Bio-Inspired Dielectric Resonator Antenna for Wideband Sub-6 Ghz Range

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Article Bio-Inspired Dielectric Resonator Antenna for Wideband Sub-6 GHz Range

Luigi Melchiorre 1 , Ilaria Marasco 1,* , Giovanni Niro 1, Vito Basile 2 , Valeria Marrocco 2 , Antonella D’Orazio 1 and Marco Grande 1,*

1 Politecnico di Bari, Dipartimento di Ingegneria Elettrica e dell’Informazione, Via E. Orabona 4, 70125 Bari, Italy; [email protected] (L.M.); [email protected] (G.N.); [email protected] (A.D.) 2 STIIMA CNR, Institute of Intelligent Industrial Technologies and Systems for Advanced Manufacturing, National Research Council, Via P. Lembo, 38/F, 70124 Bari, Italy; [email protected] (V.B.); [email protected] (V.M.) * Correspondence: [email protected] (I.M.); [email protected] (M.G.)

Received: 10 November 2020; Accepted: 7 December 2020; Published: 10 December 2020

Abstract: Through the years, inspiration from nature has taken the lead for technological development and improvement. This concept firmly applies to the design of the antennas, whose performances receive a relevant boost due to the implementation of bio-inspired geometries. In particular, this idea holds in the present scenario, where antennas working in the higher frequency range (5G and mm-wave), require wide bandwidth and high gain; nonetheless, ease of fabrication and rapid production still have their importance. To this aim, polymer-based 3D antennas, such as Dielectric Resonator Antennas (DRAs) have been considered as suitable for fulfilling antenna performance and fabrication requirements. Differently from numerous works related to planar-metal-based antenna development, bio-inspired DRAs for 5G and mm-wave applications are at their beginning. In this scenario, the present paper proposes the analysis and optimization of a bio-inspired Spiral shell DRA (SsDRA) implemented by means of Gielis’ superformula, with the goal of boosting the antenna bandwidth. The optimized SsDRA geometrical parameters were also determined and discussed based on its fabrication feasibility exploiting Additive Manufacturing technologies. The results proved that the SsDRA provides relevant bandwidth, about 2 GHz wide, and satisfactory gain (3.7 dBi and 5 dBi, respectively) at two different frequencies, 3.5 GHz and 5.5 GHz.

Keywords: bio-inspiration; dielectric resonator antennas; Gielis’ superformula; wideband sub-6 GHz applications

1. Introduction The use of peculiar geometries and shapes inspired by nature has demonstrated, through the years, to be an intriguing and successful option capable of supporting the development of advanced electronic devices. In particular, these bio-inspired designs are able to cope with the main criticalities related to metal-based antenna systems aimed at WLNA, WiMAX, 5G and mm-wave communication applications: wide bandwidth and high radiation efficiency. In this viewpoint, Panda et al. [1] presented the design of a microstrip antenna resembling a flower shape, conceived on a defective ground structure (DGS); the numerical results showed that a dramatic improvement of the bandwidth and return loss was achieved at the operating frequency (15 GHz). Abolade et al. [2] exploited the shape of Carica Papaya leaf to realize a microstrip antenna which exhibited large bandwidth and high gain for three different bands, centered at 4.3 GHz, at 7.2 GHz and 9.3 GHz, respectively, providing a compact and suitable solution for a variety of applications (GSM1900, UMTS, WLAN, LTE2300 and

Appl. Sci. 2020, 10, 8826; doi:10.3390/app10248826 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 8826 2 of 13

LTE2600, WiMAX, C-band, X-band, and sub-6GHz band). A patch antenna patterned as sunflower seeds was proposed by Singh et al. [3] to obtain omni-directional radiation properties and increased radiation efficiency between 14 and 15 GHz. Mesquita et al. [4] exploited the Oxalis triangularis plant’s leaf shape for the design and fabrication of two frequency selective surface (FSS) microstrip arrays, where the conductive elements were realized by using copper and silver ink. The results showed that the fractional bandwidth was equal to 18% for copper and 14% for silver ink, at the central resonant frequency (2.5 GHz). De Oliveira et al. [5] applied a four-leaf clover geometry to the patch elements of an array designed for wireless application, in the frequency band of 2.45 GHz. The results concerned an achieved bandwidth of 81 MHz and a maximum gain of 8.24 dBi at 2.4 GHz. Fractal based wideband microstrip antenna, conceived for 5G applications, was proposed by Malik et al. [6]: the optimized structure was characterized by a fractional bandwidth of 165% in the frequency range from 17.22 GHz to 180 GHz, with a peak gain of 10 dBi; additionally, the antenna exhibited relevant compactness in size. Self-similar fractals have been used to create multi-band antennas [7,8] and also antennas based on genetic evolution have been proposed to design high-directive antennas [9]. The opportunity to design more and more bio-inspired geometries became effectively available when Gielis introduced his superformula [10,11]. Since then, this superformula has been widely exploited to design patch antennas [12–14], metamaterial and metasurfaces [15,16], frequency selective surfaces (FSS) [17], split-ring resonators [18,19], wearable antennas [20] and, very recently, Dielectric Resonator Antennas (DRAs) [21,22]. Concerning patch antennas, the superformula was used by Poordaraee et al. [12] to implement the characteristic mode theory with the goal of designing and modifying patch antennas’ shapes and obtain circularly polarized radiated field at 2.45 GHz for ISM band application. Two designs of UWB coplanar waveguide (CPW)-fed-patch antennas designed by means of Gielis’ superformula and operating in the FCC frequency band (3.1–10.6 GHz) were proposed by Omar et al. [13]. In particular, in this work, it was shown that the super-shaped sawtooth-like circumference patch allowed to have same bandwidth (600 MHz) and gain (3.8 dBi) at the central frequency (7 GHz) of the classic circular patch; the main advantage of using such shapes consisted in a smaller patch diameter. The same compactness in the antenna size was accomplished by Naser and Dib [14], who designed an ultra-wideband microstrip-fed patch antenna, working between 3.1 GHz–10.6 GHz, by using a contour profile based on the superformula. Although plenty of works about bio-inspired geometries can be easily found for planar microstrip antenna technology, very few examples are proposed for dielectric-based antennas, such as DRAs. DRAs are successfully exploited for the design of dielectric metasurfaces, which are of paramount importance at very high frequencies, i.e., in the optical domain. Indeed, they can be used for polarization manipulation to design polarization converters [23], beam splitters [24], and polarization-based functional metalenses [25]. Another possibility is to use them for polarization detection [26] or polarization-based nano-printing [27]. As for their relevant inclination for high-frequency purposes, DRAs are currently recommended by the research community for 5G and mm-wave applications: indeed, as these structures are made of dielectric materials, they are free of conduction losses and, as such, capable of fulfilling bandwidth and radiation efficiency requirements. Additionally, as DRAs can be also made of polymers, they can be easily fabricated by means of Additive Manufacturing (AM) technologies. Very recently, optimized DRAs made of low permittivity materials providing wider bandwidth were proposed. An evaluation of dielectric materials suitable for microwave range applications was reported by Kumar and Gupta [28], who focused mainly on types of Rogers and FR4. Nonetheless, also polymers, such as polyactic Acid (PLA), were considered for the design and manufacturing of DRAs featuring simple 3D geometries [29,30]. However, although very promising for wideband specification, low permittivity—DRAs are often characterized by low radiation efficiency. Therefore, the scientific community recently focused on the use of more intricate and complex 3D geometries, such as 3D quadrupole-shaped [31,32], for WLAN (8 GHz) and 5G applications (3.5 GHz). An attempt Appl. Sci. 2020, 10, 8826 3 of 13 of using bio-inspired geometry was presented by Sankaranarayanan et al. [33]: in this work, snow-flake fractal and half split fractal rings were implemented on the classic cylindrical DRAs, thus achieving 90% of fractional bandwidth and gain enhancement in the frequency range between 4.7 and 12.4 GHz. Fractal segmented patterns were also employed by Gupta et al. [34] to design FR4-based DRAs with ultra-wideband performance (122.5% and 94.89%) from 4.8 GHz to 20 GHz and characterized by high compactness and gain at 8.5 GHz (8.75 and 15.65 dBi, respectively). Actual 3D star-super-shaped DRAs (S-DRAs) based on Gielis’ superformula were reported by Simeoni et al. [35], Petrignani et al. [36] and Basile et al. [37]. In [35], the super-shaped DRAs (S-DRA) were designed to operate at 7.65 GHz and realized by considering polyvinyl chloride (PVC), a thermoplastic material having low permittivity (εr~2.8) and negligible tangent loss. The results showed that in the single feed case study, a fractional bandwidth of 74% and gain of ~8 dBi were accomplished between 6 and 13 GHz. Conversely, in [36,37], twisted star-based S-DRAs were designed to operate in the sub-6 GHz range, at 3.5 GHz. The S-DRAs were realized by means of a photopolymer resin material having εr = 2.7 and low tangent loss, suitable for stereolithography. The experimental results showed that this kind of DRAs was able to provide high gain (around 3 dBi) and radiation efficiency (~90%) at 3.5 GHz, while keeping their volume significantly small. However, although the use of bio-inspired geometry and DRAs proved to lead to an overall improvement of the antenna performance, especially in terms of bandwidth enhancement, works about the actual combination of these two strategies for a further boost in the antenna development are still at their beginning. Indeed, very few Authors attempted to design and realize bio-inspired DRAs and, in particular, none of them considers complex and thin 3D shapes, like Button snail Modulus modulus (spiral seashell) for the DRA applications. Therefore, in this research, the design and optimization of a bio-inspired super-shaped DRA, resembling a Spiral shell of a sea mollusk, generated by means of Gielis’ superformula and suitable for sub-6 GHz applications, is presented. The numerical analyses were performed by fixing Gielis’ parameters and varying the geometrical sizes of the DRA, with the aim of accomplishing wideband behavior in the frequency range of interest. In particular, the influence of the coaxial cable pin height, DRA thickness and height on the scattering parameter S11 and antenna gain are evaluated. The impact of the exponential coefficient of Gielis’ superformula on the antenna design was also investigated in terms of antenna design and prototype fabrication, envisaged to be realized by means of Additive Manufacturing processes. The 3D radiation patterns, electric and magnetic field distributions and radiation efficiency of the optimized Spiral shell DRA are also reported. The overall performance of the SsDRA was then compared to other DRA geometries, conceived and realized by using the same low-permittivity material. Finally, a detailed discussion about fabrication feasibility and issues emerged for the realization of the Ss-DRA prototype is reported.

2. Bio-Inspired Spiral Shell DRA The Button snail Modulus modulus (spiral seashell) presented in Figure1a was the bio-inspiration for the device of the SsDRA shown in Figure1b. The SsDRA is placed in the center of a ground plane, a squared substrate with side LSUB, in the origin of the reference system; the dielectric thickness t and the height hDRA of the antenna are also indicated. The considered dielectric material has a permittivity of 2.7 and negligible loss tangent (0.008) in the frequency range of interest [36,37]. The DRA is fed by a coaxial cable (Z0 = 50 Ω, conductor diameter Ø 0.48 mm, insulation diameter Ø 1.52 mm) placed in the antenna origin: the pin height is indicated by hPIN. The shape of the SsDRA was generated by Gielis’ superformula explicated in Equation (1) [38]:

" n2 n3 # 1/n1 1 m1 1 m2 − GT(θ, f(θ), a, b, m1, m2, n1, n2, n3) = K f(θ) cos θ + sin θ (1) · · a 4 b 4 Appl. Sci. 2020, 10, 8826 4 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 13

Figure 1. (a) Picture of a Button snail Modulus modulus (spiral seashell). (b) 3D sketch of the Spiral Figure 1. (a) Picture of a Button snail Modulus modulus (spiral seashell). (b) 3D sketch of the Spiral shell Dielectric Resonator Antenna (DRA). shell Dielectric Resonator Antenna (DRA). 2.1. Gielis Parameters: Impact on the SsDRA Design The shape of the SsDRA was generated by Gielis’ superformula explicated in Equation (1) [38]: The design initiator was defined by considering that the variation of the “a” and “b” parameters / affects the sizes and volume of the DRA, and so the footprint1 itm can actually1 occupy.m The angular position GTθ,fθ,a,b,m,m,n,n,nK ∙fθ∙ cos θ sin θ (1) of the shell wave ridges remains constant, while the shella wave4 amplitudesb increase4 proportionally as “a” and “b” increase. The “m1” and “m2” parameters influence the frequency of the shell wave over2.1. Gielis the base Parameters: spiral: Impact when theseon the coeSsDRAfficients Design are increased, the shell wave number increases along the spiral. The parameters “n1”, “n2” and “n3” affect the shell wave amplitude on each loop of the The design initiator was defined by considering that the variation of the “a” and “b” parameters shell: in particular, when n1 = n2 = n3 = 2, the output geometry becomes the well-known Archimedean affects the sizes and volume of the DRA, and so the footprint it can actually occupy. The angular spiral. For values of “n1”, “n2” and “n3” higher than 2, alternate waves are overlapped on the spiral. Whenposition these of the parameters shell wave are lowerridges thanremains 2, the cons wavestant,resemble while the a rectifiedshell wave sine amplitudes (or cosine) increase with an outwardproportionally concavity, as “a” thus and orienting “b” increase. the wave The ridges“m1” and inward. “m2” Theparameters constant influence scaling factor the frequency K regulates of the overallshell wave amplitude over the of thebase geometry spiral: when and, asthese such, coe itfficients affects the are DRA increased, radius andthe volume.shell wave The number planar exponentialincreases along function the spiral. f(θ), The expressed parameters by the “n following1”, “n2” and Equation “n3” affect (2): the shell wave amplitude on each loop of the shell: in particular, when n1 = n2 = n3 = 2, the output geometry becomes the well-known

Archimedean spiral. For values of “n1”, “nf(θ2”) and= e “n(c3theta” higherθ) than 2, alternate waves are overlapped(2) on the spiral. When these parameters are lower than 2, the∗ waves resemble a rectified sine (or cosine) actswith on an the outward closeness concavity, of the wavy thus spiral orienting loops, the thus wave on the ridges space inward. actually filledThe constant by the DRA. scaling In particular, factor K theregulates parameter the overall ctheta (which amplitude is a rationalof the geometry number) and, has a as sharp such, influence it affects onthe the DRA radial radius expansion and volume. of the spiralThe planar loops, exponential i.e., the aperture function velocity fθ, expressed∆R/∆θ. by the following Equation (2): On the basis of these considerations, we fixed the starting initiator values reported in Table1 fθ e c ∗ θ (2) where the angle parameter θ is varied in the range [ 3π, 3π] (i.e., three complete rounds). acts on the closeness of the wavy spiral loops, thus− on the space actually filled by the DRA. In particular, theTable parameter 1. Gielis’ c parameterstheta (which used is a in rational Equation number) (1) to generate has thea sharp Spiral influence shell DRA. on the radial expansion of the spiral loops, i.e., the aperture velocity ΔR/Δθ. f(θ) K c a b m m n n n On the basis of these considerations,theta we fixed the 1starting2 initiator1 values2 reported3 in Table 1 where the angle parameter[-] [-]θ is varied [-] in [-]the range [-] [−3 [-]π, 3π] [-](i.e., three [-] complete [-] rounds). [-] C θ e theta· 6 0.2 1 1 10 10 5 5 5 Table 1. Gielis’ parameters used in Equation (1) to generate the Spiral shell DRA.

The deﬁned parametersf(θ lead) toK a SsDRActheta footprinta b smallerm1 m than2 n the1 groundn2 n3 plane whose dimensions are 100 100 mm2, thus with L = 100 mm. × [-] SUB [-] [-] [-] [-] [-] [-] [-] [-] [-] e∙ 6 0.2 1 1 10 10 5 5 5 2.2. Evaluation of SsDRA Design Based on the Fabrication Feasibility

The proposeddefined parameters SsDRA has lead a typical to a 2.5D SsDRA geometry, footprint since smaller it develops than as the a straight ground protrusion plane whose of a thindimensions planar section.are 100 × The 100 main mm2 fabrication, thus with issueLSUB = displayed100 mm. along the z-axis direction concerns the aspect ratio (AR) of the geometry, defined as hDRA/t. In order to guarantee the successful fabrication of a sti2.2.ff Evaluationstructure, of the Ss ARDRA should Design be Based higher on thanthe Fabrication a critical Feasibility threshold, which depends on the mechanical The proposed SsDRA has a typical 2.5D geometry, since it develops as a straight protrusion of a thin planar section. The main fabrication issue displayed along the z-axis direction concerns the Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13 Appl. Sci. 2020, 10, 8826 5 of 13 aspect ratio (AR) of the geometry, defined as hDRA/t. In order to guarantee the successful fabrication of a stiff structure, the AR should be higher than a critical threshold, which depends on the mechanicalproperties of properties the material of and the the material chosen fabricationand the ch technology.osen fabrication Therefore, technology. in the antenna Therefore, optimization, in the the values of t and h were set by taking into account this limitation. antenna optimization,DRA the values of t and hDRA were set by taking into account this limitation. TheThe spiral spiral section section evolving evolving along along the the X-Y X-Y plane plane re representspresents the the main main challenge challenge for for the the fabrication fabrication ofof the the proposed proposed geometry, geometry, and, and, as as such, such, it it dictates dictates the the actual actual selection selection of of the the most most suitable suitable Additive Additive ManufacturingManufacturing process. process. In In order order to to come come up up with with fe feasibleasible solutions solutions for for the the further further SsDRA SsDRA fabrication, fabrication, preliminarypreliminary considerations considerations were made, basing onon thethe SsDRASsDRA prototypeprototype drawingsdrawings reported reported in in Figure Figure2, 2,as as follows: follows: a.a. ByBy fixing fixing the the parameter parameter “m” “m” equal toto 10,10, the the geometry geometry has has 10 10 peaks peaks and and valleys valleys and and the step-anglethe step- anglebetween between them them is kept is constantkept constant and equal and toequa 36l degreesto 36 degrees (360/m), (360/m), independently independently of the position of the positionalong the along spiral the curve. spiral Ridges curve. and Ridges valleys and are va rounded,lleys are butrounded, the lower but the the cylindrical lower thecoordinate cylindricalθ coordinate(and distance θ (and from distance the origin from GT( theθ ))origin is, the GT( lowerθ)) is, the the radius lower of the the radius circle which of the approximates circle which approximateslocally the curve locally on the ridges curve or on valleys. ridges or In valley addition,s. In the addition, amplitude the amplitude of the oscillation of the oscillation along the alongspiral the is spiral proportional is proportional to the valuesto the values of parameters of parameters n1, n2 nand1, n2 nand3 of n the3 of the Gielis Gielis formulation formulation (1): (1):in in this this case, case, they they are are all all equal equal to to 5. 5. This This setting setting allows allows us us to haveto have smaller smaller amplitude amplitude close close to theto theorigin, origin, i.e., i.e., micro-features micro-features which which requires requires an an accurate accurate fabrication fabrication assessment. assessment. b.b. SinceSince the the radius radius of ofthe the spiral spiral increases increases monotonically monotonically from from the theorigin origin to the to end the endof the of spiral, the spiral, the smallerthe smaller features features of the geometry of the geometry are in close are prox in closeimityproximity to the origin, to thethus origin, generating thus micro-scale generating features.micro-scale features.

Figure 2. (a) Side view and (b) top view with main dimensions and rounds radii R (inset) related to the Figure 2. (a) Side view and (b) top view with main dimensions and rounds radii R (inset) related to spiral shell DRA (SsDRA). the spiral shell DRA (SsDRA). The measurement of circle approximations of the curve is important to evaluate the feasibility of The measurement of circle approximations of the curve is important to evaluate the feasibility 3Dprinting technologies in the SsDRA fabrication. Indeed, the majority of the Additive Manufacturing of 3Dprinting technologies in the SsDRA fabrication. Indeed, the majority of the Additive technologies build the objects using a layer-by-layer strategy, accomplished by moving a circular Manufacturing technologies build the objects using a layer-by-layer strategy, accomplished by end-eﬀector: in particular, the end-eﬀector is an extrusion nozzle in the Fused Deposition Modelling moving a circular end-effector: in particular, the end-effector is an extrusion nozzle in the Fused (FDM), and a laser spot in the stereolithography (SLA) [39,40]. Therefore, the previous considerations Deposition Modelling (FDM), and a laser spot in the stereolithography (SLA) [39,40]. Therefore, the lead to select an AM process that should be capable of reproducing accurately the micro-features and previous considerations lead to select an AM process that should be capable of reproducing ensuring the target value of roundness for the ridges and valleys. Detailed discussions about the accurately the micro-features and ensuring the target value of roundness for the ridges and valleys. evaluation of the best candidate among AM processes along with fabrication challenges and solutions Detailed discussions about the evaluation of the best candidate among AM processes along with about the optimized SsDRA fabrication are reported in Section4. fabrication challenges and solutions about the optimized SsDRA fabrication are reported in Section 4. Appl. Sci. Sci. 20202020,, 1010,, x 8826 FOR PEER REVIEW 6 6of of 13 13

3. Spiral Shell DRA Analysis and Optimization 3. Spiral Shell DRA Analysis and Optimization In order to evaluate the SsDRA performance and proceed with the antenna optimization, numericalIn order analyses to evaluate have been the carried SsDRA out performance on the SsDRA and geometrical proceed withparameters the antenna by means optimization, of the CST Microwavenumerical analyses Studio. have been carried out on the SsDRA geometrical parameters by means of the CST Microwave Studio.

3.1. Influence of SsDRA Thickness, Pin Height and SsDRA Height on the Scattering Parameter S11: 3.1. Inﬂuence of SsDRA Thickness, Pin Height and SsDRA Height on the Scattering Parameter S11: Evaluation of the Bandwidth

In order to optimize the SsDRA design in terms of bandwidth, the scattering parameter S11 was In order to optimize the SsDRA design in terms of bandwidth, the scattering parameter S11 was evaluated by varying the central pin height, hPIN, and the SsDRA shell thickness t, by fixing the SsDRA evaluated by varying the central pin height, hPIN, and the SsDRA shell thickness t, by ﬁxing the SsDRA height hDRA = 29 mm. The pin height hPIN is changed between 14.5 and 18 mm, while keeping the DRA height hDRA = 29 mm. The pin height hPIN is changed between 14.5 and 18 mm, while keeping the thickness equal to t = 2 mm. The trend of the scattering parameter S11 as a function of hPIN is reported DRA thickness equal to t = 2 mm. The trend of the scattering parameter S11 as a function of hPIN inis reportedFigure 3a, in where Figure it3 a,can where be noticed it can bethat noticed when thatthe whenpin height the pin increases, height increases,the impedance the impedance matching becomes wider. In particular, for a pin height hPIN = 17 mm (cyan curve), a good impedance matching matching becomes wider. In particular, for a pin height hPIN = 17 mm (cyan curve), a good impedance canmatching be achieved can be at achieved 3.5 GHz at and 3.5 GHz5.5 GHz, and 5.5leading GHz, to leading a bandwidth to a bandwidth of about of2 GHz. about Figure 2 GHz. 3b Figure depicts3b the trend of the scattering parameter S11 when hPIN is fixed at 17 mm and the SsDRA thickness t is depicts the trend of the scattering parameter S11 when hPIN is ﬁxed at 17 mm and the SsDRA thickness t varied (t = 1, 1.5 and 2 mm). The plots show that as t increases, the scattering parameter S11 values is varied (t = 1, 1.5 and 2 mm). The plots show that as t increases, the scattering parameter S11 values improve,improve, especially at 5.2 GHz, and, when tt = 22 mm mm (yellow (yellow curve), the bandwidth at −1010 dB dB is is equal equal − toto about about 2 2 GHz. GHz.

FigureFigure 3. ((aa)) Scattering parameter S 11 asas a a function of the pin height hPIN, ,by by considering considering the the DRA DRA

thicknessthickness t = 22 mm mm and and h DRA = =2929 mm; mm; (b ()b Scattering) Scattering parameter parameter S S1111 asas a afunction function of of the the DRA DRA thickness, thickness,

consideringconsidering the the pin pin height h PIN == 1717 mm mm and and DRA DRA height height h hDRADRA = 29= 29mm. mm.

3.2. Effect of the SsDRA Thickness, Pin Height and DRA Height on the Scattering Parameter S11 and Realized Gain 3.2. Effect of the SsDRA Thickness, Pin Height and DRA Height on the Scattering Parameter S11 and RealizedFigure Gain4a shows the scattering parameter S 11 when both hPIN and t are varied, while hDRA is set equal to 29 mm; the behavior of the monopole antenna (blue curve) having a pin height hPIN equal Figure 4a shows the scattering parameter S11 when both hPIN and t are varied, while hDRA is set to 17 mm is also reported for reference. The monopole exhibits a scattering parameter S11 value of equal to 29 mm; the behavior of the monopole antenna (blue curve) having a pin height hPIN equal to about 14 dB at about 5.7 GHz with a bandwidth of about 1 GHz (from 4 GHz to 5 GHz). When the 17 mm− is also reported for reference. The monopole exhibits a scattering parameter S11 value of about SsDRA is considered and its thickness t is increased, a better impedance matching is accomplished: −14 dB at about 5.7 GHz with a bandwidth of about 1 GHz (from 4 GHz to 5 GHz). When the SsDRA in particular, the antenna bandwidth at 10 dB increases from 1.5 GHz for t = 1 mm and h = 19 mm is considered and its thickness t is increased,− a better impedance matching is accomplished:PIN in (red curve), up to about 2 GHz for t = 2 mm and hPIN = 17 mm (purple curve), along with lower particular, the antenna bandwidth at −10 dB increases from 1.5 GHz for t = 1 mm and hPIN = 19 mm (red scattering parameter S11 value ( 16 dB), especially around 5.2 GHz. curve), up to about 2 GHz for t =− 2 mm and hPIN = 17 mm (purple curve), along with lower scattering Figure4b depicts the realized gain of the antenna that takes into account the losses due to the parameter S11 value (−16 dB), especially around 5.2 GHz. matching: as we can infer from the plot, as the SsDRA thickness is increased, gain values are equal to 3.3 dBi at 2.8 GHz (red curve), and increase up to 5 dBi at 5.5 GHz (purple curve). Generally, the gain values improve by about 0.2 dB up to about 2 dB with respect to the reference monopole in the overall frequency range of interest. Furthermore, the inspection of Figure4b shows that SsDRA allows the additional coverage of the WiFi band, at 2.45 GHz. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13

Appl. Sci. 2020, 10, 8826 7 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13

Figure 4. (a) Scattering parameter S11 as the pin height hPIN is varied from 17 to 19 mm and the DRA thickness t is varied in the range 1–2 mm, hDRA = 29 mm; reference monopole antenna with a height of

17 mm is reported for comparison; (b) Realized gain as the pin height hPIN is varied in the range 17–

19 mm and the DRA thickness is varied in the range 1–2 mm, hDRA = 29 mm; reference monopole antenna with a height of 17 mm is reported for comparison.

Figure 4b depicts the realized gain of the antenna that takes into account the losses due to the Figure 4. (a) Scattering parameter S11 as the pin height hPIN is varied from 17 to 19 mm and the DRA matching:Figure as 4.we (a can) Scattering infer from parameter the plot, S11 as as the the pin SsDRA height hthicknessPIN is varied is from increased, 17 to 19 gain mm andvalues the DRAare equal to thickness t is varied in the range 1–2 mm, hDRA = 29 mm; reference monopole antenna with a height 3.3 dBi thicknessat 2.8 GHz t is varied(red curve), in the range and increase1–2 mm, h upDRA to= 29 5 mm;dBi atreference 5.5 GHz monopole (purple antenna curve). with Generally, a height of the gain of 17 mm is reported for comparison; (b) Realized gain as the pin height hPIN is varied in the range values 17improve mm is reported by about for 0.2 comparison; dB up to about(b) Realized 2 dB withgain as respect the pin to height the reference hPIN is varied monopole in the range in the17– overall 17–19 mm and the DRA thickness is varied in the range 1–2 mm, hDRA = 29 mm; reference monopole 19 mm and the DRA thickness is varied in the range 1–2 mm, hDRA = 29 mm; reference monopole frequencyantenna range with aof height interest. of 17 Furthermore, mm is reported the for inspec comparison.tion of Figure 4b shows that SsDRA allows the additionalantenna coverage with a ofheight the WiFiof 17 mm band, is reported at 2.45 GHz.for comparison. FigureFigure5 5 reports reports the the evaluation evaluation of of the the scattering scattering parameter parameter S S11and and gain gain as as the the SsDRA SsDRA height height h hDRA Figure 4b depicts the realized gain of the antenna that takes11 into account the losses due to theDRA isis variedvaried between 10 10 mm mm and and 30 30 mm, mm, while while h hPIN andand t are t are fixed ﬁxed to to17 17mm mm and and 2 mm, 2 mm, respectively. respectively. As matching: as we can infer from the plot, as the PINSsDRA thickness is increased, gain values are equal to As evident from Figure5a, when the SsDRA height is increased from 10 mm and 20 mm, the bandwidth evident3.3 dBi from at 2.8 Figure GHz (red 5a, whencurve), the and SsDRA increase height up to is 5 increaseddBi at 5.5 GHz from (purple 10 mm curve). and 20 Generally, mm, the bandwidth the gain atat −10 dB increases as well, covering a range from about 1.3 GHz to 1.8 GHz (red and yellow curves). −values improve by about 0.2 dB up to about 2 dB with respect to the reference monopole in the overall Conversely,Conversely,frequency asrangeas shownshown of interest. inin FigureFigure Furthermore,5 b,5b, as as the the h thehDRADRA inspec is increased,increased,tion of Figure thethe SsDRASsDRA 4b shows gaingain that improvesimproves SsDRA inallowsin thethe rangerangethe betweenbetweenadditional 2.52.5 GHzGHzcoverage toto 4.54.5 of GHz GHzthe WiFi (red (red band, and and yellow yellowat 2.45 curvesGHz. curves are are relevantly relevantly higher higher than than the the blue blue curve), curve), while while it showsit shows negligibleFigure negligible 5 reports changes changes the aroundevaluation around 5.5 5.5of GHz. the GHz. scattering parameter S11 and gain as the SsDRA height hDRA is varied between 10 mm and 30 mm, while hPIN and t are fixed to 17 mm and 2 mm, respectively. As evident from Figure 5a, when the SsDRA height is increased from 10 mm and 20 mm, the bandwidth at −10 dB increases as well, covering a range from about 1.3 GHz to 1.8 GHz (red and yellow curves). Conversely, as shown in Figure 5b, as the hDRA is increased, the SsDRA gain improves in the range between 2.5 GHz to 4.5 GHz (red and yellow curves are relevantly higher than the blue curve), while it shows negligible changes around 5.5 GHz.

Figure 5. (a) Scattering parameter S as the DRA height is varied in the range 10–29 mm, considering Figure 5. (a) Scattering parameter S1111 as the DRA height is varied in the range 10–29 mm, considering h = 17 mm and t = 2 mm; (b) Realized gain as the DRA height is varied in the range 10–29 mm, hPINPIN = 17 mm and t = 2 mm; (b) Realized gain as the DRA height is varied in the range 10–29 mm, considering h = 17 mm and t = 2 mm. considering hPINPIN = 17 mm and t = 2 mm.

3.3. Scattering Parameter S11 and Realized Gain as a Function of the Exponential Function f(θ) of the Optimized3.3. Scattering SsDRA Parameter S11 and Realized Gain as a Function of the Exponential Function f(θ) of the Optimized SsDRA InFigure order 5. to (a show) Scattering the e parameterffect of the S11 planaras the DRA exponential height is varied function in the f(rangeθ) on 10–29 the mm, SsDRA considering performance, Inh orderPIN = 17 to mm show and thet = 2 effect mm; ( bof) Realizedthe planar gain exponential as the DRA heightfunction is varied f(θ) onin thethe range SsDRA 10–29 performance, mm, the coefficient ctheta was varied by considering three values: 0.16, 0.18 and 0.20. The geometrical the coefficientconsidering ctheta hPIN was = 17 varied mm and by t =considering 2 mm. three values: 0.16, 0.18 and 0.20. The geometrical sizes sizes of the SsDRA were kept unchanged: t = 2 mm, hDRA = 29 mm and hPIN = 17 mm. Figure6a revealsof the SsDRA that, when were this kept coe unchanged:fficient is reduced, t = 2 mm, the hDRA lower = 29 cut-omm andff frequency hPIN = 17 shiftsmm. Figure at higher 6a reveals frequencies that, when3.3. Scatteringthis coefficient Parameter is reduced, S11 and Realized the lower Gain cut-oas a Functionff frequency of the Exponentialshifts at higher Function frequencies f(θ) of the (from 3.5 (fromOptimized 3.5 GHz SsDRA to about 4 GHz), while the minimum of the scattering parameter shifts from 5 GHz GHz to about 4 GHz), while the minimum of the scattering parameter shifts from 5 GHz to 5.5 GHz. to 5.5 GHz. Figure6b shows that when c theta is reduced, the antenna gain undergoes a reduction at 3.5 GHzIn (blue order curve), to show while the effect it exhibits of the a planar slight increaseexponential (about function 0.4 dB) f(θ at) on 5.5 the GHz SsDRA (red curve).performance, the coefficient ctheta was varied by considering three values: 0.16, 0.18 and 0.20. The geometrical sizes of the SsDRA were kept unchanged: t = 2 mm, hDRA = 29 mm and hPIN = 17 mm. Figure 6a reveals that, when this coefficient is reduced, the lower cut-off frequency shifts at higher frequencies (from 3.5 GHz to about 4 GHz), while the minimum of the scattering parameter shifts from 5 GHz to 5.5 GHz. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 13

Figure 6b shows that when ctheta is reduced, the antenna gain undergoes a reduction at 3.5 GHz (blue Appl. Sci. 2020, 10, 8826 8 of 13 curve), while it exhibits a slight increase (about 0.4 dB) at 5.5 GHz (red curve).

Figure 6. (a) Scattering Parameter S and (b) gain of the optimized SsDRA as the coefficient c is Figure 6. (a) Scattering Parameter S1111 and (b) gain of the optimized SsDRA as the coefficienttheta ctheta is varied: 0.16, 0.18 and 0.20. varied: 0.16, 0.18 and 0.20. Finally, we underline that, if θ is varied in the range 0–2π (1 complete round), while other Finally, we underline that, if θ is varied in the range 0–2π (1 complete round), while other parameters are fixed—t = 2 mm, hDRA = 29 mm, hPIN = 17 mm and ctheta = 0.2—the SsDRA bandwidth parametersexperiences are afixed—t significant = 2 reduction,mm, hDRA decreasing = 29 mm, downhPIN = to 17 about mm 1.5and GHz, ctheta while = 0.2—the the realized SsDRA gain bandwidth value experiencesapproaches a significant the monopole reduction, one, in thedecreasing frequency down interval to fromabout 4.5 1.5 GHz GHz, to 6while GHz. the realized gain value approaches the monopole one, in the frequency interval from 4.5 GHz to 6 GHz. 3.4. Radiation Pattern, Realized Gain and Radiation Efficiency of the Optimized SsDRA 3.4. RadiationThe previousPattern, analysesRealized allowedGain and to Radiation define the Efficiency geometrical of the parameters Optimized of SsDRA the bio-inspired SsDRA which exhibits wider bandwidth and a satisfactory gain value at two frequencies, 3.5 GHz and 5.5 GHz: The previous analyses allowed to define the geometrical parameters of the bio-inspired SsDRA t = 2 mm, hDRA = 29 mm, hPIN = 17 mm and ctheta = 0.2. which exhibitsFigure 7wider shows bandwidth the 3D radiation and patternsa satisfactory of the optimizedgain value antenna, at two along frequencies, with the polar3.5 GHz cuts and in 5.5 GHz:the t = E 2 and mm, H h planes,DRA = 29 at mm, 3.5 GHz hPIN and = 17 5.5 mm GHz. and In c particular,theta = 0.2. when the frequency is equal to 3.5 GHz (FigureFigure7 7a–c), shows the maximumthe 3D radiation value of patterns the gain of is equalthe optimized to 3.78 dBi. antenna, The main along lobe with magnitude the polar in the cuts in the EE-plane and H ( ϕplanes,= 0 deg, at Figure3.5 GHz7b) isand equal 5.5 to GHz. 0.727 In dBi, particular, the mainlobe when direction the frequency is equal to is 53 equal deg and to 3.5 the GHz (Figureangular 7a–c), width the maximum (3 dB) is equal value to 82.7of the deg. gain Conversely, is equal to when 3.78 the dBi. H-plane The main is considered lobe magnitude (ϕ = 90 in deg, the E- planeFigure (φ = 70c), deg, the Figure main lobe 7b) magnitude is equal to is 0.727 equal dBi, to 1.05 the dBi, main while lobe the direction main lobe is directionequal to 53 isequal deg and to the angular53 deg, width with (3 andB) angular is equal width to 82.7 (3 dB) deg. of Conversely, 76.3 deg. Figure when7d–f the plot H-plane the 3D radiationis considered patterns (φ = and 90 deg, Figurefar-field 7c), the radiation main lobe patterns magnitude of the optimized is equal antenna to 1.05 atdBi, 5.5 GHz.while In the particular, main lobe in Figure direction7e referring is equal to to 53 E-plane, the maximum gain value is equal to 5.08 dBi, the main lobe magnitude at ϕ = 0 deg is equal deg, with an angular width (3 dB) of 76.3 deg. Figure 7d–f plot the 3D radiation patterns and far-field to 3.91 dBi and the main lobe direction is equal to 61.0 deg with an angular width (3 dB) of 52.5 deg. radiation patterns of the optimized antenna at 5.5 GHz. In particular, in Figure 7e referring to E-plane, In the H-plane (Figure7f), for ϕ = 90 deg, the main lobe magnitude is equal to 4.22 dBi, the main lobe the maximumdirection is gain equal value to 61.0 is deg equal and to the 5. angular08 dBi, widththe main (3 dB) lobe is equal magnitude to 50.4 deg. at φ = 0 deg is equal to 3.91 dBi and theThe main electric lobe field direction and the magnetic is equal field to 61.0 intensities deg with of the an optimized angularSsDRA width at(3 3.5 dB) GHz of and52.5 5.5 deg. GHz In the H-planeare displayed (Figure 7f), in Figure for φ8 .= The 90 higherdeg, the intensity main islobe recorded magnitude at the coaxial is equal cable to pin,4.22 but dBi, larger the part main of lobe directionit is distributed is equal to throughout 61.0 deg and the wholethe angu availablelar width SsDRA (3 dB) volume. is equal As noticeable,to 50.4 deg. at 3.5 GHz, both the electric field (Figure8a) and the magnetic field (Figure8b) intensities are symmetric with respect to the pin while, at 5.5 GHz, the electric field (Figure8c) and the magnetic field (Figure8d) intensities follow the dielectric resonator shape. In particular, in this last case, both intensities are located between the second and third loops of the shell. The analysis of the axial ratio reveals that the antenna shows a linear polarization as for the monopole over the frequency range of interest. Appl. Sci. 2020, 10, 8826 9 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 13

Figure 7. (a) 3D radiation pattern of the optimized SsDRA at 3.5 GHz; (b) E-plane of the optimized SsDRAFigure at 3.57. ( GHz;a) 3D (radiationc) H-plane pattern radiation of the patterns optimized of the SsDRA optimized at 3.5 SsDRAGHz; (b at) E-plane 3.5 GHz; of ( dthe) 3D optimized radiation SsDRA at 3.5 GHz; (c) H-plane radiation patterns of the optimized SsDRA at 3.5 GHz; (d) 3D radiation pattern of the optimized SsDRA at 5.5 GHz; (e) E-plane of the optimized SsDRA at 5.5 GHz; (f) H-plane of pattern of the optimized SsDRA at 5.5 GHz; (e) E-plane of the optimized SsDRA at 5.5 GHz; (f) H- the optimized SsDRA at 5.5 GHz. Appl. Sci. 2020plane, 10 of, xthe FOR optimized PEER REVIEW SsDRA at 5.5 GHz. 10 of 13

The electric field and the magnetic field intensities of the optimized SsDRA at 3.5 GHz and 5.5 GHz are displayed in Figure 8. The higher intensity is recorded at the coaxial cable pin, but larger part of it is distributed throughout the whole available SsDRA volume. As noticeable, at 3.5 GHz, both the electric field (Figure 8a) and the magnetic field (Figure 8b) intensities are symmetric with respect to the pin while, at 5.5 GHz, the electric field (Figure 8c) and the magnetic field (Figure 8d) intensities follow the dielectric resonator shape. In particular, in this last case, both intensities are located between the second and third loops of the shell. The analysis of the axial ratio reveals that the antenna shows a linear polarization as for the monopole over the frequency range of interest.

FigureFigure 8.8. (a(a) )Electric Electric field field and and (b ()b )magnetic magnetic field field intensities intensities at at3.5 3.5 GHz; GHz; (c) (electricc) electric field field and and (d) (magneticd) magnetic field field intensities intensities at 5.5 at GHz 5.5 GHzfor the for optimized the optimized SsDRA. SsDRA. The yellow The yellowlines define lines the define SsDRA the SsDRAcontour. contour.

TheThe radiationradiation eefficiencyﬃciency calculatedcalculated forfor thethe optimizedoptimized SsDRASsDRA isis reportedreported inin FigureFigure9 9:: the the antenna antenna exhibitsexhibits anan eefficiencyﬃciency ofof aboutabout 45%45% aroundaround 3.53.5 GHz,GHz, whilewhile itit increasesincreases upup toto aboutabout 85%85% at at 5.5 5.5 GHz. GHz.

Figure 9. Radiation Efficiency (%) of the optimized SsDRA.

4. Discussion The following Table 2 reports a comparison summarizing the performances obtained by numerical results of different DRAs, such as cylindric (C-DRA), rectangular (R-DRA), star-shaped (S- DRA) and Spiral shell (SsDRA). All antennas were modelled by considering the same low- permittivity material, Resin V04, suitable for stereolithography [36,37]. As noticeable, the optimized SsDRA displays relevant wider bandwidth behavior in the sub-6GHz range compared to other geometries, and it also covers two frequency bands, 3.5 GHz and 5.5 GHz. Additionally, good gain values are calculated at both frequencies, despite the significant reduction of dielectric material volume used for the antenna realization. In this viewpoint, the choice of bio-inspired geometry allows Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13

Figure 8. (a) Electric field and (b) magnetic field intensities at 3.5 GHz; (c) electric field and (d) magnetic field intensities at 5.5 GHz for the optimized SsDRA. The yellow lines define the SsDRA contour.

The radiation efficiency calculated for the optimized SsDRA is reported in Figure 9: the antenna Appl. Sci. 2020, 10, 8826 10 of 13 exhibits an efficiency of about 45% around 3.5 GHz, while it increases up to about 85% at 5.5 GHz.

Figure 9. Radiation Efficiency (%) of the optimized SsDRA. Figure 9. Radiation Efficiency (%) of the optimized SsDRA. 4. Discussion 4. Discussion The following Table2 reports a comparison summarizing the performances obtained by numerical resultsThe of difollowingfferent DRAs, Table such 2 reports as cylindric a comparison (C-DRA), summarizing rectangular (R-DRA),the performances star-shaped obtained (S-DRA) by andnumerical Spiral shell results (SsDRA). of different All antennasDRAs, such were as cylindric modelled (C-DRA), by considering rectangular the (R-DRA), same low-permittivity star-shaped (S- material,DRA) and Resin Spiral V04, shell suitable (SsDRA). for stereolithography All antennas were [36,37 modelled]. As noticeable, by considering the optimized the same SsDRA low- displayspermittivity relevant material, wider Resin bandwidth V04, suitable behavior for in ster theeolithography sub-6GHz range [36,37]. compared As noticeable, to other the geometries, optimized andSsDRA it also displays covers tworelevant frequency wider bands, bandwidth 3.5 GHz behavi andor 5.5 in GHz. the sub-6GHz Additionally, range good compared gain values to other are calculatedgeometries, at bothand it frequencies, also covers despitetwo frequency the significant bands, reduction3.5 GHz and of dielectric5.5 GHz. Additionally, material volume good used gain forvalues the antenna are calculated realization. at both In this frequencies, viewpoint, despite the choice the of significant bio-inspired reduction geometry of allowsdielectric us tomaterial have bandwidthvolume used improvement, for the antenna without realization. affecting In gain, this viewpoint, yet reducing the the choice required of bio-inspired material quantity. geometry allows

Table 2. Comparison of antenna performance and volume of material among the diﬀerent DRAs, conceived by using same low-permittivity material.

Frequency Fractional BW Gain Dielectric Material Antenna (GHz) (%) (dBi) Volume (cm3) C-DRA [37] 3.50 31.42 4.45 20.54 R-DRA [37] 3.50 28.57 4.40 24.12 S-DRA [37] 3.50 32.86 4.30 3.10 3.50 3.7 SsDRA 44.4 14.55 5.50 5

Concerning the realization of a prototype, if the antenna was thinner than 2 mm and taller than 29 mm, the antenna would be structurally weak. Therefore, the set t and hDRA values set the threshold corresponding to an aspect ratio AR = 14.5, enabling the actual realization of the antenna and ensuring its structural robustness. Additionally, referring to Figure2, it can be noticed that, at the end of the spiral, the bigger circle, which approximates the curve, has a radius of about 9 mm, while the smaller circle in the proximity of the origin has a radius equal to 77 µm. This minimum round radius represents the actual fabrication challenges also for 3Dprinting technology. As the technology feature resolution is defined by the diameter of the circular end-effector and being the minimum required radius equal to 77 µm, this turns into a minimum end-effector diameter of De-e_min=2 * R = 154 µm. This consideration allows us to conclude that the SsDRA geometry cannot be feasible for the FDM process, as the majority of FDM machines are typically equipped with nozzle diameters of 200 µm or 400 µm. However, the SLA technology can be successfully exploited for the fabrication of the optimized SsDRA, as the laser spot diameter of the machine allows us to accomplish a micro-feature resolution of 85 µm [37]. Appl. Sci. 2020, 10, 8826 11 of 13

5. Conclusions In this work, the design of a bio-inspired Spiral shell DRA (SsDRA) implemented by means of Gielis’ superformula was proposed. The antenna was thoroughly optimized by properly setting Gielis’ superformula parameters considering two aspects: antenna performance and fabrication feasibility via Additive Manufacturing processes. In particular, the numerical analysis shows that optimized SsDRA exhibits very wide bandwidth behavior, up to 2 GHz, comprising two main frequencies: 3.5 GHz and 5.5 GHz. This characteristic made the proposed SsDRA feasible for applications in the sub-6GHz range. Moreover, the calculated gain is satisfactory, as 3.7 dB can be found at 3.5 GHz, while a gain of 5 dB is calculated at 5.5 GHz. From the fabrication viewpoint, the evaluation of the optimized SsDRA design proved that an accurate AM process is required to realize the micro-features characterizing the spiral rounds of the antenna; in particular, as the minimum size exhibited by the design is in the order of few tens of microns, stereolithography (SLA) is the best candidate to fabricate the SsDRA prototype.

Author Contributions: Conceptualization, L.M. and M.G.; software, L.M., I.M., G.N. and M.G.; investigation, L.M., I.M., G.N.,V.B., V.M., A.D. and M.G.; writing—original draft preparation, L.M., I.M., G.N., V.M., V.B., A.D. and M.G.; writing—review and editing, I.M., G.N., V.M., A.D. and M.G.; supervision and project administration, A.D. and M.G. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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