Design of Dielectric Resonator Antenna Using Dielectric Paste

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Article Design of Dielectric Resonator Antenna Using Dielectric Paste

Hauke Ingolf Kremer 1, Kwok Wa Leung 1,*, Wai Cheung Wong 1, Kenneth Kam-Wing Lo 2 and Mike W. K. Lee 1

1 Department of Electrical Engineering, City University of Hong Kong, Hong Kong 999077, China; [email protected] (H.I.K.); [email protected] (W.C.W.); [email protected] (M.W.K.L.) 2 Department of Chemistry, City University of Hong Kong, Hong Kong 999077, China; [email protected] * Correspondence: [email protected]

Abstract: In this publication, the use of a dielectric paste for dielectric resonator antenna (DRA) design is investigated. The dielectric paste can serve as an alternative approach of manufacturing a dielectric resonator antenna by subsequently ﬁlling a mold with the dielectric paste. The dielectric paste is obtained by mixing nanoparticle sized barium strontium titanate (BST) powder with a silicone rubber. The dielectric constant of the paste can be adjusted by varying the BST powder content with respect to the silicone rubber content. The tuning range of the dielectric constant of the paste was found to be from 3.67 to 18.45 with the loss tangent of the mixture being smaller than 0.044. To demonstrate the idea of the dielectric paste approach, a circularly polarized DRA with wide bandwidth, which is based on a fractal geometry, is designed. The antenna is realized by ﬁlling a 3D-printed mold with the dielectric paste material, and the prototype was found to have an axial ratio bandwidth of 16.7% with an impedance bandwidth of 21.6% with stable broadside radiation.

Keywords: dielectric resonator antenna; dielectric paste; material measurement; wideband antenna; circularly polarized antenna; fractal antenna

Citation: Kremer, H.I.; Leung, K.W.; Wong, W.C.; Lo, K.K.-W.; Lee, M.W.K. 1. Introduction Design of Dielectric Resonator Dielectric resonator antennas (DRA) have been researched extensively for the last Antenna Using Dielectric Paste. three decades since their ﬁrst introduction in 1983 [1]. Some of the main features, which Sensors 2021, 21, 4058. https:// distinguish DRAs from other types of antennas, are their ease of excitation, comparably doi.org/10.3390/s21124058 wide bandwidths, and compact size [2,3]. Owing to manufacturing and material tolerance related issues, DRAs have not found widespread application outside of the academic world. Academic Editor: Ahmed A. Kishk For example, many DRAs employ very special geometric shapes, such as ﬂipped staired DRAs, H-shaped DRAs, T-shaped DRAs [4–6], or employ different dielectric constants, Received: 10 May 2021 such as multilayer ring DRAs or perforated DRAs [7–9]. Other structures may employ even Accepted: 8 June 2021 Published: 12 June 2021 more exotic structures, such as hook shaped DRAs [10], Y-shaped DRAs [11], pixelated DRAs [12], multiple circular sector DRAs [13], or have notches [14] and hollow regions

Publisher’s Note: MDPI stays neutral in their DRA structures [15]. These structures, even though they may possess remarkable with regard to jurisdictional claims in features, such as wide bandwidths, high gains, or multi-band operation, may not be easily published maps and institutional affil- manufactured using common methods and materials. Recently, compound dielectric iations. materials have attracted a lot of interest due to the possibility of their unconventional use. For example, in [16], a printable dielectric ink was developed, which was loaded with ferroelectric nano-particles. Using this ink, a fully printable phase shifter could be constructed. This new approach can help to avoid the use of expensive substrates, which are commonly used for such applications. Other examples of compound materials include Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. conductive materials, which can be used for flexible or conformable antenna designs, such This article is an open access article as patch antennas [17], flexible antenna substrates with adjustable dielectric constant [18], distributed under the terms and ceramic epoxy resin composite materials used for antenna miniaturization [19], or flexible conditions of the Creative Commons magnetic polymer composite substrates with equal permittivities and permeabilities for Attribution (CC BY) license (https:// antenna miniaturization [20]. Despite the obvious advantage of sparing manufacturing creativecommons.org/licenses/by/ cost, another advantage of such compound materials is that they can typically be tuned 4.0/). according to the need. This is especially useful for research and development activities.

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In this publication, a new method for DRA manufacturing is investigated. The method utilizes a dielectric paste that is realized by mixing silicone rubber and barium strontium titanate (BST) nanoparticles. The dielectric constant of the dielectric paste can be controlled flexibly by the content of the BST particles inside the paste. The paste is then used to design a circularly polarized DRA with wide bandwidth. A mold is constructed using the 3D-printing technique and then subsequently filled with the dielectric paste material. This way, geometric shapes that cannot be manufactured using conventional approaches can now be realized. For example, certain antenna types, such as fractal antennas, may require exotic shapes. As fractal antennas are known to be able to increase the bandwidth of antennas significantly, they have been investigated by researchers in the past [21]. For instance, fractal patch antennas have attracted a lot of attention [21–23]. Fractal DRAs have been investigated in the past as well [24–26]. The realization of fractal DRAs appears more challenging in practice when considering structures such as the Minkowski fractal DRA [24]. However, these types of fractals can be realized using patch antennas quite easily, as the PCB copper etching process can be utilized. Using the dielectric paste approach, new classes of DRAs could be realized. In particular, structures with complicated features or features that are located on the inside of the DRA could be realized, which would otherwise be very challenging to do using common manufacturing approaches. In this publication, a menger sponge fractal structure will be analyzed in order to demonstrate the usefulness of the dielectric paste manufacturing method. The fractal structure is used to design a circularly polarized antenna. A 3D-printed mold is utilized in order to contain the dielectric paste material, which fulfills the function of the DRA. The proposed antenna can be deployed for 2.4 GHz WiFi, ISM, and WiMAX applications. All the simulated results in this publication are generated using HFSS full wave simulation tool.

2. Dielectric Paste and Characterization In this section, the process of fabricating and characterizing the dielectric paste will be described. The dielectric paste consists of nano particle-sized barium strontium titanate (BST) powder with a measured dielectric constant and loss tangent of 20 and 0.023, respectively. The BST powder is mixed with a silicone rubber with a dielectric constant of 2.82 and a loss tangent of 0.0215. By changing the BST content relative to the silicone content, the dielectric constant of the paste can be varied according to the need. A split-post dielectric resonator is used to characterize the dielectric paste material. In this measurement, the resonance frequency and insertion loss of a single dielectric resonator (DR) element is measured. The setup is illustrated in Figure1. The dielectric resonator is embedded into a cavity, and a circular loop is used to excite DR resonance with a second loop serving as the signal output. The DR is split in half, and a gap of approximately 1.95 mm exists between the lower and upper half of the resonator with a minimum sample size of at least 40 mm × 40 mm. This gap can be used to insert a material under test (MUT) and characterize its dielectric properties. The electric ﬁeld is strong in the gap of the DR, hence, the setup is sensitive to a change of dielectric constant and loss tangent. By measuring the insertion loss and the resonance frequency of the DR before and after the MUT is inserted, the dielectric constant and loss tangent can be extracted. Sensors 2021, 21, x FOR PEER REVIEW 3 of 18

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tor. This way, the influence of the plastic sheet on the dielectric measurement was miti‐ gated. It should be noted, however, that no significant difference between the measure‐ ment result of a paste sample using an empty resonator calibration or plastic sheet cali‐ bration was found. This is understandable, because the plastic sheet has a thickness of approximately 0.1 mm and a much lower dielectric constant and loss tangent as compared to the dielectric paste. FigureFigure 1.1. SketchSketch ofof thethe split-postsplit‐post dielectricdielectric resonatorresonator measurementmeasurement setup.setup. TheThe MUTMUT isis placedplaced inin aa gap,gap, whichwhich separatesseparates thethe dielectricdielectric resonator.resonator. TheThe electricelectric fieldfield inin thisthis gapgap isis strong,strong, therefore,therefore, the the devicedevice isis sensitivesensitive toto aa changechange ofof dielectricdielectric constantconstant introducedintroduced byby thethe MUT.MUT. The The change change of of the the field field strength along the gap inside the resonator is displayed as well. The E‐field is strongest at the edges strength along the gap inside the resonator is displayed as well. The E-field is strongest at the edges of the gap close to the resonator and weakest in the center of the gap. of the gap close to the resonator and weakest in the center of the gap.

UnderNext, the normal preparation operation, of the the dielectric paste resonator samples would will be be calibrated described. by A measuring flowchart theof the resonance procedure frequency is given and in Figure insertion 2. Before loss of the the two measurement components device of the without paste, anynamely, sample the insertedBST particles into the and gap the at first.silicone As willrubber, be shown were later,mixed for together, the dielectric the pasteBST particles measurement, were apredried sample holderin an oven was used.for 20 Inmin particular, at 100 °C. a thinThis layer ensured of a that low moisture, loss plastic which sheet can was be used ab‐ sorbed by the BST particles, was evaporated. It is well known in the microwave commu‐ as a substrate for the dielectric paste. For this case, the resonator was calibrated while the plasticnity that sheet water substrate is a material was inserted with a intolarge the dielectric resonator, loss instead tangent. of Therefore, using empty moisture resonator. can Figure 1. Sketch of the split‐post dielectric resonator measurement setup. The MUT is placed in a Thisaffect way, the thedielectric influence loss of of the the plastic paste significantly sheet on the dielectricif it is absorbed measurement by the BST was powder. mitigated. After It gap, which separates the dielectric resonator. The electric field in this gap is strong, therefore, the shouldthe BST be particles noted, however, were dried, that they no significant were mixed difference with the between silicone the rubber. measurement result of device is sensitive to a change of dielectric constant introduced by the MUT. The change of the field astrength paste sample along the using gap aninside empty the resonator resonator is calibration displayed as or well. plastic The sheetE‐field calibration is strongest was at the found. edges Thisof the is gap understandable, close to the resonator because and the weakest plastic in sheet the center has a of thickness the gap. of approximately 0.1 mm and a much lower dielectric constant and loss tangent as compared to the dielectric paste. Next,Next, the the preparation preparation of of the the dielectric dielectric paste paste samples samples will will be be described. described. A flowchart A flowchart of theof the procedure procedure is given is given in in Figure Figure2. Before2. Before the the two two components components of of the the paste, paste, namely, namely, the the BSTBST particles particles and and the the silicone silicone rubber, rubber, were were mixed mixed together, together, the BST the particles BST wereparticles predried were ◦ inpredried an oven in for an 20 oven min atfor 100 20 minC. This at 100 ensured °C. This that ensured moisture, that which moisture, can be which absorbed can by be the ab‐ BSTsorbed particles, by the was BST evaporated. particles, was It is evaporated. well known It in is the well microwave known in community the microwave that watercommu is‐ anity material that water with a is large a material dielectric with loss a large tangent. dielectric Therefore, loss moisturetangent. Therefore, can affect themoisture dielectric can lossaffect of the the dielectric paste significantly loss of the if paste it is absorbedsignificantly by theif it BSTis absorbed powder. by After the BST the powder. BST particles After werethe BST dried, particles they were were mixed dried, with they the were silicone mixed rubber. with the silicone rubber.

Figure 2. Flowchart of the dielectric paste processing. The BST powder was pre‐dried at 100 °C for 20 min. After that, it was thoroughly mixed with the silicone rubber, resulting in a paste with smooth consistency. The resulting paste was then dried again for 2 h at 80 °C or until it was dry.

The paste was thoroughly mixed in order to prevent lumps of BST material sur‐ rounded by the silicone rubber inside the mixture, and a smooth paste was obtained. The paste was then transferred into the measurement fixture such that the fixture was filled up to the edges, creating a thin layer of dielectric paste. A 3D‐printed frame with a thick‐ ness of approximately 0.8 mm was used as a boundary to contain the dielectric paste on

FigureFigure 2. 2.Flowchart Flowchart of of the the dielectric dielectric paste paste processing. processing. The The BST BST powder powder was was pre-dried pre‐dried at at 100 100◦ C°C for for 2020 min. min. After After that, that, it it was was thoroughlythoroughly mixed mixed with with the the silicone silicone rubber, rubber, resulting resulting in in a a paste paste with with smooth smooth consistency. The resulting paste was then dried again for 2 h at 80 °C or until it was dry. consistency. The resulting paste was then dried again for 2 h at 80 ◦C or until it was dry. The paste was thoroughly mixed in order to prevent lumps of BST material sur‐ rounded by the silicone rubber inside the mixture, and a smooth paste was obtained. The paste was then transferred into the measurement fixture such that the fixture was filled up to the edges, creating a thin layer of dielectric paste. A 3D‐printed frame with a thick‐ ness of approximately 0.8 mm was used as a boundary to contain the dielectric paste on

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The paste was thoroughly mixed in order to prevent lumps of BST material surrounded Sensors 2021, 21, x FOR PEER REVIEW 4 of 18 by the silicone rubber inside the mixture, and a smooth paste was obtained. The paste was then transferred into the measurement fixture such that the fixture was filled up to the edges, creating a thin layer of dielectric paste. A 3D-printed frame with a thickness of theapproximately plastic sheet. 0.8 This mm way, was used the thickness as a boundary of the to dielectric contain the paste dielectric layer was paste approximately on the plastic thesheet. same This as way,the frame the thickness thickness, of which the dielectric is important paste layerfor the was calculation approximately of the thedielectric same constantas the frame and loss thickness, tangent which of the is paste. important Next, forthe thepaste calculation was dried of in the an dielectricoven at 80 constant °C for 2 ◦ hand or until loss tangentit solidified. of the After paste. solidification, Next, the paste the paste was was dried ready in an to oven be measured at 80 C in for the 2 split h or resonatoruntil it solidified. setup. After solidification, the paste was ready to be measured in the split resonatorPhotographs setup. of dielectric paste samples [27] and their fixtures and substrates for dif‐ ferentPhotographs weight percentages of dielectric of the paste BST samplespowder [are27] shown and their in Figure fixtures 3. andFor substratesrelatively low for contentsdifferent of weight the BST percentages (40%, 60%, of theand BST 70%), powder the paste are shownis smooth, in Figure as shown3. For in relatively Figure 3a–c. low Whencontents the of BST the content BST (40%, was 60%,further and increased, 70%), the the paste paste is started smooth, to asbecome shown increasingly in Figure3a–c. vis‐ cous.When Eventually, the BST content the BST was content further was increased, so high the that paste the dielectric started to paste become started increasingly to have cracksviscous. after Eventually, drying, resulting the BST content in poor was mechanical so high that properties. the dielectric This is paste the startedcase for to a have BST contentcracks after of more drying, than resulting 80% and inis poorshown mechanical in Figure 3d. properties. A rough Thissurface is theand case cracks for can a BST be observedcontent of all more along than the 80% surface and isof shownthe sample. in Figure Due3 d.to Athe rough increased surface viscosity and cracks in its can liquid be observed all along the surface of the sample. Due to the increased viscosity in its liquid state, the paste with more than 80% BST weight content was also very difficult to handle, state, the paste with more than 80% BST weight content was also very difficult to handle, because it turned very sticky, and processing it into a smooth surface was nearly impos‐ because it turned very sticky, and processing it into a smooth surface was nearly impossible. sible. It was also found that the paste was very brittle after drying for such high BST con‐ It was also found that the paste was very brittle after drying for such high BST contents tents and, thus, may not be suitable for practical applications. On the other hand, for lower and, thus, may not be suitable for practical applications. On the other hand, for lower weight percentages of the BST powder, the mechanical properties were mainly dominated weight percentages of the BST powder, the mechanical properties were mainly dominated by the silicone rubber, and thus, smooth surfaces were achieved, as seen from Figure 3a– by the silicone rubber, and thus, smooth surfaces were achieved, as seen from Figure3a–c. c.

(a) (b)

Figure 3. Photographs ofof fourfour of of the the fabricated fabricated measurement measurement samples samples of of the the dielectric dielectric paste: paste: (a )(a 40%) 40% weight weight percent percent BST, BST, (b) 60%(b) 60% weight weight percent percent BST, BST, (c) 70%(c) 70% weight weight percent percent BST, BST, and and (d) 80%(d) 80% weight weight percent percent BST. BST. With With increasing increasing BST BST content, content, the driedthe dried dielectric dielectric paste paste became became more more brittle. brittle.

Figure 4 shows the result of the measurement of samples of the dielectric paste with different weight content of the BST particles, given in percentage. With reference to the figure, the dielectric constant increases with increasing BST content, which is expected. The lowest and highest BST content, i.e., 0% and 100%, denote the cases of silicone rubber

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Figure4 shows the result of the measurement of samples of the dielectric paste with different weight content of the BST particles, given in percentage. With reference to the and BST particles only, respectively. A non‐linear relationship between the BST weight ﬁgure, the dielectric constant increases with increasing BST content, which is expected. The content and the dielectric constant of the paste was found generally. For lower values of lowest and highest BST content, i.e., 0% and 100%, denote the cases of silicone rubber and the BST content, the dielectric constant of the paste changes very slowly. In the range of BST particles only, respectively. A non-linear relationship between the BST weight content 40–80% BST content, a more rapid increase of the dielectric constant of the paste with and the dielectric constant of the paste was found generally. For lower values of the BST increasing BST content is observed. From 80% to 100%, the increase of the dielectric con‐ content, the dielectric constant of the paste changes very slowly. In the range of 40–80% stant with increasing BST content is slowed down again. BST content, a more rapid increase of the dielectric constant of the paste with increasing BST content is observed. From 80% to 100%, the increase of the dielectric constant with increasing BST content is slowed down again.

24 0.05

20 0.04 16

12 0.03 Loss tangent Loss Dielectric constant Dielectric 8 0.02 4 Measurement Curve fitting 0 0.01 0 20406080100 BST content in weight %

Figure 4. Dielectric constant and dielectric loss tangent of the dielectric paste. The BST content is given in weight percent. A Figure 4. Dielectric constant and dielectric loss tangent of the dielectric paste. The BST content is sigmoid curve fit is shown in the graph as well for the dielectric constant of the paste. given in weight percent. A sigmoid curve fit is shown in the graph as well for the dielectric constant of the paste. The dielectric loss tangent for different dielectric pastes is shown in Figure4 as well. As can be seen, the dielectric loss increases with a higher amount of weight percent of the The dielectricBST toloss a certaintangent degree. for different This isdielectric surprising, pastes because is shown it was in Figure found 4 that as well. both the BST and As can be seen,the the silicone dielectric had loss similar increases loss tangents. with a higher Therefore, amount mixing of weight both percent materials of should the result in a BST to a certainsimilar degree. loss This tangent, is surprising, no matter because the weight it was percentage found that of both each the constituent. BST and the silicone had similarHowever, loss tangents. interestingly, Therefore, the mixing loss tangent both materials of the mixture should was result somewhat in a sim higher‐ than the ilar loss tangent,loss no tangent matter of the both weight individual percentage materials. of each It constituent. is suspected that this could be due to one or However,several interestingly, of the following the loss tangent reasons. of As the mentioned mixture was before, somewhat the BST higher powder than has the ability to the loss tangentabsorb of both moisture. individual Therefore, materials. even It is though suspected the powderthat this iscould dried be before due to mixing one it with the or several of thesilicone, following it can reasons. absorb As moisture mentioned during before, the drying the BST process powder of has the the dielectric ability paste. It was to absorb moisture.found Therefore, that the drying even temperaturethough the powder of the silicone is dried mustbefore be mixing limited it to with below the 100 ◦C or the silicone, it cansilicone absorb inmoisture the paste during started the to drying cast a significantprocess of the number dielectric of bubbles, paste. It which was resulted in a found that thepaste drying with temperature very poor mechanicalof the silicone properties, must be aslimited well as to high below surface 100 °C roughness. or the Therefore, silicone in thethe paste drying started temperature to cast a significant could not benumber increased of bubbles, beyond which 100 ◦C. resulted Another in possible a reason paste with verycould poor be mechanical that, after properties, mixing both as well components, as high surface the BST roughness. powder mayTherefore, have absorbed the the drying temperaturesolvent, which could kept not thebe increased silicone in beyond its liquid 100 state. °C. Another Instead possible of evaporating, reason some of the could be that, solventafter mixing may have both stayedcomponents, trapped the inside BST thepowder silicone. may According have absorbed to our the experience, sol‐ this may vent, which kepthave the led silicone to an increasein its liquid of the state. loss Instead tangent of ofevaporating, the paste. Itsome was of found the solvent that dielectric paste may have stayedsamples trapped that inside were notthe totallysilicone. dried According usually to exhibited our experience, higher lossthis comparedmay have to when they led to an increasewere of totally the loss dry. tangent As the of surface the paste. of the It was paste found dried that much dielectric faster duepaste to samples its direct contact with that were notair, totally it might, dried therefore, usually haveexhibited happened higher that loss some compared amount to of when the solvent they waswere trapped inside totally dry. Asthe the mixture, surface of finally the paste increasing dried themuch loss faster tangent due of to the its direct paste. contact with air, it might, therefore, have happened that some amount of the solvent was trapped inside the mixture, finally increasing the loss tangent of the paste.

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To allow for easy application of the dielectric paste, a sigmoid curve (or logistic curve) was used in order to represent the relationship between the dielectric constant of the paste and the BST content in weight percent:

24.02 ε = (1) r,paste 1 − exp(−0.05(x − 62.2))

where x denotes the amount of BST in weight percent that is mixed with the silicone. The curve is ﬁtted to the measured results of the paste’s dielectric constant, as shown in Figure4 . The ﬁtted curve agrees reasonably well with the measured results and could serve as a starting point for determining the desired dielectric constant of the paste depending on the BST content.

3. Antenna Design In this section, the structure of the antenna, which will serve as an example design for the use of the dielectric paste, will be analyzed. The basic antenna shape is based on the so called menger sponge fractal. An illustration of the second iteration of a menger sponge fractal DRA is shown in Figure5. A microstripline slot feeding is used to excite the DRA, as indicated by the dashed line in Figure5. The slot has a length and width of ls and ws, respectively. The microstripline has a width of wstrip and extends the slot by a length of lstub. The shape of the menger sponge DRA is defined by an enclosure or mold (depicted by the red solid line in Figure5), which ensures that the dielectric paste (depicted in white color) in its liquid form stayed in place after being inserted into the mold. The mold was obtained by 3D-printing, and the mold material has a dielectric constant of 3. The inside of the mold was then filled with a dielectric paste of dielectric constant 10.14, corresponding to a dielectric paste with 60% BST content. The DRA has a length, width and height of a, b and h, respectively. The basic shape of the menger sponge fractal consists of a cube with openings inside the dielectric paste in each of the faces, penetrating from one face to the adjacent face on the opposite side of the cube. The openings are realized in practice by using the mold to shape the dielectric paste. The mold itself corresponds to the negative of the shape of the dielectric paste or the menger sponge fractal shape. With an increasing number of iterations of the menger sponge fractal structure, the amount of removed dielectric paste material sections is increased. The construction principle of the menger sponge fractal for different iterations is illustrated in Figure6 using a single face of the 3-dimensional structure as an example. For the 0th iteration, the menger sponge fractal corresponds to a cube with no parts of the structure removed. In the first iteration, however, a rectangular slab of material is removed from the center of each of the faces penetrating through the whole depth of the cube. The removed section has a sidelength of a/3 or b/3 (or h/3), respectively, depending on which side of the cube is considered. Note that other fractions of the side length of the removed sections could be used as well. The removed section penetrates through the whole structure, as is illustrated in Figure5, effectively removing a slab of material. After the first iteration, each face of the cube can be subdivided into nine new regions, as shown in Figure6, each of the new regions having the same width and length (for example a/3 and b/3). In the second iteration, each of the new regions has a slab of material removed in their center with a width and length of 1/9 of the original width and length of the large surface or 1/3 of the value of the side lengths of the newly introduced regions. This process can be repeated to reach the next iteration. Sensors 2021, 21, x FOR PEER REVIEW 7 of 18

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Sensors 2021, 21, x FOR PEER REVIEW Figure 5. Sketch of the menger sponge fractal DRA in its second iteration The8 DRAof 18 is enclosed by

a mold, indicated by the red, solid lines surrounding the DRA. The mold controls the shape of the dielectric paste, which is ﬁlled inside and depicted in white color. The DRA has a length, width, and Figure 5. Sketch of the menger sponge fractal DRA in its second iteration The DRA is enclosed by a height of a, b, h, respectively. The structure is accommodated by a feeding slot of length and width l are spacedmold, apart indicated by 0.62 by GHz, the red, and solid the linesreflection surrounding coefficient the DRA. is larger The thanmold − controls10 dB between the shape of the s the two dielectricresonances.and paste,ws and which is backed is filled by inside a microstrip and depicted line with in white width color.wstrip ,The which DRA extends has a length, the slot width, by a length and lstub. height of a, b, h, respectively. The structure is accommodated by a feeding slot of length and width ls and ws and is backed by a microstrip line with width wstrip, which extends the slot by a length lstub.

The construction principle of the menger sponge fractal for different iterations is il‐ lustrated in Figure 6 using a single face of the 3‐dimensional structure as an example. For the 0th iteration, the menger sponge fractal corresponds to a cube with no parts of the structure removed. In the first iteration, however, a rectangular slab of material is removed from the cen‐ ter of each of the faces penetrating through the whole depth of the cube. The removed section has a sidelength of a/3 or b/3 (or h/3), respectively, depending on which side of the cube is considered. Note that other fractions of the side length of the removed sections Figure 6. ConstructionFigure 6.could Construction principle be used of principle the as well. menger ofThe the sponge removed menger fractal. sponge section The fractal. zeroth penetrates The iteration zeroth through corresponds iteration the wholecorresponds to the structure, original to surface as is the original surface without any modifications. In the first iteration, a slab of material is removed in without any modifications.illustrated In the in first Figure iteration, 5, effectively a slab of material removing is removed a slab of in material. the center After of the the face. first The iteration, cross section each of the center of the face. The cross section of this slab corresponds to one third of side lengths of the this slab correspondsface to one of thirdthe cube of side can lengths be subdivided of the rectangle. into nine In the new second regions, iteration, as shown the surface in Figure of the 6, rectangle each of is rectangle.the In new the second regions iteration, having the surfacesame width of the and rectangle length is (forsubdivided example into a/3 nine and smaller b/3). In sur the‐ second subdivided intofaces nine with smaller side lengths surfaces a/3 with and b side/3. For lengths each ofa/3 those and smallerb/3. For surfaces, each of thosethe process smaller of surfaces, the first iteration the process of the iteration, each of the new regions has a slab of material removed in their center with a first iterationis is repeated, repeated, such such that that a a slab slab of of material material with with cross cross section section aa/9/9 and and b/9b/9 is isremoved. removed. width and length of 1/9 of the original width and length of the large surface or 1/3 of the value of theA side plot lengths of the reflection of the newly coefficient introduced of a regions. microstripline This process slot fed can menger be repeated sponge to fractal reach theDRA, next as iteration. pictured in Figure5, for different iterations of the menger sponge fractal is shown ReflectionAin plot Figure of theCoefficient7. For reflection each of coefficient(dB) the iterations, of a microstripline the feeding circuit slot wasfed menger optimized sponge to maximize fractal the 0DRA, asimpedance pictured bandwidthin Figure 5, performance,for different iterations whereas of the the geometrical menger sponge dimensions fractal of is theshown structure in Figureremained 7. For each unchanged. of the iterations, The feeding the parametersfeeding circuit for was each optimized case are given to maximize in the caption the of impedanceFigure bandwidth7. In particular, performance, for each whereas iteration the of thegeometrical menger spongedimensions fractal of the DRA, structure the feeding remainedparameters unchanged.lslot and Thel stubfeedingwere parameters optimized to for achieve each case the maximumare given impedancein the caption bandwidth. of th -10 FigureFor 7. In the particular, 0 iteration, for twoeach resonant iteration modesof the menger are found sponge spaced fractal far away DRA, from the eachfeeding other on parametersthe frequency lslot and l spectrum,stub were optimized and the individual to achieve resonance the maximum bandwidths impedance are notbandwidth. broad enough For theto 0 mergeth iteration, the modes two resonant to form modes a wide are impedance found spaced bandwidth. far away In particular,from each theother resonances on − -20 the frequencyare spaced spectrum, apart by and 0.62 the GHz, individual and the resonance reflection coefficientbandwidths is largerare not than broad10 enough dB between to mergethe the two modes resonances. to form a wide impedance bandwidth. In particular, the resonances 0th Iteration st -30 1 Iteration 2nd Iteration 2nd Iteration modified -40 23 Frequency (GHz)

Figure 7. Variation of the reflection coefficient of the menger sponge fractal for different iterations with a = b = h = 25 mm and a dielectric constant of 10.14. The feeding circuit for each iteration is optimized such that maximum bandwidth can be achieved. The feeding parameters for each itera‐ tion are: lslot,0 = 20 mm, lstub,0 = 6 mm, lslot,1 = 21 mm, lstub,1 = 6.5 mm, lslot,2 = 21 mm, lstub,2 = 5.5 mm, and lslot,2mod = 21 mm, lstub,2mod = 6.5 mm.

After the first iteration, the two resonant modes are spaced much more closely (ap‐ proximately 0.52 GHz) and give rise to a much wider impedance bandwidth. The band‐ widths for the 0th iteration are 5.3% (2.03 GHz to 2.14 GHz) and 8.5% (2.58 GHz to 2.81 GHz). After the first iteration, the bandwidth was improved to 29.4% (2.26 GHz to 3.04 GHz). Notably, the individual resonances appear to have a broadened bandwidth, which can be seen from the fact that the reflection coefficient of the individual resonances of the 0th iteration are much narrower on the frequency spectrum. The reflection coefficients of

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are spaced apart by 0.62 GHz, and the reflection coefficient is larger than −10 dB between the two resonances.

Figure 6. Construction principle of the menger sponge fractal. The zeroth iteration corresponds to the original surface without any modifications. In the first iteration, a slab of material is removed in the center of the face. The cross section of this slab corresponds to one third of side lengths of the rectangle. In the second iteration, the surface of the rectangle is subdivided into nine smaller sur‐ faces with side lengths a/3 and b/3. For each of those smaller surfaces, the process of the first iteration Sensors 2021, 21, 4058 is repeated, such that a slab of material with cross section a/9 and b/9 is removed. 8 of 17

Reflection Coefficient (dB) 0

-10

-20 0th Iteration st -30 1 Iteration 2nd Iteration 2nd Iteration modified -40 23

Figure 7. Variation of the reﬂectionFrequency coefﬁcient of (GHz) the menger sponge fractal for different iterations

with a = b = h = 25 mm and a dielectric constant of 10.14. The feeding circuit for each iteration is Figureoptimized 7. Variation such that of the maximum reflection bandwidth coefficient can of be the achieved. menger Thesponge feeding fractal parameters for different for each iterations iteration with a = b = h = 25 mm and a dielectric constant of 10.14. The feeding circuit for each iteration is are: l = 20 mm, l = 6 mm, l = 21 mm, l = 6.5 mm, l = 21 mm, l = 5.5 mm, and optimizedslot,0 such that maximumstub,0 bandwidthslot,1 can be achieved.stub,1 The feedingslot,2 parametersstub,2 for each itera‐ l = 21 mm, l = 6.5 mm. tionslot,2mod are: lslot,0 = 20 mm,stub,2mod lstub,0 = 6 mm, lslot,1 = 21 mm, lstub,1 = 6.5 mm, lslot,2 = 21 mm, lstub,2 = 5.5 mm, and lslot,2mod = 21 mm, lstub,2mod = 6.5 mm. After the first iteration, the two resonant modes are spaced much more closely (approximately 0.52 GHz) and give rise to a much wider impedance bandwidth. The bandwidths After the first iteration, the two resonant modes are spaced much more closely (ap‐ for the 0th iteration are 5.3% (2.03 GHz to 2.14 GHz) and 8.5% (2.58 GHz to 2.81 GHz). After proximately 0.52 GHz) and give rise to a much wider impedance bandwidth. The band‐ the first iteration, the bandwidth was improved to 29.4% (2.26 GHz to 3.04 GHz). widths for the 0th iteration are 5.3% (2.03 GHz to 2.14 GHz) and 8.5% (2.58 GHz to 2.81 Notably, the individual resonances appear to have a broadened bandwidth, which GHz). After the first iteration, the bandwidth was improved to 29.4% (2.26 GHz to 3.04 can be seen from the fact that the reflection coefficient of the individual resonances of the GHz). 0th iteration are much narrower on the frequency spectrum. The reflection coefficients of Notably, the individual resonances appear to have a broadened bandwidth, which the two resonances of the 1st iteration are not as sharp but vary more slowly with respect can be seen from the fact that the reflection coefficient of the individual resonances of the to a change in frequency. This can be explained with the quality factor of the DRA. In the 0th iteration are much narrower on the frequency spectrum. The reflection coefficients of structure, at the positions where holes or removed slabs were introduced, the dielectric paste with a dielectric constant of 10.14 was replaced with a material low dielectric constant, in this case a 3D-printed material with a dielectric constant of 3. Thus, the average dielectric constant of the DRA is decreased, leading to a reduction of the quality factor of the DRA, finally, broadening the bandwidth of the individual resonances. After the first iteration, the antenna can only be marginally matched across its passband. In order to achieve better matching, the iteration number can be increased. For the second iteration of the structure, the distance of the resonances on the frequency spectrum is further decreased, and the quality factor is reduced again, as elaborated previously. The modes are spaced more closely, and a better impedance match was achieved throughout the passband of the antenna compared to the first iteration. Even though, in this work, the dielectric paste approach is used to construct the DRA, the second iteration of the menger sponge fractal is still too complicated to be realized. Therefore, the structure will be simplified in order to allow for an easier fabrication of a 3D-printed mold. A modified version of the menger sponge fractal structure is shown in Figure8a. As compared to the second iteration, as shown in Figure5, the horizontal slabs of 3D-printed material of the second iteration of the menger sponge fractal have been removed in order to ease the fabrication of this structure, whereas all the vertical slabs are retained. Using our in-house 3D-printer, horizontal bars cannot be printed without any supporting material, which would have to be removed after the 3D printing process. Therefore, removing all of the horizontal slabs of the second iteration of the menger sponge Sensors 2021, 21, 4058 9 of 17

fractal DRA guarantees a much easier fabrication of the 3D-printed mold. The mold, which is used to contain the dielectric paste, is shown in Figure8b. It consists of two separate parts, which are required due to the limitation of the 3D-printing process and in order to reduce the amount of supporting structures. Figure8c depicts the inside of the 3D-printed mold. The horizontal arms can be seen, which give rise to the “holes” in the dielectric paste structure, as shown in Figure8a. The reflection coefficient of the modified second iteration excited by a simple slot (compare Figure5) is also shown in Figure7. Notably, due to the removal of the horizontal slabs of the menger sponge fractal, the resonance frequencies of both resonant modes are shifted downward, but similar bandwidth and Sensors 2021, 21, x FOR PEER REVIEW 10 of 18 matching compared to the second iteration are achieved. The impedance bandwidth of the linearly polarized, modified menger sponge fractal DRA can cover frequencies ranging from 2.33 GHz to 3.13 GHz, including ISM, WiFi, as well as the WiMAX frequency bands.

(a) (b)

(c)

Figure 8. (a) ModifiedFigure menger 8. (a) sponge Modiﬁed fractal menger DRA structure. sponge fractal The dielectric DRA structure. paste is highlighted The dielectric in white, paste whereas is highlighted the outer part of the plasticin mold white, is indicated whereas theby a outer solid partline. ofAs the compared plastic to mold the isoriginal indicated menger by asponge solid line.(see Figure As compared 5), the hori to ‐ zontal bars of the second iteration have been removed in order to allow for an easier fabrication. (b) Exploded view of the the original menger sponge (see Figure5), the horizontal bars of the second iteration have been 3D‐printed mold structure, which is used for manufacturing process. The mold is split into two parts allowing for an easier manufacturing. Theremoved mold is in then order subsequently to allow for filled an easierwith the fabrication. dielectric paste (b) Exploded material. ( viewc) Perspective of the 3D-printed view of the mold inside of the 3D‐printedstructure, mold showing which the is horizontal used for manufacturing arms that give rise process. to the The“holes” mold in isthe split dielectric into two paste parts in (a allowing). for an easier manufacturing. The mold is then subsequently ﬁlled with the dielectric paste material. (c) Perspective viewIn order of the to inside analyze of thethe 3D-printed operating moldmechanism showing of the the horizontal circularly arms polarized that give antenna, rise the to the “holes”resonant in the modes dielectric inside paste the in (linearlya). polarized antenna, excited by a simple slot as shown in Figure 5, are characterized first. The electric field distribution of the modified menger sponge fed by a simple slot are shown in Figure 9a,b at their resonance frequencies at 2.45 GHz and 2.9 GHz (compare Figure 7), respectively. The field distributions at 2.45 GHz indicate that the DRA operates in its fundamental TEδ11 mode. At 2.9 GHz, the field distri‐ butions resemble those of the TEδ13 mode.

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In order to analyze the operating mechanism of the circularly polarized antenna, the resonant modes inside the linearly polarized antenna, excited by a simple slot as shown in Figure5, are characterized first. The electric field distribution of the modified menger sponge fed by a simple slot are shown in Figure9a,b at their resonance frequencies at 2.45 GHz and 2.9 GHz (compare Figure7), respectively. The field distributions at 2.45 GHz Sensors 2021, 21, x FOR PEER REVIEW 11 of 18 indicate that the DRA operates in its fundamental TEδ11 mode. At 2.9 GHz, the field distributions resemble those of the TEδ13 mode.

(a) (b) Figure 9. Electric field distributions of modified menger sponge fractal DRA. (a) 2.45 GHz; (b) 2.9 GHz.

The feeding mechanism of the right hand circularly polarized antenna design, along with the DRA structure, are shown in Figure 10a,b. A cross‐slot feeding is used in order to generate the orthogonal modes required for obtaining a circularly polarized antenna. The cross‐slot is rotated by an angle φr = 45°, and the PCB substrate has a thickness of tsub = 1 mm. Using the cross‐slot arrangement, orthogonal DRA modes can be excited. In particu‐ lar, the slot with length lslot,1 excites TEb modes, whereas the slot with length lslot,2 excites TEa modes, where the superscripts a and b denote the directions along the dimensions a (a) (b) and b of the DRA, as indicated by the vectors a and b in Figure 10b. Because the slots have FigureFigure 9. 9. ElectricElectricdifferent field ﬁeld distributions distributions lengths, theof of modified modiﬁed resonance menger frequencies sponge fractal of the DRA. orthogonal ( a) 2.45 modes GHz; ( bare) 2.9 slightly GHz. different. This translates to the modes resonating with different phases with respect to each other. For theThe Theright feeding feeding choice mechanismof mechanism the slot lengths, of of the the right rightthe phase hand hand difference circularly circularly ispolarized polarized approximately antenna antenna 90°, design, resulting along in withwithcircular the the polarization.DRA DRA structure, structure, In thisare are showndesign, in each Figure slot 10a,b.excites10a,b. A A two cross cross-slot DRA‐slot modes, feeding feeding namely, is is used used TE in ina/b order δ11 andtoto TEgenerate generatea/b δ13, thus, the the wideorthogonal orthogonal axial ratio modes modes bandwidth required required isfor for achieved. obtaining obtaining a a circularly circularly polarized polarized antenna. antenna. ◦ TheTheResults cross cross-slot‐ slotfor isthe is rotated rotated circularly by by an polarized an angle angle φ ϕr antenna=r =45°, 45 and, will and the thebe PCB discussed PCB substrate substrate in hasthe has ameasurements thickness a thickness of t sub of section.=tsub 1 mm.= 1 mm. Using the cross‐slot arrangement, orthogonal DRA modes can be excited. In particu‐ lar, the slot with length lslot,1 excites TEb modes, whereas the slot with length lslot,2 excites TEa modes, where the superscripts a and b denote the directions along the dimensions a and b of the DRA, as indicated by the vectors a and b in Figure 10b. Because the slots have different lengths, the resonance frequencies of the orthogonal modes are slightly different. This translates to the modes resonating with different phases with respect to each other. For the right choice of the slot lengths, the phase difference is approximately 90°, resulting in circular polarization. In this design, each slot excites two DRA modes, namely, TEa/b δ11 and TEa/b δ13, thus, wide axial ratio bandwidth is achieved. Results for the circularly polarized antenna will be discussed in the measurements section.

(a) (b)

Figure 10. (a) Perspective view of the menger sponge fractal from Figure8, showing its dimensions, along with the

feeding mechanism. (b) Top view of the feeding PCB with a cross slot with lengths lslot,1, lslot,2, and width wslot. The slot is accommodated by a microstrip feed line with a width wstrip and extends the center of the cross slot by a length lstub. The ground plane has a length and width of lG and wG, respectively. The feeding substrate has a thickness of tsub. The feeding

slot is rotated by an angle of ϕr.

(a) (b)

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Using the cross-slot arrangement, orthogonal DRA modes can be excited. In particular, b a the slot with length lslot,1 excites TE modes, whereas the slot with length lslot,2 excites TE Figure 10. (a) Perspective viewmodes, of the where menger the sponge superscripts fractal froma and Figureb denote 8, showing the directions its dimensions, along along the with dimensions the feedinga and mechanism. (b) Top view ofb ofthe the feeding DRA, PCB as with indicated a cross byslot the with vectors lengthsa lslot,1and, lslot,2b in, and Figure width 10 wb.slot. BecauseThe slot is the accommo slots have‐ dated by a microstrip feed differentline with a lengths, width wstrip the and resonance extends the frequencies center of the of thecross orthogonal slot by a length modes lstub. are The slightly ground plane different. has a length and width of lThisG and translates wG, respectively. to the The modes feeding resonating substrate with has a different thickness phasesof tsub. The with feeding respect slot to is eachrotated other. by an angle of φr. For the right choice of the slot lengths, the phase difference is approximately 90◦, resulting a/b in circular polarization. In this design, each slot excites two DRA modes, namely, TE δ11 4. Measurementsa/b and TE δ13, thus, wide axial ratio bandwidth is achieved. ResultsIn this section, for the circularly the measured polarized and simulated antenna will results be discussedof the antenna in the prototype measurements will be section.presented. A photograph of the antenna prototype is displayed in Figure 11, with its final dimensions given in the caption of the figure. The structure of the DRA is the same as the 4.one Measurements depicted in Figure 8a. The DRA was attached to the cross‐slot feeding using the die‐ lectricIn thispaste section, as a glue the in measured order to andprevent simulated air gaps, results which of thecould antenna otherwise prototype affect will the bean‐ presented.tenna performance. A photograph The feeding of the antenna PCB has prototype a dielectric is displayed constant of in 2.65 Figure and 11 a, thickness with its final of 1 dimensionsmm. It should given be inpointed the caption out that of the the antenna figure. Thewas structure constructed of thein several DRA is iterations the same of as a thefilling one and depicted drying in process. Figure8 a.Because The DRA of a wasmuch attached increased to thevolume cross-slot and thickness feeding using compared the dielectricto the dielectric paste as paste a glue samples, in order as todescribed prevent in air the gaps, first which section could of this otherwise publication, affect longer the antennadrying time performance. was necessary. The feeding However, PCB the has same a dielectric temperature constant for of the 2.65 dielectric and a thickness paste sam of‐ 1ples mm. was It should used for be pointeddrying the out thatBST thepowder antenna and was the constructed dielectric paste in several after iterationsfilling the of 3D a‐ fillingprinted and mold. drying The process. antenna Because was made of awith much a dielectric increased paste volume with and dielectric thickness constant compared 10.14 toor the 60% dielectric BST content, paste and samples, the 3D as‐printed described mold in thehad first a dielectric section constant of this publication, of 3. longer dryingA time comparison was necessary. of the However,measured the and same simulated temperature reflection for the coefficients dielectric pasteof the samples antenna wasprototype used for is dryinggiven in the Figure BST powder 12. With and reference the dielectric to the figure, paste after reasonable filling the agreement 3D-printed was mold.obtained, The antennaand the wasmeasured made withand simulated a dielectric impedance paste with bandwidth dielectric constant are 21.6% 10.14 (2.39–2.97 or 60% BSTGHz) content, and 23.4% and the(2.26–2.86 3D-printed GHz), mold respectively. had a dielectric constant of 3.

FigureFigure 11.11. PhotographPhotograph of ofthe the fabricated fabricated antenna antenna prototype prototype with withthe following the following dimensions: dimensions: a = 25.6 mm, b = 25 mm, h = 41 mm, wslot = 5.2 mm, lslot,1 = 32.6 mm, lslot,2 = 18.7 mm, lstub = 8.5 mm, lG = wG = 90 a = 25.6 mm, b = 25 mm, h = 41 mm, wslot = 5.2 mm, lslot,1 = 32.6 mm, lslot,2 = 18.7 mm, lstub = 8.5 mm, mm, and wstrip = 2.7 mm. A dielectric constant of 10.14 or 60% BST content was used to construct the l = w = 90 mm, and w = 2.7 mm. A dielectric constant of 10.14 or 60% BST content was used to Gantenna.G strip construct the antenna.

A comparison of the measured and simulated reflection coefficients of the antenna prototype is given in Figure 12. With reference to the figure, reasonable agreement was obtained, and the measured and simulated impedance bandwidth are 21.6% (2.39–2.97 GHz) and 23.4% (2.26–2.86 GHz), respectively.

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Reflection Coefficient (dB) 0 Reflection Coefficient (dB) 0

-10 -10 Simulation Measurement Simulation ResimulationMeasurement -20 2.2 2.4 2.6 2.8 3.0 3.2Resimulation 3.4 -20 Frequency (GHz) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Figure 12. Measured and simulated reflectionFrequency coefficients. (GHz) The measured and simulated impedance

bandwidth are 21.6% (2.39–2.97 GHz) and 23.4% (2.26–2.86 GHz). For the resimulation, the follow‐ ingFigure valuesFigure 12. have 12.MeasuredMeasured been used:and and simulated a = simulated 24 mm, reflection b reﬂection= 24 mm, coefficients. coefﬁcients.and a dielectric The The measured constant measured and of and the simulated dielectric simulated impedance paste impedance of εbandwidthr,pastebandwidth = 9.5. are are 21.6% 21.6% (2.39–2.97 (2.39–2.97 GHz) GHz) and and 23.4% 23.4% (2.26–2.86 (2.26–2.86 GHz). GHz). For For the the resimulation, resimulation, the the follow following‐ ingvalues values havehave beenbeen used: a = 24 24 mm, mm, bb == 24 24 mm, mm, and and a dielectric a dielectric constant constant of ofthe the dielectric dielectric paste paste of of εr,pasteεr,pasteMeasured = 9.5.= 9.5. and simulated axial ratios are shown in Figure 13. The axial ratios are smaller than 3 dB from 2.575 GHz to 3.05 GHz and 2.44 GHz to 2.91 GHz in measurement and simulation.MeasuredMeasured andAgain, and simulated simulatedreasonable axial axial agreement ratios ratios are arewas shown shown obtained, in inFigure Figure with 13. measured13 The. The axial axial and ratios ratiossimu are‐ are latedsmallersmaller axial than ratio than 3 dB bandwidths 3 dBfrom from 2.575 2.575 (axial GHz GHz ratioto 3.05 to < 3.05 3GHz dB) GHz andof and16.7% 2.44 2.44 GHzand GHz 17.6%.to 2.91 to 2.91 GHz GHz in measurement in measurement andand simulation. simulation. Again, Again, reasonable reasonable agreement agreement was was obtained, obtained, with measuredmeasured and and simulated simu‐ latedaxial axial ratio ratio bandwidths bandwidths (axial (axial ratio ratio < 3 < dB) 3 dB) of 16.7%of 16.7% and and 17.6%. 17.6%.

Axial Ratio (dB) 12 Axial Ratio (dB) 12 9 9 6 6

3 Simulation 3 Measurement Simulation Resimulation 0 Measurement 2.2 2.4 2.6 2.8 3.0 Resimulation 3.2 3.4 0 Frequency (GHz) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 FigureFigure 13. Measured 13. Measured and simulated and simulated axialFrequency axial ratios ratios of the of(GHz) right the right hand hand circularly circularly polarized polarized antenna. antenna. Meas Mea-‐

uredsured and simulated and simulated axial axial ratio ratio bandwidths bandwidths of 16.7% of 16.7% and and17.6% 17.6% were were obtained. obtained. For the For resimulation the resimulation Figurethe following13. Measured values and have simulated been used: axial aratios= 24mm, of theb right= 24mm hand and circularly a dielectric polarized constant antenna. of the dielectricMeas‐ ured and simulated axial ratio bandwidths of 16.7% and 17.6% were obtained. For the resimulation paste of εr,paste = 9.5.

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the following values have been used: a = 24mm, b = 24mm and a dielectric constant of the dielectric Sensors 2021, 21, 4058 paste of εr,paste = 9.5. 13 of 17

Discrepancies between the measured and simulated reflection coefficients and axial ratios are most likely caused by measurement inaccuracies of paste dielectric constant us‐ ing the splitDiscrepancies‐post resonator between measurement. the measured Even and though simulated a 3D‐printed reflection frame coefficients was used and to axial controlratios the arethickness most likelyof the causeddielectric by paste measurement samples, it inaccuracies was very difficult of paste to dielectric obtain totally constant flat samplesusing the of split-post the dielectric resonator paste measurement.in practice. For Even the measurement though a 3D-printed of the samples, frame was an used averageto control thickness the was thickness used for of the the calculation dielectric pasteof the samples,dielectric itconstant. was very This difficult leads to to in obtain‐ accuraciestotally in flat the samples dielectric of theconstant dielectric calculation, paste in because practice. the For thickness the measurement is one of the of the inputs samples, for thean measurement average thickness software. was This used causes for the the calculation dielectric ofpaste the measurement dielectric constant. to be subject This leads to someto inaccuracies tolerance in inthe the dielectric dielectric constant constant and calculation, loss tangent because measurement. the thickness Other is factors one of the that contributeinputs for to the the measurement frequency shift software. of the antenna This causes are the the manufacturing dielectric paste tolerances, measurement for to instance,be subject caused to by some the limited tolerance accuracy in the of dielectric the 3D printer, constant which and was loss used tangent in the measurement. experi‐ ment.Other However, factors overall, that contribute the results to show the frequency the feasibility shift of of the the antenna dielectric are paste the manufacturingapproach. The deviationstolerances, of for the instance, measurements caused by from the limitedthe simulated accuracy results of the are 3D further printer, analyzed which was in used in the experiment. However, overall, the results show the feasibility of the dielectric paste the section “Discussion”. approach. The deviations of the measurements from the simulated results are further The measured and simulated broadside gains of the circularly polarized antenna are analyzed in the section “Discussion”. shown in Figure 14. A maximum measured broadside gain of 6 dBic was found, whereas The measured and simulated broadside gains of the circularly polarized antenna are the simulated counterpart was 5.9 dBic, at 2.6 GHz and 2.4 GHz, respectively. shown in Figure 14. A maximum measured broadside gain of 6 dBic was found, whereas the simulated counterpart was 5.9 dBic, at 2.6 GHz and 2.4 GHz, respectively.

Realized Antenna Gain (dBic)

Simulation Measurement 0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Frequency (GHz)

FigureFigure 14. Measured 14. Measured and simulated and simulated gain of gain the of right the righthand hand circularly circularly polarized polarized antenna. antenna. The measured and simulated radiation patterns are shown in Figure 15a at 2.6 GHz The measured and simulated radiation patterns are shown in Figure 15a at 2.6 GHz and in Figure 15b at 2.9 GHz for ϕ = 0◦ and ϕ = 90◦, respectively. Good agreement with the and in Figure 15b at 2.9 GHz for φ = 0° and φ = 90°, respectively. Good agreement with simulated results was found, and the backlobe radiation of the antenna is generally much the simulated results was found, and the backlobe radiation of the antenna is generally lower than −10 dB. The cross polarization (or left hand circularly polarized radiation) is much lower than −10 dB. The cross polarization (or left hand circularly polarized radia‐ generally low and close to −10 dB. Stable broadside radiation over the whole antenna tion) is generally low and close to −10 dB. Stable broadside radiation over the whole an‐ passband is observed. tenna passband is observed. In Figure 16, the measured and simulated antenna efﬁciencies are displayed. Again, reasonable agreement between simulation and measurement was found. The peak efﬁcien- cies for measurement and simulation are 82.3% and 84%, respectively. This is surprisingly large, considering the loss tangent of the dielectric paste. However, it should be noted that the antenna is an effective DRA, consisting of parts with higher and lower dielectric constants, i.e., dielectric paste and the low loss 3D-printed plastic. The 3D-printed plastic lessens the effect of loss tangent of the dielectric paste to some extent.

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(a)

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FigureFigure 15. Measured 15. Measured and simulated and simulated radiation radiation patterns patterns of the right of the hand right circularly hand circularly polarized polarized an‐ antenna. tenna.( (aa)) 2.62.6 GHZ and and ( (bb)) 2.9 2.9 GHz. GHz.

In FigureTotal 16, the Antenna measured Efficiency and simulated (%) antenna efficiencies are displayed. Again, reasonable100 agreement between simulation and measurement was found. The peak effi‐ ciencies for measurement and simulation are 82.3% and 84%, respectively. This is surpris‐ ingly large, considering the loss tangent of the dielectric paste. However, it should be noted that80 the antenna is an effective DRA, consisting of parts with higher and lower die‐ lectric constants, i.e., dielectric paste and the low loss 3D‐printed plastic. The 3D‐printed plastic lessens the effect of loss tangent of the dielectric paste to some extent. 60

40 Simulation Measurement 20 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Frequency (GHz)

Figure 16. Measured and simulated total antenna efﬁciencies, including the mismatch of the antennas. Figure 16. Measured and simulated total antenna efficiencies, including the mismatch of the anten‐ nas.

5. Discussion The dielectric constant of the dielectric paste sample with 60% BST content is shown in Figure 17. The red marker indicates the nominal, calculated dielectric constant of 10.14 for an averaged thickness of the sample of 0.457 mm. Varying the thickness of the sample in the calculation software, the estimated dielectric constant of the sample changes. For a thicker sample thickness, the dielectric constant is reduced, whereas for a thinner thick‐ ness, it is increased. For a thickness deviation of ± 0.025 mm, the dielectric constant changes by a value of approximately ± 0.5. Therefore, in practice, a measurement error of the dielectric constant of the order of ± 0.5 should be anticipated. Furthermore, the dielectric paste samples were not totally flat, causing additional measurement error. The electric field strength in the gap of the SPDR setup in Figure 1 is not homogeneous. In particular, the electric field strength is strongest at the edges of the gap and weakest in the center of the gap. If a sample is warped, part of the sample will be at a location of weaker electric field. Therefore, the resonance frequency of the SPDR will be affected relatively less compared to the case of the flat sample. This will lead to a de‐ crease of the measured dielectric constant. Lastly, it was found that the 3D‐printed mold was suspect to manufacturing toler‐ ance. In particular, the samples were slightly smaller than the values used in the simula‐ tion. The antenna was resimulated, taking into account measurement inaccuracies of the dielectric constant and manufacturing tolerances of the 3D‐printed mold, and the results are shown in Figures 12 and 13. Much better agreement with the measured results can be observed for the resimulated antenna for both reflection coefficient, as well as axial ratio.

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it is increased. For a thickness deviation of ± 0.025 mm, the dielectric constant changes by a value of approximately ± 0.5. Therefore, in practice, a measurement error of the dielectric constant of the order of ± 0.5 should be anticipated.

Dielectric Constant 12

0.40 0.42 0.44 0.46 0.48 0.50 0.52 Layer thickness (mm)

FigureFigure 17. Dielectric 17. Dielectric constant constant measurement measurement of the of 60% the 60%weight weight percent percent BST BSTsample sample with with varying varying inputinput thicknesses thicknesses for the for calculation the calculation software. software. The nominal The nominal averaged averaged thickness thickness of the sample of the is sample0.457 is mm 0.457with a mm calculated with a calculated dielectric constant dielectric of constant 10.14. of 10.14.

6. ConclusionsFurthermore, the dielectric paste samples were not totally flat, causing additional measurement error. The electric field strength in the gap of the SPDR setup in Figure1 is In this publication, a new approach for designing dielectric resonator antennas is pre‐ not homogeneous. In particular, the electric field strength is strongest at the edges of the sented. The method employs a dielectric paste and a 3D‐printed mold, which is filled with gap and weakest in the center of the gap. If a sample is warped, part of the sample will the dielectric paste material. A dielectric paste can be obtained by mixing BST nano parti‐ be at a location of weaker electric field. Therefore, the resonance frequency of the SPDR cle sizedwill be powder affected with relatively a silicone less rubber. compared By controlling to the case the of BST the flat to rubber sample. ratio, This the will dielec lead‐ to a tric constantdecrease of of the the paste measured can be dielectric flexibly constant.controlled with a dielectric constant ranging from 3.67 to 18.45,Lastly, corresponding it was found thatto a the BST 3D-printed powder content mold was of 20% suspect to 80% to manufacturing in weight percent. tolerance. The Inloss particular, tangent of the the samples paste was were found slightly to smallerbe generally than thelower values than used 0.044. in Using the simulation. the die‐ lectric paste,The a antenna circularly was polarized resimulated, menger taking sponge into fractal account DRA measurement was constructed. inaccuracies The 3D of‐ the printingdielectric technique constant was and used manufacturing to obtain a mold tolerances structure, of the which 3D-printed defines mold, the shape and theof the results dielectricare shown paste in after Figures it is inserted 12 and 13 into. Much the mold better and agreement dried. The with antenna the measured was found results to have can be an impedanceobserved for bandwidth the resimulated of 21.6%, antenna whereas for boththe axial reflection ratio coefficient,bandwidth as was well found as axial to be ratio. 16.7%, with stable broadside radiation pattern. A peak efficiency of the antenna of 82.3% was 6.obtained Conclusions by measurement. The measured overlapping bandwidth (reflection coeffi‐ cient < −10In dB this and publication, axial ratio a< 3 new dB) approachwas found for to designingbe from 2.575 dielectric GHz to resonator 2.97 GHz antennasor 14%. is The presented.measured antenna The method prototype employs is suitable a dielectric for WiMAX paste and applications. a 3D-printed mold, which is filled with the dielectric paste material. A dielectric paste can be obtained by mixing BST nano Authorparticle Contributions: sized powder Investigation, with a silicone analysis rubber.methodology, By controlling and experiment, the BST H.I.K.; to rubber manufactur ratio,‐ the ing anddielectric experiment, constant W.C.W.; of the pastesupervision can be and flexibly project controlled administration, with a dielectricK.W.L., K.K. constant‐W.L., rangingand M.W.K.L. All authors have read and agreed to the published version of the manuscript. from 3.67 to 18.45, corresponding to a BST powder content of 20% to 80% in weight percent. Funding: This work was supported by the General Research Fund (GRF) from the Research Grants Council of Hong Kong Special Administrative Region, China. (Project no. CityU 11218819) (Corre‐ sponding author: Kwok Wa Leung) Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable.

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The loss tangent of the paste was found to be generally lower than 0.044. Using the dielectric paste, a circularly polarized menger sponge fractal DRA was constructed. The 3D-printing technique was used to obtain a mold structure, which defines the shape of the dielectric paste after it is inserted into the mold and dried. The antenna was found to have an impedance bandwidth of 21.6%, whereas the axial ratio bandwidth was found to be 16.7%, with stable broadside radiation pattern. A peak efficiency of the antenna of 82.3% was obtained by measurement. The measured overlapping bandwidth (reflection coefficient < −10 dB and axial ratio < 3 dB) was found to be from 2.575 GHz to 2.97 GHz or 14%. The measured antenna prototype is suitable for WiMAX applications.

Author Contributions: Investigation, analysis methodology, and experiment, H.I.K.; manufacturing and experiment, W.C.W.; supervision and project administration, K.W.L., K.K.-W.L. and M.W.K.L. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the General Research Fund (GRF) from the Research Grants Council of Hong Kong Special Administrative Region, China. (Project no. CityU 11218819) (Corre- sponding author: Kwok Wa Leung). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to thank Yip Tsz Hang for the help in manufacturing the dielectric paste samples. The authors would also like to thank the reviewers for their useful comments. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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