosing the rl = = √ , (3) antenna with a radiation shield [8]. The radius2π of2 theπ radiationε shield is equal to the radian 𝑟 r, (3) length, where the far-field and near-field have the same√ intensity. The radian length 𝑟 in wherefreeλ0 isspace the is wavelength as follows: in a vacuum, λg is the wavelength in the media. In lossy media, where 𝜆 is the wavelength0 in a vacuum, 𝜆 is the wavelength in the media. In lossy the radian length rl can be calculated as follows: 𝑟 ′ 𝑟 , (3) media, the radian length can be calculated as √follows: 0 1 where 𝜆 is the wavelength in= a vacuum, 𝜆 is the wavelength in the media. In lossy rl 𝑟′ ., , (4)(4) n 2 2o0.25 media, the radian length 𝑟′ can be (calculatedεµω2) + as( follows:ωµσ) where 𝜀 is the permittivity, 𝜇 is the𝑟 ′ permeability, 𝜎 ,is the conductivity, 𝜔 is the angu- . (4) wherelar frequency.ε is the permittivity, µ is the permeability, σ is the conductivity, ω is the angular frequency.where 𝜀 is the permittivity, 𝜇 is the permeability, 𝜎 is the conductivity, 𝜔 is the angular frequency.

(a) (b) (a) (b) Figure 3. (Figurea) Structure 3. (a) Structure of the of antenna the antenna isolated isolated from from the the lossylossy me mediumdium by bythe theinsulating insulating layer and layer the andWheeler the cap. Wheeler (b) cap. Equivalent circuit model of antenna within the Wheeler cap. (Figureb) Equivalent 3. (a) Structure circuit model of the of antenna antenna isolated within the from Wheeler the lossy cap. medium by the insulating layer and the Wheeler cap. (b) Equivalent circuit model of antenna within the Wheeler cap. Appl. Sci. 2021, 11, x 4 of 10 Appl. Sci. 2021, 11, 1862 4 of 10

3. Analysis of the Wheeler Cap Method of Antenna Surrounded by the Lossy Media 3.1.3. Analysis Simulation of the Wheeler Cap Method of Antenna Surrounded by the Lossy Media 3.1. Simulation 3.1.1. Simulation Setup 3.1.1. Simulation Setup The radiation efficiency evaluation method is validated by stepwise analysis accord- The radiation efficiency evaluation method is validated by stepwise analysis according ing to the change in the dielectric constant and conductivity of the medium encompassing to the change in the dielectric constant and conductivity of the medium encompassing the antenna. The radiation efficiency analysis using the Wheeler method is conducted the antenna. The radiation efficiency analysis using the Wheeler method is conducted through ANSYS HFSS. A normal-mode helical antenna (NMHA) resonating at a fre- through ANSYS HFSS. A normal-mode helical antenna (NMHA) resonating at a frequency quency of 172 MHz in air and an insulation layer are designed using copper wire and of 172 MHz in air and an insulation layer are designed using copper wire and Teflon (εr = 𝜀 δ Teflon2.1, tan (δ== 0.001),2.1, tan respectively.= 0.001), respectively. The detailed The dimensions detailed dimensions of the antenna of the are antenna illustrated are illustrated(Figure4a). (Figure The metallic 4a). The cavity metallic is designed cavity is as designed a hemisphere as a hemisphere consisting of consisting PEC (Figure of PEC4b). (FigureThe space 4b). inside The space the insulation inside the layerinsulation is modeled layer is as modeled air and remainedas air and remained identical acrossidentical all acrossexperiments. all experiments. The simulation The simulation setup is presented setup is presented in Figure 4inc. Figure The size 4c. of The the size lossy of mediumthe lossy mediumis 1000 mm is 1000× 1000 mm mm × 1000× 500 mm mm. × 500 mm.

FigureFigure 4. 4. GeometryGeometry of of simulation simulation setup: setup: (a ()a cross-sectional) cross-sectional view view of ofNMHA NMHA and and (b) ( bwith) with metallic metallic cavity, (c) perspective view. (da = 20, pa = 3, ha = 6.4, ta = 0.8, r = 15, h = 40, t = 1, rg = 500, tg = 1, cavity, (c) perspective view. (𝑑 = 20, 𝑝 = 3, ℎ = 6.4, 𝑡 = 0.8,i 𝑟 = 15,i ℎ = i40, 𝑡 = 1, 𝑟 = 500, t = 5. Unit: mm. 𝑡w = 1, 𝑡 = 5. Unit: mm. 3.1.2. Radiation Efficiency in Media with Dielectric Constant 3.1.2. Radiation Efficiency in Media with Dielectric Constant The radiation efficiency is analyzed for a medium with a high dielectric constant in a losslessThe state. radiation In this efficiency scenario, is only analyzed the dielectric for a medi constantum with of thea high material dielectric is controlled. constant Thein a losslessresults are state. sampled In this atscenario, a single only frequency the dielectric at which constant a resonance of the occurs material at each is controlled. medium. The results are sampled at a single frequency at which a resonance occurs at each medium. cavity length rw is expressed as a ratio of length-to-wavelength. The cavity length 𝑟 is expressed as a ratio of length-to-wavelength. The efficiency ηWR calculated according to the metallic cavity radius rw is compared The efficiency 𝜂 calculated according to the metallic cavity radius 𝑟 is compared with the efficiency ηMRcalculated based on the field computation (Figure2). The radiation withresistance the efficiency can be extracted 𝜂 calculated using a radiation based on shield the field with co amputation radius equal (Figure to the 2). radian The length.radia- tionThe comparisonresistance can shows be extracted that the using same radiationa radiation efficiency shield with can bea radius obtained equal when to the the radian cavity length. The comparison shows that the same radiation efficiency can be obtained when radius rw is equal to the radian length rl for each medium (Figure5). This ascertains that thethe cavity Wheeler radius method 𝑟 is applicableequal to the even radian for medialength featuring𝑟 for each a dielectric medium constant(Figure 5). other This than as- certains1. The radiation that the efficiencyWheeler method is maintained is applicab overle the even radian for media length featuring range. a dielectric constant other than 1. The radiation efficiency is maintained over the radian length range. Appl. Sci. 2021, 11, x 5 of 10

Appl.Appl. Sci. Sci.20212021, 11, 11x , 1862 5 of5 10 of 10

Figure 5. The radiation efficiency 𝜂 versus cavity radius 𝑟 with changes in the dielectric constant. 𝜂 is marked with a dash for the same color line. The radian length 𝑟 is marked with black lines.

3.1.3. Radiation Efficiency in Lossy Media The dielectric constant of the material is fixed at 1 and the conductivity is set as a variable. The results are sampled at a single frequency at which resonance occurs at each medium. The efficiency 𝜂 calculated according to the metallic cavity radius 𝑟 is compared with the efficiency 𝜂 calculated based on the field computation (Figure 2). As mentioned above, 𝜂 can obtain the uniform radiation efficiency in lossless media (Fig- ure 5), but it cannot be applicable in lossy media. As radial distance 𝑑 increases, the

propagation loss increases and the radiation efficiency 𝜂 decreases rapidly (Figure 6). 𝜂 𝑟 FigureFigure 5. WhenThe 5. The radiation the radiation conductivity efficiency efficiency isη WRas versus lowversus as cavity cavity0.01 radius S/m, radius therw efficiency withwith changes 𝜂 in the is almost dielectric similar constant.con- to stant. 𝜂 is marked with a dash for the same color line. The radian length 𝑟 is marked with ηtheMR radiationis marked withefficiency a dash 𝜂 for the calculated same color by line. the The field radian calculator length r(Figurel is marked 2) in with a short black propa- lines. black lines. gation distance range. Additionally, the radiation efficiency of 𝜂 and 𝜂 show good 3.1.3. Radiation Efficiency in Lossy Media agreement when the cavity radius 𝑟 is equal to the radian length 𝑟′ of each medium. 3.1.3. Radiation Efficiency in Lossy Media This Theclearly dielectric confirms constant that the of Wheeler the material method is can fixed be at applicable 1 and the to conductivity lossy media. is set as a variable.TheHowever, dielectric The when resultsconstant the are conductivityof sampledthe material at is a relatively is single fixed frequency at high, 1 and the the aterrorwhich conductivity is significantly resonance is set occursincreased as a at variable.eachas 𝑟 medium. The becomes results The larger are efficiency sampled than theη WRatradian acalculated single length frequency according𝑟′. The at coupling which to the resonance metallic resistance cavity occurs between radius at each therw an-is medium.comparedtenna andThe withefficiencythe cavity the efficiency mode𝜂 calculated of theηMR radiationcalculated according shield based to thecauses on metallic the errors field cavity in computation the radius efficiency 𝑟 (Figureis measure- com-2). paredAsment mentionedwith [29,30]. the efficiency When above, theη MR𝜂 cavitycan calculated resonator obtainthe based is uniform fill oned thewith radiation field lossy computation material, efficiency the in(Figure quality lossless 2). factormedia As is (Figure5), but it cannot be applicable in lossy media. As radial distance d increases, the mentionedlowered above, [31]. Therefore, 𝜂 can obtainthe increased the uniform 𝑍 radiation due to the efficiency cavity mode in lossless causesr media errors (Fig- over a urepropagationwide 5), but range. it cannot lossA radiation increases be applicable shield and theshould in radiation lossy be media.selected efficiency As in anradialη MRappropriate decreasesdistance shape.𝑑 rapidly increases, (Figure the6). propagation loss increases and the radiation efficiency 𝜂 decreases rapidly (Figure 6). When the conductivity is as low as 0.01 S/m, the efficiency 𝜂 is almost similar to the radiation efficiency 𝜂 calculated by the field calculator (Figure 2) in a short propagation distance range. Additionally, the radiation efficiency of 𝜂 and 𝜂 show good agreement when the cavity radius 𝑟 is equal to the radian length 𝑟′ of each medium. This clearly confirms that the Wheeler method can be applicable to lossy media. However, when the conductivity is relatively high, the error is significantly increased as 𝑟 becomes larger than the radian length 𝑟′. The coupling resistance between the antenna and the cavity mode of the radiation shield causes errors in the efficiency measurement [29,30]. When the cavity resonator is filled with lossy material, the quality factor is lowered [31]. Therefore, the increased 𝑍 due to the cavity mode causes errors over a wide range. A radiation shield should be selected in an appropriate shape.

𝜂 𝑟 FigureFigure 6.6. TheThe radiationradiation efﬁciencyefficiencyη WRversus versus cavity cavity radius radiusrw with with changes changes in thein the conductivity conductivity and and 𝜂 versus radial distance 𝑑 is marked with a dash for the same color line. The radian 0 ηMR versus radial distance dr is marked with a dash for the same color line. The radian length rl is length 𝑟 ′ is marked with black lines. marked with black lines.

When the conductivity is as low as 0.01 S/m, the efficiency ηWR is almost similar to the radiation efficiency ηMR calculated by the field calculator (Figure2) in a short propagation distance range. Additionally, the radiation efficiency of ηWR and ηMR show good agreement 0 when the cavity radius rw is equal to the radian length rl of each medium. This clearly confirms that the Wheeler method can be applicable to lossy media. However, when the conductivity is relatively high, the error is significantly increased 0 as rw becomes larger than the radian length rl . The coupling resistance between the antenna and the cavity mode of the radiation shield causes errors in the efficiency measure-

Figurement 6. The[29, 30radiation]. When efficiency the cavity 𝜂 resonator versus cavity is ﬁlled radius with 𝑟 lossy with changes material, in thethe conductivity quality factor is andlowered 𝜂 versus [31]. radial Therefore, distance the 𝑑 increased is marked ZwithWC adue dash to for the the cavity same color mode line. causes The radian errors over a lengthwide 𝑟′ range. is marked A radiation with black shield lines. should be selected in an appropriate shape. Appl.Appl. Sci. Sci. 2021 2021,, ,11 11,, ,x 1862 x 66 of of 10 10

3.2.3.2.3.2. Measurement MeasurementMeasurement 3.2.1.3.2.1.3.2.1. Measurement MeasurementMeasurement Setup SetupSetup AAA UHF UHFUHF band bandband antenna antennaantenna was waswas devised deviseddevised and andand the the radiation radiation efficiency efﬁciencyefficiency was was measured measured when when thethethe antenna antennaantenna was waswas submerged submergedsubmerged within withinwithin an anan artifici artiﬁcialartificialal lossylossy material.material. The TheThe detailed detaileddetailed measurement measurementmeasurement setupsetupsetup isisis introduced introducedintroduced in inin Figures FiguresFigures7 and 77 and8and. The 8.8. AUT TheThe AUT wasAUT made waswas of mademade NMHA ofof NMHA typeNMHA and typetype was and blockedand waswas blockedfromblocked the from from medium the the medium medium by a capsule-shaped by by a a capsule-shaped capsule-shaped polyimide polyimide polyimide (εr = 3.5, ( 𝜀(𝜀 tan = = 3.5, 3.5,δ = tan 0.008)tanδδ = = 0.008) insulation0.008) insulation insulation layer layer(Figurelayer (Figure (Figure7a). Antenna 7a). 7a). Antenna Antenna in the UHFin in the the band UHF UHF within band band thewithinwithin lossy the the medium lossy lossy medium medium are described are are described described in Table 1in .in TableRadiationTable 1. 1. Radiation Radiation shields withshields shields three with with radii three three (20, radii radii 30, 70.(2 (20,0, Unit:30, 30, 70. 70. mm) Unit: Unit: were mm) mm) designed were were designed designed for demonstration. for for demon- demon- stration.Itstration. was fabricated It It was was fabricated fabricated by covering by by covering acovering copper a sheeta copper copper on sheet asheet hemisphere on on a a hemisphere hemisphere model using model model a 3D using using printing a a 3D 3D printingmethodologyprinting methodology methodology (Figure7 b).(Figure (Figure 7b). 7b).

(a(a) ) (b(b) )

FigureFigure 7.7. Illustration IllustrationIllustration of ofof ( (a(a)) )normal-mode normal-mode helical helical antenna antenna and and capsule-shapedcapsule-shaped insulation insulation layer, layer, (b(b) ) hemisphere-shapedhemisphere-shaped hemisphere-shaped radiationradiation shield. shield.

FigureFigureFigure 8. 8.8. Measurement MeasurementMeasurement system systemsystem for forfor evaluating evaluatingevaluating the thethe radi radiationradiationation efficiency efﬁciencyefficiency of of a a submerged submerged antenna. antenna.

Table 1. Fabricated Antenna Parameter. TableTable 1. Fabricated Antenna Parameter.

ParameterParameter 𝒅𝒅𝒂𝒂 𝒑𝒑𝒂𝒂 𝒉𝒉𝒂𝒂 𝒕𝒕𝒂𝒂 𝒓𝒓𝒊 𝒊 Parameter da pa ha ta ri ValueValue (mm) (mm) 9 9 3 3 2 2 0.8 0.8 5 5 Value (mm) 9 3 2 0.8 5 ParameterParameter 𝒉𝒉𝒊 𝒊 𝒕𝒕𝒊 𝒊 𝒓𝒓𝒈𝒈 𝒕𝒕𝒈𝒈 𝒕𝒕𝒘𝒘 h t r t t ParameterValueValue (mm) (mm) i 1313 i 11 g 100100 g 0.070.07 0.07w0.07 Value (mm) 13 1 100 0.07 0.07 TheThe overall overall measurement measurement syst system,em, including including a a lossy lossy medium medium and and container, container, is is de- de- scribedscribedThe in in overallFigure Figure 8. measurement8. The The material material system,with with the the includingelectrical electrical properties aproperties lossy medium ( 𝜀(𝜀 = = 58, 58, and 𝜎𝜎= = container,0.82 0.82 S/m) S/m) at isat 400 de-400 MHzscribedMHz waswas in Figurecomposedcomposed8. The ofof material deionizeddeionized with waterwater the electrical (51.(51.16%),16%), properties sodiumsodium chloride (chlorideεr = 58, (1.49%),σ(1.49%),= 0.82 sugar S/m)sugar (46.78%),at(46.78%), 400 MHz bactericide bactericide was composed (0.05%), (0.05%), of and and deionized hydroxyethyl hydroxyethyl water (51.16%),cellulose cellulose (0.52%) sodium (0.52%) [28]. chloride[28]. The The (1.49%),lossy lossy medium medium sugar (46.78%), bactericide (0.05%), and hydroxyethyl cellulose (0.52%) [28]. The lossy medium Appl.Appl.Appl. Sci.Sci. Sci. 20212021 2021,, 11,11 11,, 1862,x x 777 ofof of 1010 10

filled a 200 mm × 200 mm × 100 mm container. The antenna was placed in the center of ﬁlledfilled aa 200200 mmmm ×× 200 mm ×× 100100 mm mm container. The antenna was placed in thethe centercenter ofof the ground. thethe ground.ground.

3.2.2.3.2.2. MeasurementMeasurement ResultResult TheThe reflectionreflection reflection characteristicscharacteristics characteristics measurement measurement measurement of of of the the the antenna antenna antenna was was was carried carried carried out out out with with with a vectora a vec- vec- networktortor networknetwork analyzer analyzeranalyzer (VNA). (VNA).(VNA). The antennaTheThe antennaantenna radiation radiationradiation efficiency efficiencyefficiency measurement measurementmeasurement was conducted waswas con-con- usingductedducted three using using different three three different different radiation radiation radiation shields to shields shields measure to to themeasure measure resistance the the resistance resistance of the antenna of of the the in antenna antenna each case. in in each case. The radiation efficiency 𝜂 measured at 400 MHz is compared with the two Theeach radiation case. The efficiency radiationη efficiencyWR measured 𝜂 at measured 400 MHz at is 400 compared MHz is with compared the two with simulation the two resultssimulationsimulation in Figure results results9. Asin in Figure theFigure cavity 9. 9. As As radius the the cavity becomescavity radius radius larger becomes becomes than the larger larger radian than than length, the the radian theradian error length, length, due tothethe the error error cavity due due mode to to the the ofcavity cavity the shield mode mode itselfof of the the [ 30shield shield] is similarly it itselfself [30] [30] confirmed is is similarly similarly in confirmed confirmed the measurement in in the the meas- meas- and simulation.urementurement and and The simulation. simulation. measurement The The measurement measurement results are in resu goodresultslts agreement are are in in good good with agreement agreement the simulation with with the the results simu- simu- usinglationlation theresults results Wheeler using using method. the the Wheeler Wheeler method. method.

Figure 9. The measured and simulation radiation efficiency 𝜂 versus cavity radius 𝑟 and Figure 9. The measured andand simulationsimulation radiationradiation efﬁciency efficiencyη MR𝜂versus versus cavity cavity radius radiusrw 𝑟and and simula- simulation 𝜂𝜂 versus radial distance 𝑑 𝑑. The radian length0 𝑟𝑟′′ is marked with black lines. tionsimulationηMR versus radial versus distance radial distancedr. The radian. The length radianr lengthl is marked is withmarked black with lines. black lines.

TheThe efﬁciencyefficiency efficiency valuesvalues values measuredmeasured measured withwith with aa a radiationradiation radiation shieldshield shield havinghaving having aa a radiusradius radius (20(20 (20 mm)mm) mm) closeclose close to the radian length 0𝑟 ′ (14.4 mm) is compared with the simulated values in Figure 10. toto thethe radianradian length lengthr l𝑟(14.4′ (14.4 mm) mm) is comparedis compared with with the the simulated simulated values values in Figure in Figure 10. The 10. calculatedTheThe calculated calculated error error error from from from 300 to300 300 600 to to MHz 600 600 MHz MHz is less is is thanless less than 3%.than 3%. 3%.

0.40.4

0.30.3

0.20.2

0.10.1

00 300300 400 400 500 500 600 600 Frequency [MHz] Frequency [MHz] Figure 10. The measured and simulated radiation efficiency (𝑑 = 𝑟 = 20 mm). Figure 10. The measured and simulated radiationradiation efﬁciencyefficiency ((d𝑑r= = rw𝑟= = 2020 mm).mm).

ThisThis study studystudy is isis the thethe first firstfirst to toto experimentally experimentallyexperimentally validate validatevalidate the thethe Wheeler WheelerWheeler method methodmethod for for thefor the conditionthe condi-condi- oftiontion lossy ofof lossylossy media. media.media. In previous InIn previousprevious studies studiesstudies of modified ofof modifiedmodified radiation radiationradiation efficiency, efficiency,efficiency, an ideal anan idealideal dipole dipoledipole or sourceoror source source was was was used used used or or limitedor limited limited only only only to to to numerical numerical numerical analysis. analysis. analysis. In In In comparison, comparison, comparison, we we we designeddesigned designed andand and measuredmeasured aa a practicalpractical practical UHFUHF UHF bandband band NMHANMHA NMHA thatthat that isis is applicableapplicable applicable forfor for submergedsubmerged submerged scenariosscenarios scenarios usingusing using Appl. Sci. 2021, 11, 1862 8 of 10

an artificial lossy material. The radiation efficiency measured at the theoretical radian length is in good agreement with that proposed in a previous study [16]. Table2 summarizes the performance comparisons between the proposed method and the state-of-the-art method. The proposed method uses the change in the resistance characteristic inside the cavity, whereas the principle of the other methods is based on the power of the electromagnetic field. It is noted that the proposed method measured the radiation efficiency only via the Wheeler cap, whereas [32] requires a lot of space and chambers for the measurement, including a shielded room. Therefore, the proposed method measures radiation efficiency in a fast and inexpensive way.

Table 2. Comparison of the proposed method with other works.

Required Measurement Error Between Acquisition Method for Ref. Facilities or Essential Simulation and Radiation Efﬁciency Accessories Measurement Average static power 2.4 × 2.4 × 2.4 m (Shield [32] transfer function at <4.5% room), reference antenna different 3 position Power integral normal [26]- Only simulation to the sphere Variation of the input This work Lossy medium, Wheeler cap <3% resistance

4. Conclusions We propose the Wheeler method to measure the radiation efficiency of an antenna submerged in lossy media as an alternative to gain comparison methods which are carried out in the far-field. The concept of modified radiation efficiency in lossy media has been studied but is still limited to theory and simulation [16,17,26,27]. This work empirically studies the application method of the Wheeler method to achieve a breakthrough in the limitations of previous studies. Also, the radiation efficiency measured at the theoretical radian length is highly correlated with that proposed in a previous study [16], indicating that this method can be further applied to different frequencies and scenarios in the future. The proposed method achieves very fast and inexpensive efficiency measurements without the need for other antennas or an expensive chamber. Additionally, the modified radiation efficiency can be used as a new figure of merit for evaluating submerged antennas for applications such as underwater, underground, and in-body communication systems. Furthermore, since the antenna radiation efficiency and propagation loss can be separated using the method presented in [26], it is expected to be useful for calculating the link budget of submerged channel modeling scenarios.

Author Contributions: Research conceptualization and methodology, D.C. and W.H.; Design and simulation, Y.O. and D.C.; Fabrication and measurement, Y.O. and D.C.; Writing-original draft, Y.O. and D.C.; Writing-review and editing, Y.O., J.-Y.L., and W.H. For other cases, all authors have participated. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) under Grant 2018R1A4A1025679, in part by the Basic Science Research Program through the NRF of Korea funded by the Ministry of Education under Grant 2018R1A6A3A01013261. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to thank ANSYS Korea for their generous support. Conﬂicts of Interest: The authors declare no conﬂict of interest. Appl. Sci. 2021, 11, 1862 9 of 10

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