Profiled Horn Antenna with Wideband Capability Targeting Sub-Thz

electronics

Article Proﬁled Horn Antenna with Wideband Capability Targeting Sub-THz Applications

Jay Gupta 1 , Dhaval Pujara 1,* and Jorge Teniente 2

1 Department of Electronics and Communication Engineering, Institute of Technology, Nirma University, Ahmedabad 382481, India; [email protected] 2 Antenna Group & Institute of Smart Cities (ISC), Electric, Electronic and Communication Engineering Department, Public University of Navarra, Campus de Arrosadia, E-31006 Pamplona, Spain; [email protected] * Correspondence: [email protected]

Abstract: This paper proposes a wideband proﬁled horn antenna designed using the piecewise biarc Hermite polynomial interpolation and validated experimentally at 55 GHz. The proposed design

proves S11 and directivity better than −22 dB and 25.5 dB across the entire band and only needs 3 node points if compared with the well-known spline proﬁled horn antenna. Our design makes use of an increasing radius and hence does not present non-accessible regions from the aperture, allowing its fabrication with electro erosion techniques especially suitable for millimeter and submillimeter wavelengths.

Keywords: electro erosion; Hermite polynomial interpolation; proﬁled smooth circular waveguide

horn; plasma diagnostics; spline proﬁle

Citation: Gupta, J.; Pujara, D.; Teniente, J. Profiled Horn Antenna with Wideband Capability Targeting 1. Introduction Sub-THz Applications. Electronics Horn antennas are widely used for applications such as radio astronomy, satellite, and 2021, 10, 412. https://doi.org/ terrestrial communication, plasma diagnostics, etc. A detailed description of different horn 10.3390/electronics10040412 antenna configurations was provided by Olver and Clarricoats [1]. Many researchers have proposed novel horn designs, including Potter horns [2], corrugated horns [3], matched- Academic Editors: Rashid Mirzavand, feed horns [4], dielectric horns [5–7], metamaterial horns [8], etc., with an aim to improve Mohammad Saeid Ghaffarian and the radiation performance of horn antennas, reducing their size, manufacturing complexity, Mohammad Mahdi Honari optimization time, etc. Among various horn antenna options, the corrugated horn antenna Received: 16 December 2020 is widely used due to several advantages. However, due to a complex mode-converter Accepted: 5 February 2021 structure, the radial corrugated horn design becomes challenging especially at millime- Published: 8 February 2021 ter and submillimeter waves [9] and terahertz frequencies [10]. Some of the alternative solutions are axial corrugated horn [11,12], hybrid corrugated horn [13,14], spline profiled Publisher’s Note: MDPI stays neutral horn [9,15], and horn antennas designed using interpolation [16]. All such configurations with regard to jurisdictional claims in have their merits and drawbacks in terms of performance, fabrication complexity, cost, published maps and institutional affil- computational effort, etc. iations. This paper describes the design, fabrication, and measurement of a profiled smooth circular waveguide horn antenna. This horn antenna has been designed using biarc Hermite polynomial interpolation with only 3 node points. The simulated results for this horn are compared with a spline profiled horn [9] to achieve the same performance. The horn Copyright: © 2021 by the authors. has been designed for D-band with potential application in the reflectometry system for Licensee MDPI, Basel, Switzerland. plasma diagnostics. The reflectometry system has stringent antenna specifications in terms This article is an open access article of high directivity, suppressed sidelobes, and Gaussian-like radiation characteristics. More distributed under the terms and details on antennas for the plasma diagnostics system can be found in [17]. Based on the conditions of the Creative Commons performance comparison of various D-band profiles, two of the horn profiles are scaled- Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ down to the V-band frequencies for testing reasons. Then, the V-band horns are fabricated, 4.0/). and the radiation performance has been verified and compared with simulations.

Electronics 2021, 10, 412. https://doi.org/10.3390/electronics10040412 https://www.mdpi.com/journal/electronics Electronics 2021, 10, 412 2 of 15

This paper is divided into six sections. Section2 discusses the design and geometry of the horn antenna design using biarc Hermite polynomial interpolation method. Moreover, the importance of the proposed profile compared to the spline profile is included. Section3 includes the comparative study of the performance of various biarc Hermite polynomial interpolation profile options. Section4 describes the scaled-down model of the D-band horn antenna and the fabrication of the V-band horn antenna. The comparison of measured results with that of the simulated ones is covered in Section5. In Section6, conclusions are derived.

2. Profiled Smooth Circular Waveguide Horn Design Using Biarc Hermite Polynomial Interpolation Polynomial interpolation is a method of estimating mid-points between the known data points with successive tangents [18]. As a part of curve fitting, many interpolation methods [19], such as spline, trigonometric, Birkhoff, multivariate, Hermite interpolation, etc., can be chosen to connect the selected node points. These techniques may help in smoothening the curvature of a profiled horn antenna design. As compared to the spline profile [9,15], the profile using polynomial interpolation has more degrees of freedom with less intermediate node points and this aspect is very important to reduce computation time. To develop a similar kind of curved/wavy profile as the one we are presenting in the following paragraphs, having a comparable performance with spline interpolation, at least 9 node points (7 intermediate and 2 end node points) are required, which increases the optimization time and resources if spline profile design method is to be used. It is important to remark that, a spline profiled horn antenna optimized using a large number of node points can obtain a very good radiation performance with the cost of optimization time. However, it is very challenging to fabricate it or even impossible using electro erosion techniques, since it may have flare angle changes with non-accessible zones from the aperture, and it usually presents a wavy internal profile. There are other manufacturing techniques as the ones that make use of a lathe which can solve this problem, but as frequency increases and approximates the end of the millimeter-wave frequency band, they are not accurate enough except expensive electroforming fabrication techniques; but we want to avoid these techniques due to cost restrictions. The profile results with non-accessible regions in case of spline interpolation since the radius of the successive node points may have a smaller value than that of the preceding ones. Due to this, it is very difficult and time-consuming optimization for a spline profiled horn antenna, to maintain the radius of the successive node points in increasing order since the curve between nodes is somewhat wavy due to the nature of spline interpolation technique. To overcome these limitations, we propose a new profile formulation in this paper which also presents a lower number of node points, i.e., 3, and then reduces computation time. It is important to remark that for millimeter and submillimeter waves, manufacturing by electro erosion techniques is very suitable for a tiny smooth-walled horn antenna. This is because the roughness of electro erosion surface finish that can be limiting in terms of losses for other feed components; it does not impact too much in horn antenna losses since a proper design in terms of length and slopes maintains the electric fields far from metallic walls except in the throat region with a small reduction in aperture efficiency that usually is not very important for these tiny horns. Only mechanical post-processing in the manufacturing of these tiny horns is usually needed for the input waveguide part, where the strength of the fields in the metallic walls is higher, but this can be solved usually by finishing the horn with a smaller circular waveguide and ream post-processing to the final input circular waveguide size. This manufacturing method is not expensive, and the result can be very nice compared to split-block manufacturing techniques where the alignment between both parts can be critical at upper frequencies of the millimeter wavelengths and submillimeter wavelengths. If we compare electro erosion manufacture with electroforming manufacturing techniques which are very suitable for these frequencies, the cost reduction is high. This is probably one of the main advantages of the profile optimization technique Electronics 2021, 10, x FOR PEER REVIEW 3 of 15

Electronics 2021, 10, 412 between both parts can be critical at upper frequencies of the millimeter wavelengths3 and of 15 submillimeter wavelengths. If we compare electro erosion manufacture with electroforming manufacturing techniques which are very suitable for these frequencies, the cost reduction is high. This is probably one of the main advantages of the profile optimization indicated in this paper as it has been explained in the previous paragraph. The proposed technique indicated in this paper as it has been explained in the previous paragraph. The profile allows direct manufacturing by electro-erosion and a reduction in the optimization proposed profile allows direct manufacturing by electro-erosion and a reduction in the complexity. It is to be noted that to employ the electrical discharge machining (EDM) optimizationtechnique, the complexity. horn antenna It is profileto be noted must that present to employ a decreasing the electrical profile discharge from the aperture.machin- ingHence, (EDM) spline technique, profile the having horn antenna non-accessible profile partsmust present cannot a be decreasing manufactured profile using from thisthe aperture.technology. Hence, spline profile having non-accessible parts cannot be manufactured using this technology.In Reference [16], the authors of this paper have presented the preliminary design of the profiledIn Reference horn antenna[16], the usingauthors Hermite of this polynomial paper have interpolation presented the approach. preliminary The design geometry of the profiled horn antenna using Hermite polynomial interpolation approach. The geome- for the same is shown in Figure1. It has two node points P1 and P2, one at the throat trysection for the and same the other is shown at the in aperture Figure 1. section It has oftwo the node horn, points respectively. P1 and BothP2, one node at the points throat are section and the other at the aperture section of the horn, respectively. →Both node points taken as origin, i.e., (0, 0) for the individual sections of the horn. Here, n1 is the principal are taken as origin, i.e., (0, 0) for the individual sections of the horn. Here, is→ the prin- unit normal vector point made by connecting points P1 and (x1, y1). Similarly, n2 is made cipal unit normal vector point made by connecting→ points P1 and (x1→, y1). Similarly,→ → is by connecting the points P2 and2 (x2, y2).2 t12 is the tangent vector to n1 and t2 is for n2. In made by connecting the points P and (x , y ). is the tangent→ → vector →to and is for Hermite. In Hermite polynomial polynomial interpolation, interpolation, successive successive tangents tangents (ts1, (ts2,, ...,…tsn ) are) are generated generated in → → in order to connect with as shown in Figure 1. order to connect t1 with t2 as shown in Figure1. As may be seen in Figure 1, the input radius is “rin”, the aperture radius is “rap”, and As may be seen in Figure1, the input radius is “ rin”, the aperture radius is “rap”, and “L” “L” is the length of the horn. The region between the vectors→ → and at throat section is the length of the horn. The region between the vectors n1 and t1 at throat section is indi- is indicated by “∆”, and the region between→ → and at aperture section is indicated by “cated▲”. The by “ ∆mathematical”, and the region formulation between nexplained2 and t2 at above aperture is sectionimportant is indicated to reconstruct/opti- by “N”. The mize/improvemathematical formulationthe profile. This explained profile above can be is designed important with to reconstruct/optimize/improvethe Curve Fitting Toolbox that usesthe profile. MATLAB This function profile can “rscvn”, be designed making with a planar the Curve piecewise Fitting biarc Toolbox Hermite that uses interpolation MATLAB curve.function “rscvn”, making a planar piecewise biarc Hermite interpolation curve.

FigureFigure 1. 1. GeometryGeometry of of the the proposed proposed profile profile smooth smooth circ circularular waveguide waveguide horn horn (with (with 2 node 2 node points) points) designed using biarc Hermite polynomial interpolation with principal unit normal vector points designed using biarc Hermite polynomial interpolation with principal unit normal vector points as (x1, y1) = (x2, y2) = (0, 1); rin = 0.8 mm; rap = 8.50 mm; L = 50 mm for a center frequency of 140 GHz as (x , y ) = (x , y ) = (0, 1); r = 0.8 mm; r = 8.50 mm; L = 50 mm for a center frequency of [16]. 1 1 2 2 in ap 140 GHz [16]. The profile of the horn antenna discussed in Figure 1 is used to make a mirror image The profile of the horn antenna discussed in Figure1 is used to make a mirror image profile as shown in Figure 2. The complete profile is developed in two equal parts of profile as shown in Figure2. The complete profile is developed in two equal parts of length lengthL/2 each. L/2 Theeach. necessary The necessary steps tosteps form to theform geometry the geometry are listed are below:listed below: StepStep 1: 1: The The first first half of thethe profileprofile indicatedindicated as as “I” “I” is is the the replica replica of of the the profile profile shown shown in inFigure Figure1. It1. should It should be clearbe clear that that the the profiling profiling is exactly is exactly the same;the same; however, however, the length the length and andradius radius are differentare different as indicated as indicated in Figure in Figure2. 2. StepStep 2: 2: “I” “I” is is mirror-imaged mirror-imaged to to form form “II”. “II”. StepStep 3: 3: “II” “II” is is horizontally horizontally flipped flipped to to form form “III”, “III”, i.e., i.e., the the second second half half of of the the mirror imageimage profile. profile.

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FigureFigure 2. Steps 2. Steps to design to design a mirror a mirror image image profile. profile. proﬁle.

UsingUsing the mirror-imaged the mirror-imaged profile profileprofile shown shown shown in Fi in gurein Figure Figure 2, the2, 2, the proposed the proposed proposed horn horn horn antenna antenna antenna (hav- (having (having 3ing3 node node 3 node points) points) points) is is designed is designed as shown as shown in FigureFigure in Figure3 3.. To To formulate3. formulate To formulate the the profile profilethe profile having having having 3 node3 3 nodenodepoints, points, points, one one can canone use usecan the theuse flip flipthe array arrayflip functions array func tionsfunc (intions MATLAB)(in MATLAB) (in MATLAB) on the on 2the nodeson 2the nodes profile. 2 nodes profile. Once profile. it is OnceOncedone, it is done, it the is done, second the second the part second (flippedpart part(flipped one) (flipped one) is to one)is be to clubbed isbe to clubbed be withclubbed with the firstwith the first one the asonefirst demonstrated asone demon- as demon- in stratedstratedFigure in Figure2 in. Figure 2. 2.

FigureFigure 3. Geometry 3. Geometry of mirror of mirror image imageimage profile proﬁleprofile horn horn hornantenna antennaante (havingnna (having (having 3 node 3 3 node nodepoints) points) points) using using using biarc biarc biarcHer- Hermite Her- mite polynomialmite polynomial interpolation interpolation with withprin principalcipal prin cipalunit normal unit normal vector vector points points as as ( (xx1 1as, ,yy 1(1)x )=1, = (yx (12x), 2 =y, 2(y)x 2=2), (0, =y2 (0,) 1);= 1);(0, r1);in = rin = 0.8r0.8in =mm;mm; 0.8 mm;raprap = =8.50 rap 8.50 = mm;8.50 mm; mm;L L= =50 L 50 mm = mm50 formm for center for center center frequency frequency frequency of of 140 140 of GHz. 140 GHz. GHz. → → 0 0 Here,Here, ′ andn1′ and and′ n are2are′ the are the principal the principal principal unit unit unitnormal normal normal vector vector vector points points points for for the for the second the second second half half ofhalf of the of → → → → 0 ′ 0′ the geometrythegeometry geometry and and are inverted invertedare inverted vectorsvectors vectors of ofn 1 andof andn2 ,and respectively. , respectively. , respectively. Similarly, Similarly, Similarly,t1 and t 2 andare and the → → ′are the′are inverted the inverted tangent tangent vectors vectors of of and and, respectively. , respectively. The symbolsThe symbols “▼” “and▼” “and∇” “∇” inverted tangent vectors of t1 and t2, respectively. The symbols “H” and “∇” indicate the indicateindicate the regions the regions for the for second the second half ofhalf th ofe geometries. the geometries. The radiusThe radius at the at center the center of the of the regions for the second half of the geometries. The radius at the center of the proﬁle is rin/2 profileprofile is rin /2is +rin r/2ap/2. + rap/2. + rap/2.

3. Comparative3. Comparative Comparative Study Study of the of Performance the Performance of Various of Various Profile ProfileProfile Options OptionsOptions In theIn case the casecaseof spline ofof splinespline horn horn horn [9] with [ 9[9]] with with 9 node 9 9 node node points, points, points, the the number the number number of ofoptimization optimizationof optimization varia- variables, variables, bles,i.e.,i.e., the thei.e., radii radiithe ofradii of the the intermediateof intermediatethe intermediate node node points node points arepo areints 7; this 7; are this value 7; valuethis turned value turned out turned to out be to theout be minimum to the be the minimumminimumnumber number of number node of pointsnode of node points to achieve points to achieve similarto achieve similar performance. similar performance. performance. The proposed The proposedThe profile proposed profile has 3profile node has 3haspoints node 3 node andpoints canpoints and be optimizedcanand becan optimized be using optimized only using two using only variables, onlytwo variables,two i.e., variables, (x1, y i.e.,1) and (i.e.,x1 (, xy 2(1x,) y1and,2 y),1) the (andx2 principal, y (2x),2 , y2), the principaltheunit principal normal unit vector unitnormal normal points. vector vector By points. changing points. By changing the By locationchanging the of locationthe these location vectors, of these of theirthese vectors, corresponding vectors, their their corresponding→ vectors→ and vary; this in turn results in a change of their tangent correspondingvectors n1 and nvectors2 vary; this and in turn resultsvary; this in ain change turn results of their in tangent a change vectors of their accordingly. tangent vectorsvectorsSince accordingly. this accordingly. profile Since is controlled Since this profilethis profile by is the controlled vectorsis controlled (notby the byby vectors thethe radiusvectors (not of by(not the the by intermediate radius the radius of the of node the intermediateintermediatepoints), itsnode successive node points), points), nodeits successive its points successive will node not node po haveints po awillints smaller notwill have not radius have a smaller than a smaller the radius preceding radius than than one, the precedingtheas in preceding the caseone, of one,asspline in as the in optimizationcase the caseof spline of spline and optimization this optimization is very and important thisand isthis very at is least veryimportant forimportant electro at least erosionat least for electroformanufacture electro erosion erosion techniques. manufacture manufacture To techniques. clarify, techniques. the main To clarify, To difference clarify, the main ofthe this main difference technique difference of is this that of tech- reallythis tech- the niqueniqueprofile is that is is reallythat not madereally the profile overthe profile multiple is not is made radiinot made butover over overmultiple the multiple inclination radii radii but of overbut the overthe profile inclination the sections inclination of which of the profilethehas profile several sections sections advantages which which has for several manufacturinghas several advantages advantages techniques for manufacturing for drawn manufacturing before. techniques techniques drawn drawn before.before.

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Different locations of the principal unit normal vector points under consideration are Different locations of the principal unit normal vector points under consideration are shown in Table 1. TheDifferent different locations profiles of with the principal2 node points unit normalare shown vector in Figure points 4a under where consideration are shown in Table 1. The different profiles with 2 node points are shown in Figure 4a where x1 and x2 are variedshown from inTable −0.4 to1. The0 with different a step of profiles 0.1 while with y1 2 and node y2 pointsare kept are constant shown inas Figure1. 4a where x1 and x2 are varied from −0.4 to 0 with a step of 0.1 while y1 and y2 are kept constant as 1. The same conceptx1 and is appliedx2 are varied for the from mirror−0.4 im toage 0 withprofiled a step horn of 0.1antenna while iny1 orderand y 2toare carry kept constant as 1. The same concept is applied for the mirror image profiled horn antenna in order to carry out the comparativeThe same study. concept Different is applied profiles for for the the mirror same imageare shown profiled in Figure horn antenna4b. in order to carry out the comparativeout the study. comparative Different study. profiles Different for the profiles same are for shown the same in Figure are shown 4b. in Figure4b. Table 1. Values of unit normal vector points for various profiling options. Table 1. Values of unit normal vector points for various profiling options. Table 1. Values of unit normal vector points for various profiling options. Principal Unit Normal Vector Points Principal Unit Normal Vector Points (x1, y1) Principal(x2, Unit y2) Normal Vector Points (x1, y1) (x2, y2) (0, 1) (x1, y1)(x2, y2) (0, 1) (−0.1, 1) (−0.1, 1) (0, 1) (−0.2, 1) (0,(− 1);0.1, (− 1)0.1, 1); (−0.2, 1); (−0.3, 1); (−0.4, 1) (−0.2, 1) (0, 1); (−0.1, 1); (−0.2, 1); (−0.3, 1); (−0.4, 1) (−0.3, 1) (−0.2, 1) (0, 1); (−0.1, 1); (−0.2, 1); (−0.3, 1); (−0.4, 1) (−0.3, 1) (−0.3, 1) (−0.4, 1) (−0.4, 1) (−0.4, 1)

Accordingly, using this interpolation technique, all the possible geometries of the Accordingly, usingAccordingly, this interpolation using this technique, interpolation all technique,the possible all geometries the possible of geometriesthe of the horn antenna are designed and simulated using the commercially available antenna de- horn antenna arehorn designed antenna and are designedsimulated and using simulated the commercially using the commercially available antenna available de- antenna design sign software—Ansys HFSS and CHAMP by TICRA. Figure 5 shows the influence on the sign software—Ansyssoftware—Ansys HFSS and HFSSCHAMP and by CHAMP TICRA. Figure by TICRA. 5 shows Figure the 5influence shows the on inﬂuencethe on the directivity of the profiled horn antenna (having 3 node points) due to variation in the directivity of thedirectivity profiled ofhorn the antenna proﬁled (having horn antenna 3 node (having points) 3 due node to points)variation due in tothe variation in the values of x1 andvalues x2. of x and x . values of x1 and x2. 1 2

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

Figure 4. Different profiling options for (x1, y1) and (x2, y2) as ({x1}, 1) and ({x2}, 1). (a) Profile possi- Figure 4. DifferentFigure 4. profiling Different options profiling for options (x1, y1) for and (x (1x, y2,1)y and2) as (x ({2x, 1y},2) 1)as and({x1}, ({ 1)x2 and}, 1). ({ (xa2)}, Profile1). (a) Profile possibilities possi- with 2 node bilities with 2 node points; (b) mirror image profile possibilities with 3 node points. points; (b) mirrorbilities imagewith 2 profile node points; possibilities (b) mirror with image 3 node profile points. possibilities with 3 node points.

(a) (b) (a) (b) Figure 5. Cont.

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(e)

1 Figure 5. DirectivityFigure index 5. Directivity (dB) by varying index the(dB) position by varying of principal the position unit normalof principal vector unit points normal (x1, yvector1) and points (x2, y2 )(x as, (a) (0, 1) and ({x2}, y1) and (x2, y2) as (a) (0, 1) and ({x2}, 1); (b) (−0.1, 1) and ({x2}, 1); (c) (−0.2, 1) and ({x2}, 1); (d) (−0.3, 1) 1); (b)(−0.1, 1) and ({x2}, 1); (c)(−0.2, 1) and ({x2}, 1); (d)(−0.3, 1) and ({x2}, 1); (e)(−0.4, 1) and ({x2}, 1). and ({x2}, 1); (e) (−0.4, 1) and ({x2}, 1). By observing the obtained results, it can be seen that the directivity is improved for By observingthe middlethe obtained values results, of x2 and it can has be the seen best that performance the directivity when isx 2improvedis around for−0.2 and −0.1. It the middle valuesis also of x important2 and has the to remarkbest performance that the variation when x along2 is around the band −0.2 canand be−0.1. modulated It with x1 is also importantand to the remark variation that isthe less vari whenationx 1alongequal the to −band0.1. Ascan this be valuemodulated is reduced, with x the1 directivity is and the variationreduced is less for when lower x1 frequenciesequal to −0.1. of As the this band value and increasedis reduced, for the higher directivity frequencies is of the band. reduced for lowerThe comparativefrequencies of results the band in terms and ofincreased directivity for athigher 140 GHz frequencies for horn of antennas the with 2 and band. The comparative3 node points results are in shownterms of in directivity Figure6. Similarly,at 140 GHz the for performance horn antennas of thewith profiles 2 having 2 and 3 node pointsand are 3 node shown points in Figure in terms 6. Simi of thelarly, spillover the performance efficiency of for the different profiles taper having levels is shown in 2 and 3 node pointsFigures in7 terms and8 ,of respectively. the spillover It canefficiency be seen for from different the results taper that levels the is spillover shown performance in Figures 7 andis 8, more respectively. dependent It on can the be variation seen from of the results vectors that at the the aperture spillover side. perfor- It can be improved mance is more whendependent the vectors on the at variation the aperture of the end vectors create at more the aperture opening, side. and It it can is reduced be while the improved whenprofiles the vectors are wavier at the in aperture nature. end create more opening, and it is reduced while the profiles areIn wavier the case in ofnature. profiles having 2 node points, there is a trade-off between directivity In the caseand of profiles spillover having performance. 2 node poin However,ts, there in is the a trade-off case of profiles between having directivity 3 node points, both and spillover performance.the performance However, characteristics in the ca canse of be profiles improved having when 3 node the values points, of bothx2 is around −0.2; the performancethis characteristics means that thiscan be value improved of x2 is when quite the interesting, values of to x2 beginis around with. −0.2; Moreover, this the modal means that this analysisvalue of ofx2 is different quite interesting, profiles has to begin beencarried with. Moreover, out. The normalizedthe modal analysis power in TE and TM of different profilesmodes has at been the aperture carried out. of these The normalized horn antennas power is as in shown TE and in TM Figure modes9. Here, at only power the aperture of distributionthese horn antennas in TE11, TEis as12 ,show and TMn in11 Figureare shown, 9. Here, as only they power are having distribution almost 99% of the total input power. From the simulated modal distribution, it can be seen that the hybrid mode

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Electronics 2021, 10, 412 7 of 15 in TE11, TE12, and TM11 are shown, as they are having almost 99% of the total input power. in TE11, TE12, and TM11 are shown, as they are having almost 99% of the total input power. From the simulated modal distribution, it can be seen that the hybrid mode (HE11) is prop- From the simulated modal distribution, it can be seen that the hybrid mode (HE11) is propagating through a horn antenna for a particular design region (when x2 is around −0.2 and agating through a horn antenna for a particular design region (when x2 is around −0.2 and −−0.1)0.1) which (HEwhich11 )results results is propagating in in better better performance. throughperformance. a horn More More antennaover,over, it for it can can a particularbe be observed observed design how how regionthe the variation variation (when x2 is inin profiling profilingaround is is− affecting 0.2affecting and − the 0.1)the modal modal which distribution resultsdistribution in better in in repetitive repetitive performance. nature. nature. Moreover, In In other other it words, canwords, be observedthe the modalhow distribution the variation for any in profilingparticular is value affecting of x1 thewith modal variation distribution in x2 has ina repetitive repetitive nature nature. In modal distribution for any particular value of x1 with variation in x2 has a repetitive nature for differentother words, values the of modal x1. Based distribution on the result for any analysis, particular Figure value 10 of includesx1 with variation the Region in x of2 has a for different values of x1. Based on the result analysis, Figure 10 includes the Region of x InterestInterestrepetitive (RoI) (RoI) proposed proposed nature for for for different designing designing values the the mirro ofmirro1.r Basedrimage image on profile profile the result horn horn analysis,antenna. antenna. FigureIt It is is defined defined 10 includes the Region of Interest (RoI) proposed for designing the mirror image profile horn antenna. onlyonly for for the the middle middle of of the the profile, profile, as as the the performance performance is is less less influenced influenced by by variation variation in in the the valuesIt isof definedx1. only for the middle of the profile, as the performance is less influenced by values of x1. variation in the values of x1.

Figure 6. Comparison of directivity (at 140 GHz) for horn antennas with 2 and 3 node points. FigureFigure 6. Comparison 6. Comparison of directivity of directivity (at 140 (atGHz) 140 for GHz) horn for antennas horn antennas with 2 withand 3 2 node and 3 points. node points.

FigureFigureFigure 7. 7. Comparison Comparison 7. Comparison of of directivity directivity of directivity (at (at 140 140 (atGHz) GHz) 140 for GHz)for horn horn for antennas hornantennas antennas with with 2 2withand and 3 2 3node and node 3 points. nodepoints. points.

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FigureFigure 8. 8.Comparison Comparison of of spillover spillover efficiency efficiency for for severa several edgel edge tapers tapers (at (at 140 140 GHz) GHz) for for horn horn antennas antennas FigureFigure 8. Comparison 8. Comparison of spillover of spillover efficiency efﬁciency for severa for severall edge tapers edge tapers (at 140 (at GHz) 140 GHz)for horn for antennas horn antennas withwith 3 node3 node points. points. with 3with node 3 nodepoints. points.

FigureFigure 9. Normalized 9. power in TEmn and TMmn modes for different values of x1 andx x2. x FigureFigure 9. 9.Normalized NormalizedNormalized power power power in inTEmn TEmn in TEmn and and TMmn and TMmn TMmn modes modes modes for for different fordifferent different values values values of ofx1 xand of1 and 1x2and .x 2. 2.

FigureFigure 10. RoI 10. atRoI the at middle the middle section section of the of profile the proﬁle for designing for designing the themirror mirror image image profile proﬁle horn horn an- antenna. FigureFigure 10. 10. RoI RoI at atthe the middle middle section section of ofthe the profile profile for for designing designing the the mirror mirror image image profile profile horn horn an- an- tenna. tenna.tenna.

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Further, to obtain the cutoff frequency for TE and TM modes for the circular waveguide,Further, Equations to obtain (1) and the (2) cutoff can be frequency used, respectively. for TE and TM modes for the circular waveg-

uide, Equations (1) and (2) can be used, respectively.1 ′ , , (1) 2√0 1 p mn fc, mn = √ , (1) 2π εµ1 a , , (2) 2√ 1 pmn fc, mn = √ , (2) where, , is the cut off frequency; m is 2theπ numberεµ a of full wave patterns along the circumference; n is the number of half wave patterns along the diameter; is the permittiv- where, f is the cut off frequency; m is the number of full wave patterns along the ity of thec, mnmedium; is the permeability of the medium; a is the radius of the circular circumference; n is the numberth of half wave patterns along the diameter; ε is theth permit- waveguide; is the n zero of Bessel function ; ′ is the n zero of tivity of the medium; µ is the permeability of the medium; a is the radius of the circular , i.e., the first derivative of the Bessel function; 0 is the cut off wave number.0 waveguide; pmn is the nth zero of Bessel function Jm(kca); p mn is the nth zero of J m(kca), The values of zeros of ′ and for TE and TM modes are given in Ta- i.e., the ﬁrst derivative of the Bessel function; kc is the cut off wave number. bles 2 and 3, respectively. 0 The values of zeros of J m(kca) and Jm(kca) for TE and TM modes are given in Tables2 and3, respectively. Table 2. Values of ′ for TE modes of circular waveguide. Table 2. Values of p0 for TE modes of circular waveguide. ′mn n = 1 n = 2 n = 3 0 m = 0 0 3.8317 7.0156 J m(kca)=0 n = 1 n = 2 n = 3 m = 1 1.8412 5.3314 8.5363 m = 0 0 3.8317 7.0156 m = 2 3.0542 6.7061 9.9695 m = 1 1.8412 5.3314 8.5363 m = 2 3.0542 6.7061 9.9695 Table 3. Values of for TM modes of circular waveguide.

Table 3. Values ofpmn for TM modes of circularn = waveguide. 1 n = 2 n = 3 m = 0 2.4048 5.5201 8.6537 J (kca)=0 n = 1 n = 2 n = 3 m m = 1 3.8317 7.0156 10.1735 m = 0m = 2 2.40485.1356 5.52018.4172 8.653711.6198 m = 1 3.8317 7.0156 10.1735 m = 2 5.1356 8.4172 11.6198 Putting different values of the zeros of the Bessel function to the equations, one can find Puttingthe lowest different cutoff valuesfrequency. of the Hence, zeros ofit becomes the Bessel clear function that the to theTE11 equations, mode is the one domi- can ﬁndnant the mode lowest in case cutoff of frequency. the circular Hence, wavegui it becomesde. Other clear higher that theorder TE 11modesmode can is the be dominantcalculated modeusing inEquations case of the (1) circular and (2). waveguide. The series Other of the higher circular order waveguide modes can modes be calculated can be seen using in EquationsFigure 11. (1) and (2). The series of the circular waveguide modes can be seen in Figure 11.

Figure 11. Mode series for the circular waveguide. Figure 11. Mode series for the circular waveguide. It should be clear that the RoI shown in Figure 10 is for the first half of the total profile; It should be clear that the RoI shown in Figure 10 is for the first half of the total profile; the second half will automatically be formed with the mirror image concept, as explained in the second half will automatically be formed with the mirror image concept, as explained Section2. In this paper, the profiles are optimized for the directivity and spillover efficiency in Section 2. In this paper, the profiles are optimized for the directivity and spillover effi- in case of the profiles having 2 and 3 node points. Further, it can be optimized for the ciency in case of the profiles having 2 and 3 node points. Further, it can be optimized for various radiation characteristics such as cross-polarization. Moreover, new profiles can bethe designed various byradiation increasing characteristics the node points such oras bycross-polarization. introducing some Moreover, other techniques new profiles like multiple mirrored geometry.

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can be designed by increasing the node points or by introducing some other techniques Electronics 2021, 10, 412 like multiple mirrored geometry. 10 of 15

4. Scaled-Down Models of D-Band Horn Antennas In the above section, the simulated results for various profiles of the D-band (110– 4. Scaled-Down Models of D-Band Horn Antennas 170 GHz) horn antennas are discussed. To verify the simulated performance with the measurementIn the above results, section, two the scal simulateded-down results horns for at various V-band profiles (one ofhaving the D-band 2 and (110–170another GHzwith) horn3 nodes) antennas have arebeen discussed. manufactured. To verify Figure the 12 simulated shows the performance simulation with design the as measurement well as the results,manufactured two scaled-down horn antennas. horns Scaling at V-band has been (one done having to 2reduce and another the fabrication with 3 nodes)complexity have beenand manufactured.cost of D-band Figure antennas 12 shows and theallow simulation measurement design aswith well our as theavailable manufactured facilities. horn It antennas.should be Scalingnoted that has the been scaling done todoes reduce not change the fabrication any radiation complexity characteristics and cost ofor D-bandmodal antennascontent, and and the allow performance measurement of V-band with our horn availables would facilities. be identical It should to the be D-band noted that horns. the scalingThe high-frequency does not change horn any is radiationsimply converted characteristics to the or lower modal band content, by using and a the multiplication performance offactor. V-band Accordingly, horns would the be geometrical identical to paramete the D-bandrs horns.of the Thescaled-down high-frequency modelhorn (V-band) is simply are convertedcalculated toand the shown lower bandin Table by using4. The a values multiplication for the principal factor. Accordingly, unit normal the vector geometrical points parameters(x1, y1); (x2, ofy2) theare scaled-down(−0.2, 1); (−0.1, model 1) and (V-band) (−0.3, 1); are (− calculated0.2, 1) for the and profiles shown having in Table 24 .and The 3 valuesnode points, for the respectively. principal unit normal vector points (x1, y1); (x2, y2) are (−0.2, 1); (−0.1, 1) and (−0.3, 1); (−0.2, 1) for the profiles having 2 and 3 node points, respectively.

(a)

(b) (c)

FigureFigure 12.12. PhotographsPhotographs of of the the (a ()a )simulated simulated design design of ofV-band V-band ho hornrn having having 3 node 3 node points points (thm (th = 3m = 5.45 mm 3mm, mm , λ c = 5.45 mm);); fabricated fabricated V-band V-band horn horn ante antennasnnas with with 2 2and and 3 3node node points points (b (b) )lateral lateral view view (c ()c ) frontfront view.view.

Table 4. Geometrical parameters of the scaled-down model (scaling factor = 2.545). Table 4. Geometrical parameters of the scaled-down model (scaling factor = 2.545). Geometrical Parameter Values in mm Geometrical Parameter Values in mm rin 2.09 r 2.09 in rap 21.67 r 21.67 ap L 127.26 L 127.26

The performance of the fabricated horn antennas has been measured at the Space

Applications Centre, Indian Space Research Organisation (SAC-ISRO), Ahmedabad. ElectronicsElectronics 20212021,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 1111 ofof 1515

Electronics 2021, 10, 412 11 of 15 TheThe performanceperformance ofof thethe fabricatedfabricated hornhorn antennasantennas hashas beenbeen measuredmeasured atat thethe SpaceSpace ApplicationsApplications Centre,Centre, IndianIndian SpaceSpace ResearchResearch OrganisationOrganisation (SAC-ISRO),(SAC-ISRO), Ahmedabad.Ahmedabad.

5.5. ResultsResults Results andand and DiscussionDiscussion InIn thisthis section, section, simulated simulatedsimulated andand measuredmeasuredmeasured performance performanceperformance for forfor the thethe proposed proposedproposed smooth smoothsmooth circular circu-circu- larlarwaveguide waveguidewaveguide horn hornhorn designed designeddesigned using usingusing the thethe piecewise piecewisepiecewise biarc biarcbiarcHermite HermiteHermite polynomial polynomialpolynomial interpolationinterpolation (having(having 22 andand 33 node node points) points) are are compared compared with with that that of of a aa spline spline horn. horn. The The spline spline profile profileprofile isis designeddesigned usingusing splinespline curvecurve fittingfitting fitting formulaeformulae suchsuch thatthat itit follows follows the the curvature curvature of of the thethe proposedproposed profile. profile.profile. AsAs discusseddiscussed inin thethe previousprevious section,section, thethe splinespline profileprofile profile requires requires 9 9 nodes nodes toto followfollow thethe curvaturecurvature likelike thethe one one proposed. proposed. AllAll thethe profilesprofiles profiles (with (with 2 2 and and 3 3 node nodenode points pointspoints andand splinespline profileprofile profile with with 9 9 node node points) points) designed designed at at V-band V-band are are shown shown in in FigureFigure 1313.13.. The comparativecomparative resultsresults in in terms terms of of S S1111 (dB)(dB)(dB) areare are asas as shownshown shown inin in FigureFigure Figure 14. 14.14 .

FigureFigure 13.13. ComparisonComparison ofof profilesprofiles proﬁles withwith 2 2 andand 3 3 node node points points and and 9 9 nodes nodes spline spline profile proﬁleprofile horn. horn.

FigureFigure 14.14. ComparisonComparison ofof simulated simulated (A (Ansys(Ansysnsys HFSS) HFSS) andand measuredmeasured SS111111 (dB)(dB) for forfor profiled proﬁledprofiled hornhorn antennaan-an- tennatennawith 2 withwith and 2 32 and nodeand 33 pointsnodenode pointspoints and 9 and nodesand 99 nodesnodes spline splinespline proﬁle profileprofile horn. horn.horn.

FromFrom FigureFigure 14, 14,14 , itit it isis is evidentevident evident thatthat that simulasimula simulatedtedted resultsresults results areare are inin in closeclose close agreementagreement agreement andand and meas-meas- mea- ureduredsured resultsresults results presentpresent present aa a worseworse worse performanceperformance performance atat at hihi higherghergher frequencies frequencies butbut still still acceptable. acceptable. This This differencedifference may may be be due due to to fabrication fabrication and/or and/or calibrationcalibration calibration measurementmeasurement measurement errorerror error uncertainties.uncertainties. uncertainties. Similarly,Similarly, thethe the radiationradiation radiation patternspatterns patterns werewere were measmeas measureduredured forfor for thethe thefabricatedfabricated fabricated hornhorn horn antennas.antennas. antennas. TheThe photographphotographThe photograph ofof thethe of radiationradiation the radiation patternpattern pattern measuremmeasurem measuremententent setupsetup issetupis shownshown is shown inin FigureFigure in Figure 15.15. TheThe 15 anten-anten-. The nasnasantennas werewere measuredmeasured were measured inin aa rolloverrollover in a rollover azimuthazimuth azimuth fafar-fieldr-field far-field range.range. TheThe range. measuredmeasured The measured radiationradiation radiation patternspatterns andandpatterns directivitydirectivity and directivity ofof bothboth thethe of antennasantennas both the (profiles(profiles antennas havinghaving (profiles 22 andand having 33 nodenode 2 and points)points) 3 node areare points) comparedcompared are compared with the simulated spline profile horn as shown in Figures 16 and 17, respectively. As discussed, the profile is optimized only for the directivity and spillover performances. Hence, the other radiation characteristics like cross-polarization are not covered in the Electronics 2021, 10, x FOR PEER REVIEW 12 of 15 Electronics 2021, 10, x FOR PEER REVIEW 12 of 15

Electronics 2021, 10with, 412 the simulated spline profile horn as shown in Figures 16 and 17, respectively. As 12 of 15 with the simulated spline profile horn as shown in Figures 16 and 17, respectively. As discussed, the profile is optimized only for the directivity and spillover performances. discussed, the profile is optimized only for the directivity and spillover performances. Hence, the other radiation characteristics like cross-polarization are not covered in the Hence, the other radiation characteristics like cross-polarization are not covered in the results. However, the worst cross-polarization isolation for φ = 45° plane is better◦ than results.results. However,However, thethe worstworst cross-polarizationcross-polarization isolation isolation for forϕ φ= =45 45°plane plane isisbetter betterthan than −20 dB. −−20 dB.

Figure 15. Photograph of the radiation pattern measurement setup of horn antennas at SAC-ISRO Figure 15. Photograph of the radiation pattern measurement setup of horn antennas at SAC-ISRO facility. Figure 15. Photograph of the radiation pattern measurement setup of horn antennas at SAC-ISRO facility. facility.

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

Electronics 2021, 10, x FOR PEER REVIEW 13 of 15 Electronics 2021, 10, x FOR PEER REVIEW 13 of 15

Electronics 2021, 10, 412 13 of 15

(e) (f) (e) (f) Figure 16. Comparison of simulated and measured radiation patterns for profiled horn antenna Figure 16. Comparison of simulated and measured radiation patterns for profiled horn antenna Figure 16. Comparison of simulatedwith and 2 node measured points at radiation (a) 50 GHz; patterns (b) 55 for GHz; profiled (c) 60 horn GHz, antenna profile with 3 2 node points points and at (a spline) 50 GHz; with 2 node points at (a) 50 GHz; (b) 55 GHz; (c) 60 GHz, profile with 3 node points and spline (b) 55 GHz; (c) 60 GHz, profile withprofile 3 node horn points at (d and) 50 splineGHz; ( profilee) 55 GHz; horn (f at) 60 (d )GHz. 50 GHz; (e) 55 GHz; (f) 60 GHz. profile horn at (d) 50 GHz; (e) 55 GHz; (f) 60 GHz.

Figure 17. Comparison of simulated and measuredmeasured directivitydirectivity indexindex (dB).(dB). Figure 17. Comparison of simulated and measured directivity index (dB). As seen from from the the results, results, the the measured measured radi radiationation patterns patterns are arevery very similar similar to the to sim- the As seen from the results, the measured radiation patterns are very similar to the sim- simulatedulated ones ones for both for both profiles profiles having having 2 and 2 3 and nodes. 3 nodes. Moreover, Moreover, the spline the spline profile profile horn (hav- horn ulated ones for both profiles having 2 and 3 nodes. Moreover, the spline profile horn (hav- (havinging 9 node 9 node points) points) has hasa similar a similar performance performance as that as that of ofthe the mirror mirror image image profile profile having having 3 ing 9 node points) has a similar performance as that of the mirror image profile having 3 3nodes nodes since since it ithas has been been designed designed with with simila similarr purposes. purposes. The The measured directivity is inin nodes since it has been designed with similar purposes. The measured directivity is in close agreement with that of of the the simulated simulated results results having having the the maximum maximum uncertainty uncertainty of of ± close agreement with that of the simulated results having the maximum uncertainty of ± ±0.50.5 dB, dB as, as the the measured measured one one ha hass been been derived derived from from the the radiation pattern with onlyonly twotwo 0.5 dB, as the measured one ◦has been◦ derived from the radiation pattern with only two phiphi cutscuts (at(at 00° andand 9090°).). The measuredmeasured directivitydirectivity accuracyaccuracy cancan definitelydefinitely bebe improvedimproved phi cuts (at 0° and 90°). The measured directivity accuracy can definitely be improved (having(having uncertaintyuncertainty aroundaround± ±0.150.15 dB) in case case of of having having the the full full spherical spherical radiation pattern, (having uncertainty around ±0.15 dB) in case of having the full spherical◦ radiation pattern, measured with aa higherhigher numbernumber ofof phiphi cutscuts (<5(<5° stepstep size).size). The 33 dBdB beamwidthbeamwidth cancan bebe measured with a higher number of phi cuts (<5° step size). The 3 dB beamwidth can be estimated fromfrom thethe directivitydirectivity andand radiationradiation patternspatterns asas forfor thethe metallicmetallic hornhorn antenna.antenna. TheThe estimated from the directivity and radiation patterns as for the metallic horn antenna. The measured radiation pattern for angles from 30 to 6060 degreesdegrees hashas somesome noisenoise butbut onlyonly forfor measured radiation pattern for angles from 30 to 60 degrees has some noise but only for H-plane cut in the measured profileprofile withwith threethree nodes.nodes. TheThe reasonreason forfor thethe noisenoise maymay bebe thethe H-plane cut in the measured profile with three nodes. The reason for the noise may be the movement of absorbent material during rotationrotation at thethe endend ofof thethe measurement.measurement. InIn anyany movement of absorbent material during rotation at the end of the measurement. In any case, wewe considerconsider thethe results results accurate accurate enough enough to to validate validate the the proposed proposed design design in thisin this paper. pa- case, we consider the results accurate enough to validate the proposed design in this paper. per. 6. Conclusions

A profiled smooth circular waveguide horn using piecewise biarc Hermite polynomial interpolation has been designed and fabricated. It has more degrees of freedom compared to the spline profile and less intermediate node points (one-third of the spline profile),

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which reduces the optimization time and resources. As the polynomial interpolation profile is controlled by the vectors and not the radius of the intermediate node points, the limitation of the spline profile, i.e., successive node points having a smaller radius than that of the preceding ones, has been eliminated. Hence, the profile can be easily manufactured with electro erosion techniques, which are very suitable for millimeter-wave and even submillimeter-wave frequencies to reduce the manufacturing cost. Moreover, the performance of the proposed design can be optimized only by changing the location of the principal unit normal vector points. The S11 and radiation patterns have been measured and are in close agreement with the simulated results for both the scaled down V-band horn antennas (having 2 and 3 node points). A comparison has been made with a spline profile horn that needs at least 9 node points to achieve similar performance with an increase in computation complexity; this amount of node points adds. As a conclusive remark, Table5 shows the comparison of the proposed horn antenna with the spline profiled horn [9].

Table 5. Resulting comparison of the proposed horn with spline proﬁled horn antenna.

Radiation Type of Horn Number Frequency Manufacturing Manufacturing with S (dB) Pattern Antenna of Nodes (GHz) 11 with a Lathe EDM 1 Optimization Difficult or even not Time Difficult for Spline profiled possible as the profile 7 80–120 GHz <−25 consuming due frequencies higher horn [9] usually derives to have to many nodes than 50 GHz non-accessible zones Spline horn 2 9 50–60 GHz <−22 - - - Difficult for Proposed Non-accessible zones 3 50–60 GHz <−22 Easy and fast frequencies higher horn 3 are avoided than 50 GHz 1 Electrical discharge machining (EDM), also known as spark machining, spark eroding, die sinking, wire burning or wire erosion, is a metal fabrication process whereby a desired shape is obtained by using electrical discharges (sparks). 2 To design the proposed profile using spline interpolation, it requires at least 9 nodes. 3 Having comparable performance to the spline profiled horn (with 9 nodes).

Author Contributions: Conceptualization, J.G.; methodology, J.G., D.P., and J.T.; software, J.G.; validation, J.G.; formal analysis, J.G., D.P., and J.T.; investigation, J.G.; resources, J.G., D.P., and J.T.; data curation, J.G., D.P., and J.T.; writing—original draft preparation, J.G.; writing—review and editing, J.G., D.P., and J.T.; visualization, J.G., D.P., and J.T.; supervision, D.P. and J.T.; project administration, J.G., D.P., and J.T.; funding acquisition, J.G., D.P., and J.T. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Visvesvaraya Ph.D. Scheme for Electronics and IT, Ministry of Electronics and Information Technology, Government of India, grant number MEITY-PHD-1363 and “The APC was funded by Public University of Navarra, Spain”. This research was funded by the Spanish State Research Agency, Project No. PID2019-109984RB-C43/AEI/10.13039/501100011033. Acknowledgments: The authors of this paper are sincerely thankful to Nirma University, Ahmed- abad, India, and to the Public University of Navarra, Pamplona, Spain, for the necessary support. Thanks are also due to the scientists of Space Applications Centre—Indian Space Research Organisa- tion (SAC-ISRO), Ahmedabad, for providing the measurement facility. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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