Enlarged Frequency Bandwidth of Truncated Log-Periodic Dipole Array Antenna

electronics

Article Enlarged Frequency Bandwidth of Truncated Log-Periodic Dipole Array Antenna

Roman Kubacki * , Mirosław Czy˙zewski and Dariusz Laskowski

Faculty of Electronics, Military University of Technology, 00-908 Warsaw, Poland; [email protected] (M.C.); [email protected] (D.L.) * Correspondence: [email protected]

Received: 1 July 2020; Accepted: 11 August 2020; Published: 13 August 2020

Abstract: Many telecommunication applications require antennas capable of operating in a wide (or even ultrawide) frequency band. While LPDA (log-periodic dipole array) antennas are very practical in real-world applications, their usefulness is impeded due to frequency limitations caused by their truncated structures. To increase the upper-frequency range of the LPDA antenna, an additional parameter—the ratio factor—was introduced during the antenna geometry design process. This parameter allows us to improve the properties of an antenna with truncated geometry. In this paper, the proposed technique was used to design, manufacture and present an antenna capable of operating in a frequency range between 760 MHz to 18 GHz. The electrical properties of the proposed antenna were compared with a reference antenna. The designed antenna was experimentally validated, and the simulated results were veriﬁed as well.

Keywords: wideband antenna; LPDA (log-periodic dipole array); microstrip antennas

1. Introduction Nowadays, wireless communication is the fastest growing sector in the telecommunication systems industry. In the context of these systems, antenna design remains a challenging issue, especially in applications that work best with a wideband antenna. For example, broadband antenna properties are a requisite in communication systems, metrology of electromagnetic field (EM) and EM field sensing. In addition, some systems, such as cognitive radio, require an antenna capable of dynamically and autonomously emitting and/or receiving signals in the desired frequency ranges [1]. Furthermore, in MIMO, WLAN and similar applications, communication systems should be equipped with an antenna capable of supporting a wideband or even ultra-wideband (UWB) frequency range, e.g., [2,3]. Frequency independence is required in antennas used for EMC measurements as these involve scanning a wide band of frequencies. Special attention should be paid to broadband antennas used as probes for measuring radiation from cellular base station equipment. What is more, the probe must be able to measure all frequencies at the same efficiency. In this case, the probe’s antenna must be capable of delivering good performance and must demonstrate a constant measuring efficiency for all measured frequencies [4]. The log-periodic dipole array (LPDA) antenna would be the best candidate for the applications described above, as such antennas offer relatively good broadband properties. Log-periodic antennas have the same radiation resistance over their entire frequency range, and LPDA antennas based on microstrip structures are easy to design and implement. The properties of these antennas vary periodically with the logarithm of frequency. The structure of the LPDA antenna is based on linear dipoles placed in an alternating layout, which enables a 180-degree change in phase between adjacent elements. For frequency-independent antennas, this design is amongst one of the most useful.

Electronics 2020, 9, 1300; doi:10.3390/electronics9081300 www.mdpi.com/journal/electronics Electronics 2020, 9, 1300 2 of 11

Electronics 2020, 9, x FOR PEER REVIEW 2 of 11 The geometry and electrical properties of log-periodic antennas were developed in the 1950s and 1960s.The The geometry concepts and for theelectrical most recognized properties LPDA of log antennas-periodic wereantennas introduced were developed by DuHamel in andthe Isbell,1950s whoand 1960s. revealed The the concepts log-periodic for the properties most recognized of the array LPDA [5,6 ].antennas Generally were speaking, introduced the LPDA by DuHamel is a coplanar and Isbell,array ofwho unequally revealed spaced the log linear-periodic dipoles properties with unequal of the array lengths [5,6]. and Generally diameters. speaking, In fact, the in LPDA an LPDA is a coplanararray, the array dipole of lengths unequally are related spaced by linear a constant dipoles scale with factor, unequal as deﬁned lengths below, and diameters. and are laid Inalong fact, in lines an LPDAthat meet array, at thethe virtualdipole apex.lengths Dipoles are related are fed by bya constant a twisted scale (crisscross) factor, as balanced defined line,below, as presentedand are laid in alongFigure lines1. that meet at the virtual apex. Dipoles are fed by a twisted (crisscross) balanced line, as presented in Figure 1.

Figure 1. Schematic view of the log-periodic dipole antenna with a criss-cross feeder line. Dipoles Figure 1. Schematic view of the log-periodic dipole antenna with a criss-cross feeder line. Dipoles lying on the upper side of the substrate are illustrated with a darker shade. lying on the upper side of the substrate are illustrated with a darker shade. The LPDA antennas are very useful in practical applications, but they are not without their The LPDA antennas are very useful in practical applications, but they are not without their disadvantages, which should be noted herein. To obtain good periodic performance, the antenna disadvantages, which should be noted herein. To obtain good periodic performance, the antenna needs to have many dipoles, which increases the size of the structure. For some applications, to reduce needs to have many dipoles, which increases the size of the structure. For some applications, to the overall dimension of the antenna, meandered dipoles were proposed to reduce dipole length [7], reduce the overall dimension of the antenna, meandered dipoles were proposed to reduce dipole but the most popular design decision is to truncate the array. Such an approach allows us to miniaturize length [7], but the most popular design decision is to truncate the array. Such an approach allows us the overall dimensions of the antenna, but such antennas are not frequency-independent due to the to miniaturize the overall dimensions of the antenna, but such antennas are not limitation in their bandwidth. frequency-independent due to the limitation in their bandwidth. In this work, a new approach for LPDA antenna design process is proposed. The novelty of In this work, a new approach for LPDA antenna design process is proposed. The novelty of the the proposed antenna lies in modifying the lengths of the smallest dipoles. This paper compares the proposed antenna lies in modifying the lengths of the smallest dipoles. This paper compares the performance of an LPDA antenna designed according to well-accepted rules against the performance performance of an LPDA antenna designed according to well-accepted rules against the of the newly modiﬁed antenna. performance of the newly modified antenna. 2. General Principles of LPDA Antenna 2. General Principles of LPDA Antenna The LPDA structure is characterized by its periodic property in the logarithm of frequency. The dimensionsThe LPDA structure of the elements is characterized are scaled by itsscaling periodic constant property(τ). In in fact, the all logarithm geometrical of frequency. dimensions The of  dimensionsdipoles are scaledof the byelementsτ from elementare scaled to by element scaling [8 constant,9]. ( ). In fact, all geometrical dimensions of dipoles are scaled by  from element to element [8,9]. ln Rn sn τ = 푙푛 = 푅푛 = 푠푛 (1) 휏 = ln+1 = Rn+1 =s n+1 (1) 푙푛+1 푅푛+1 푠푛+1 In addition, the spacing factor (σ)) shouldshould alsoalso bebe takentaken intointo accountaccount asas aa secondsecond parameter.parameter.

d푑n푛 휎σ == (2(2)) 44l n푙푛 where ln—the half of the length of the nth dipole (total length of the nth dipole is Ln = 2 ln), ln—theRn— halfdistance of the from length the of apex the n toth the dipole nth element, (total length of the nth dipole is Ln = 2 ln), Rn—distancesn—width from of the the n apexth dipole, to the nth element, sn—widthdn—distance of the n betweenth dipole, the nth and (n + 1)th elements. dn—distanceWith the between above relationships, the nth and (n LPDA+ 1)th elements. antennas have periodic properties in the logarithm of frequency in accordance with the scaling constant.

푓푛 휆푛+1 휏 = = (3) 푓푛+1 휆푛

Electronics 2020, 9, 1300 3 of 11

With the above relationships, LPDA antennas have periodic properties in the logarithm of frequency in accordance with the scaling constant. Electronics 2020, 9, x FOR PEER REVIEW 3 of 11 fn λn+ τ = = 1 (3) In the log-periodic dipole array with its fgeometricaln+1 λn properties defined by (1)–(2), the dipole ends are laid along two lines. Each line has a virtual apex in the coordinate origin and is inclined at In the log-periodic dipole array with its geometrical properties defined by (1)–(2), the dipole ends an angle of  [8,10]: are laid along two lines. Each line has a virtual apex in the coordinate origin and is inclined at an angle 1 − 휏 of α [8,10]: −1 훼 = 푡푎푛 ( ) (4) 1 1 4 τ휎 α = tan− − (4) The available literature accurately describes a step4 σ by step procedure for designing an LPDA antenna.The available Generally literature speaking, accurately only the describes two factors a step (1) by and step procedure (2) need to for be designing considered an LPDA when designingantenna. Generally an LPDA speaking, antenna. only the two factors τ (1) and σ (2) need to be considered when designing an LPDA antenna. 3. Reference-Truncated LPDA Antenna 3. Reference-Truncated LPDA Antenna With an infinite structure, one could achieve an ideal frequency-independent antenna. However,With an in infinitepractical structure, applications, one could the infinite achieve structure an ideal frequency-independentis often truncated, therefore antenna. limiting However, the numberin practical of available applications, dipoles. the This infinite means structure that the is structure often truncated, starts with therefore any small limiting dipole the and number stops ofat theavailable largest dipoles. one. Such This a meansstructure that radiates the structure most of starts the energy with any through small dipolea limited and number stops at of the adjacent largest elements.one. Such By a structure its nature, radiates the trun mostcated of the antenna energy has through limited a limited bandwidth. number The of adjacenthighest oper elements.ating frequencyBy its nature, occurs the truncatedwhen the antennashortest hasdipole limited is nearly bandwidth. /2, and The the highestlowest frequency operating is frequency determined occurs by λ λ whenthe /2 the length shortest of the dipole longest is nearly element./2, and the lowest frequency is determined by the /2 length of the longestThe element. investigation of truncation effects was discussed in the literature [9,11,12]. Carrel [9] showTheed that investigation the elements of truncation shorter than effects the was resonating discussed dipoles in the were literature important [9,11,12 for]. Carrelsmall values [9] showed of  τ duethat to the remarkable elements shorterdegradation than theof gain resonating and input dipoles impedance. were important Karoui et foral. smallinvestigated values the of numberdue to ofremarkable dipoles in degradation the function of of gain , showing and input that impedance., depending Karoui on the et al.bandwidth, investigated the the optimum number number of dipoles of dipolesin the function can be ofas τlittle, showing as 16 that,for a dependingrelatively broad on the frequency bandwidth, range the optimumand as much number as 40 of for dipoles broader can bandsbe as little [12]. as 16 for a relatively broad frequency range and as much as 40 for broader bands [12]. A significant significant number of practical calculations for the total number of dipoles were proposed by De Vito etet al.al. [[1313],], where where the the number number of of all all dipoles dipoles depends depends on on the the number number of resonatingof resonating dipoles dipoles in the in theactive active region. region. The The miniaturization miniaturization of the of arraythe array can becan achieved be achieved when when the scaling the scaling constant constant (1) is small,(1) is small,but, on but the, on other the hand,other thehand small, the valuesmall ofvalueτ results of  results in reduced in reduced average average gain [8 gain,10]. [8,10]. In this work, the LPDA microstrip antenna has been designed and developed with with 12 12 dipoles, dipoles, printed onon thethe toptopand and bottom bottom sides sides of of the the substrate. substrate. This This antenna antenna has has been been designed designed according according to the to thescale scale Formulas formula (1)–(2), (1)–(2) with, with a valuea value of ofτ =  0.79= 0.79 and andσ =σ 0.153.= 0.153. Such Such an an antenna, antenna, presented presented in in Figure Figure1, will1, will be be treated treated as as the the reference reference antenna, antenna and, and is is the the first first antenna antenna versionversion developeddeveloped forfor comparison with the modifiedmodified antenna, which has been elaborated upon in the next chapter.chapter. The antenna was based onon thethe dielectricdielectric substrate substrate FR-4. FR-4. Values Values of of its its electrical electrical properties properties depend depend of frequency of frequency and theyand thareey as are follow: as follow: at 1 at GHz 1 GHzε = 4.4,ε = 4.4, tan tanδ = δ0.005; = 0.005; at at 10 10 GHz, GHz,ε =ε =4.3, 4.3, tan tanδ δ= =0.025; 0.025; atat 1818 GHz,GHz, εε == 4.25,4.25, tan δ = 0.02. The substrate is 1.5 mm thick, and the total length of the longest dipole is L = 134 mm. tan δ = 0.02. The substrate is 1.5 mm thick, and the total length of the longest dipole is L1212 = 134 mm. The simulated and measured VSWR of this referencereference LPDALPDA antennaantenna areare presentedpresented inin FigureFigure2 2..

Figure 2. SimulatedSimulated and and measured measured VSWR of the reference LPDA antenna.

Accepting VSWR = 2 as the maximum threshold, the reference LPDA antenna operates in a frequency range of 760 MHz to 6 GHz. The measured value coincides relatively closely with the simulation. For the higher frequency, this value can also be calculated analytically based on the length of the shortest dipole. The wavelength min can be determined as follows:

Electronics 2020, 9, 1300 4 of 11

λmin = 2 L1 (5) and the highest cutoff frequency fmax can be determined from the relationship: c fmax = (6) √εe f λmin where: εef – effective dielectric constant, according to [14,15]. The length of 1st dipole is L1 = 5.012 mm, and using (6), the upper frequency cutoff is approximately fmax = 8.7 GHz. However, for the reference antenna, the upper frequency value (in both simulations and measurements), as illustrated in Figure2, is approx. 6 GHz—a less favorable result. A real reference antenna value of fmax is a bit lower than the theoretical value, as predicted with the relationship (6). The existing divergence between the analytical assessment of the value (using (6)) and simulation/measurement is due to the simplicity of the Equation (6), which was developed for microstrip antennas with simple shapes, without other adjacent dipoles. Smith [16] proposed experimental relationships for assessing fmax, but these equations can only be used when the parameter τ is high enough, i.e., τ > 0.95, which is significantly higher than the value accepted in the work (τ = 0.79).

4. LPDA with Modified Truncation The main goal of this work is to increase the upper frequency range without increasing the footprint of the antenna. To obtain better matching properties of the LPDA antenna with truncated structure in higher frequencies, we propose to shorten the first few dipoles. In this case, the rule of scaling all dipoles with the same scaling constant (τ) will not apply, as the value τ will be different for shorter dipoles. The same can be said for the electrical influence of the first few dipoles on the remaining dipoles in the structure. To analyze this problem, the well-accepted concept of active regions may be useful to interpret energy conveyed along the LPDA [16]. According to the concept of active regions, the LPDA structure is viewed as if it were composed of three separate regions: the transmission-line region, the active region, and the reflection region [16]. In the transmission region, the dipole lengths are shorter than resonating lengths, and the impedance of this part of the antenna can be treated as capacitive. In the active region, the dipole lengths are comparable to λ/2, and these dipoles are responsible for radiating energy. Because of the resistive component of impedance in the resonance, a significant part of conveyed energy is decayed. In the third region, dipole lengths are greater than λ/2 and, in addition, they are supplied by a small amount of energy. Taking into account this concept of conveying energy along the antenna, in the first step of the analysis there is a need to interpret the change of impedance when the few shorter dipoles are completely removed (creating a truncated structure), as presented in Figure1. Therein, one can observe a so-called gap region (without dipoles) between the first existing dipole and coordinate origin. In fact, non-complete structures, such as the one presented in Figure1, are often used in LPDA antenna design, as they allow to reduce its overall dimensions. However, in a truncated structure, a range of higher frequencies does not appear in the transmission-line region and the input impedance has a resistive value, resulting in deterioration of the matching. The question remains regarding how many dipoles can be shortened and which shortening function can guarantee the best matching condition. Nevertheless, the issue of the shortening function is still relevant for matching. Electronics 2020, 9, 1300 5 of 11

First of all, there is a need to decide how many dipoles must be shortened. In the work, three dipoles were additionally shortened, making up 25% of the total number of antenna elements. This guarantees that the remaining number of elements (remaining dipoles) protect the scaling factor of τ = 0.79. The ﬁrst, intuitive approach, is to shorten the dipoles using a linear shortening function, as it isElectronics presented 2020 in,, 9,, Figurexx FORFOR PEERPEER3. In REVIEWREVIEW fact, such a simple attempt is not optimal from the matching point of view.5 of 11

n4 n3 n2 n1

 

FigureFigure 3.3. SchematicSchematic viewview ofof thethe PLDAPLDA antennaantenna withwith thethe firstfirst threethree dipolesdipoles linearlylinearly shortenedshortened (not(not optimal);optimal); n1,n1, n2,2, n3, n3, n4 n4 are are element element numbers numbers.. For the optimized shortening technique, the shortening function is an important task. In the For the optimized shortening technique, the shortening function is an important task. In the simplest case, presented in Figure3, the ends of the three first elements lie along the line inclined at simplest case, presented in Figure 3, the ends of the three first elements lie along the line inclined at angle β. This bigger angle β results in a lower value of τ (=τ2). For such linear shortening, the values angle This bigger angle  results in a lower value of  ( =  For such linear shortening, the values of τ for the first seven dipoles are presented in Figure4. One can notice that values for elements 4–12 of  for the first seven dipoles are presented in Figure 4. One can notice that values for elements 4–12 are equal to τ = 0.79, while for elements of a lower number, τ has a lower value. are equal to = 0.79, while for elements of a lower number,  has a lower value.

Figure 4. Values of scaling constants for the first seven dipoles of an antenna with simple linear Figure 4. Values of scaling constants for the first seven dipoles of an antenna with simple linear shortened elements; x—distance from the apex. shortened elements; x—distance from the apex. Taking into account that the matching condition with linear shortening depends also on the value of angleTakingβ the into electrical account properties that the of matching the whole condition antenna can with be evenlinear worse. shortening This is depends because the also presence on the ofvalue two of angles angle ( αand the electricalβ) in one properties structure is of against the whole the log-periodicantenna can rule.be even Nevertheless, worse. This it is is because possible the to findpresence a shortening of two angles function (α whichand β)can in one beconsidered structure is optimal against forthe the log purposes-periodic ofrule. matching. Nevertheless, it is possibleThe optimal to find shorteninga shortening function function can which be found, can but be notconsidered by analyzing optimal the for lengths the purposes of elements of (accordingmatching. to (1)), as is presented in the literature. Rather, it is necessary to take into consideration differencesThe optimal between shortening shortened function dipole lengths. can be Thefoun proposedd, but notratio by factor analyzing(τ∆) can the be lengths defined of as elements follows: (according to (1)), as is presented in the literature. Rather, it is necessary to take into consideration differences between shortened dipole lengths. The∆l nproposed ratio factor () can be defined as τ∆ = (7) follows: ∆ln+1

∆푙푛 where 휏∆ = (7) ∆푙 ∆ln = ln 푛ln+11 (8) − − where ∆l + = l + ln n 1 n 1 − ∆푙 = 푙 − 푙 (8) For the structure with an inﬁnite number∆푙푛 of = dipoles, 푙푛 − 푙 the푛−1 ratio factor is equal to the scaling constant.(8)

∆푙푛+1 = 푙푛+1 − 푙푛 τ∆ = τ (9) For the structure with an infinite number of dipoles, the ratio factor is equal to the scaling constant. 1 constant.Equation (9) can be easy proved by substituting ln 1 = τ ln and ln+1 = ln into (8) and (7). Because − τ of relationship (9) the log periodic properties of휏∆ the = structure 휏 can be protected using also parameter(9) τ∆. The advantage of proposed ratio factor can be seen when the structure has been truncated. Value 1 Equation (9) can be easy proved by substituting 푙푛−1 = 휏 푙푛 and 푙푛+1 = 푙푛 into (8) and (7). 푛−1 푛 푛+1 휏 푛 Because of relationship (9) the log periodic properties of the structure can be protected using also parameter . The advantage of proposed ratio factor can be seen when the structure has been truncated. Value of proposed parameter () is determined basing on three neighboring dipoles - (n − 1)thth , nthth and (n + 1)thth, while in conventional LPDA structure the scaling constant (τ) takes into account only two elements ie. nthth and (n + 1)thth according to (1). With (7) it is possible to optimize lengths of the shortest dipoles.

Electronics 2020, 9, 1300 6 of 11 of proposed parameter (τ∆) is determined basing on three neighboring dipoles—(n 1)th, nth and − (n + 1)th, while in conventional LPDA structure the scaling constant (τ) takes into account only two elements i.e., nth and (n + 1)th according to (1). With (7) it is possible to optimize lengths of the shortest dipoles. ElectronicsWe experimentally 2020, 9, x FOR PEER found REVIEW that a better matching condition can be obtained when the ratio6 of factor11 for the three shortened elements is linear. With this requirement in mind, the dipole lengths for the We experimentally found that a better matching condition can be obtained when the ratio factor design with modiﬁed truncation were calculated using Equation (7) and are presented in Table1. for the three shortened elements is linear. With this requirement in mind, the dipole lengths for the This table also includes dipole lengths for the reference truncated antenna, as discussed in Section3. design with modified truncation were calculated using Equation (7) and are presented in Table 1. This table also includes dipole lengths for the reference truncated antenna, as discussed in Section 3. Table 1. Dipole lengths.

Dipole Number Reference Truncated AntennaTable 1. (mm) Dipole Antenna lengths. with Modiﬁed Truncation Using (7) (mm)

DipoleL Number1 Reference Truncated5.012 Antenna (mm) Antenna with Modified 3.311 Truncation Using (7) (mm) LL21 6.3445.012 5.5533.311 LL32 6.3448.03 7.7955.553 L 10.165 10.165 L43 8.03 7.795 L5 12.867 12.867 L4 10.165 10.165 L6 16.287 16.287 L5 12.867 12.867 L7 20.617 20.617 L6 16.287 16.287 L8 26.097 26.097 L7 20.617 20.617 L9 33.034 33.034 LL108 41.81526.097 41.81526.097 LL119 33.03452.93 33.034 52.93 LL1210 41.81567 41.815 67 L11 52.93 52.93 L12 67 67 In Figure5, values of τ∆ were depicted for both antennas: for proposed shortening (antenna with modiﬁedIn truncation), Figure 5, values in Figure of 5a,were and depicted for the reference for both antennas truncated: for antenna, proposed in Figureshortening5b. (antenna with modified truncation), in Figure 5a, and for the reference truncated antenna, in Figure 5b.

Figure 5. Values of ratio factor: (a) for proposed shortening, (b) for comparison, for the reference Figure 5. Values of ratio factor: (a) for proposed shortening, (b) for comparison, for the reference truncated antenna, presented in Figure3. truncated antenna, presented in Figure 3. The function of the ratio factor for the proposed design is presented in Figure5a. For comparison, The function of the ratio factor for the proposed design is presented in Figure 5a. For in Figurecomparison5b, values, in Figure of τ∆ 5b,have values also of been  have presented also been for thepresented structure for shownthe structure in Figure shown3, i.e., in Figure with linear 3, dipolei.e., shortening. with linear dipole The introduced shortening. parameter The introducedτ∆ (8) parameter allows us  to (8) demonstrate allows us to how demonstrate gentle the how dipole shorteningsgentle the are. dipole In the shortenings case of linear are. In shortening the case of (as linear presented shortening in Figure (as presented3), due toin theFigure ratio 3),factor, due to the significantthe ratio jump factor, in the the significant function ofjumpτ∆ (Figurein the function5b) can of be  identified. (Figure 5b) can be identified. ConsideringConsidering that that the the introduced introducedratio ratio factor factor in ( (7)7) is is a a very very useful useful parameter, parameter, the the proposed proposed techniquetechnique of shortening of shortening the the first first few few elements elements maymay bebe used to to optimize optimize dipole dipole lengths lengths based based on this on this ratioratio factor. factor The. lengthsThe lengths of elements of elements have have been been calculated calculated based based on Equation on Equation (7),with (7), with a linear a linear function of τ∆function. The iterativeof . The technique iterative should technique be adopted should for be calculation, adopted for as calculation, lengths of as lower-numbered lengths of elementslower depend-numbered on adjacentelements elements.depend on Thisadjacent technique elements. was This introduced technique to was improve introduced the matching to improve of the the matching of the antenna. In the proposed model, the lengths of the first dipoles (the three first antenna. In the proposed model, the lengths of the first dipoles (the three first elements, in this work) elements, in this work) were shortened in compliance with the rule of proposed function of , as were shortened in compliance with the rule of proposed function of τ∆, as presented in Figure6. presented in Figure 6.

Electronics 2020, 9, x FOR PEER REVIEW 6 of 11

We experimentally found that a better matching condition can be obtained when the ratio factor for the three shortened elements is linear. With this requirement in mind, the dipole lengths for the design with modified truncation were calculated using Equation (7) and are presented in Table 1. This table also includes dipole lengths for the reference truncated antenna, as discussed in Section 3.

Table 1. Dipole lengths.

Dipole Number Reference Truncated Antenna (mm) Antenna with Modified Truncation Using (7) (mm)

L1 5.012 3.311 L2 6.344 5.553 L3 8.03 7.795 L4 10.165 10.165 L5 12.867 12.867 L6 16.287 16.287 L7 20.617 20.617 L8 26.097 26.097 L9 33.034 33.034 L10 41.815 41.815 L11 52.93 52.93 L12 67 67

In Figure 5, values of were depicted for both antennas: for proposed shortening (antenna with modified truncation), in Figure 5a, and for the reference truncated antenna, in Figure 5b.

Figure 5. Values of ratio factor: (a) for proposed shortening, (b) for comparison, for the reference truncated antenna, presented in Figure 3.

The function of the ratio factor for the proposed design is presented in Figure 5a. For comparison, in Figure 5b, values of  have also been presented for the structure shown in Figure 3, i.e., with linear dipole shortening. The introduced parameter  (8) allows us to demonstrate how gentle the dipole shortenings are. In the case of linear shortening (as presented in Figure 3), due to the ratio factor, the significant jump in the function of  (Figure 5b) can be identified. Considering that the introduced ratio factor in (7) is a very useful parameter, the proposed technique of shortening the first few elements may be used to optimize dipole lengths based on this ratio factor. The lengths of elements have been calculated based on Equation (7), with a linear function of . The iterative technique should be adopted for calculation, as lengths of lower-numbered elements depend on adjacent elements. This technique was introduced to improve the matching of the antenna. In the proposed model, the lengths of the first dipoles (the three first elements,Electronics 2020 in ,this9, 1300 work) were shortened in compliance with the rule of proposed function of 7 of, as 11 presented in Figure 6.

Electronics 2020, 9, x FOR PEER REVIEW 7 of 11 ElectronicsElectronics 20202020,, 99,, xx FORFOR PEERPEER REVIEWREVIEW 77 ofof 1111 Figure 6. Lengths of shortened dipoles in the modified modified antenna structure. The red dotte dottedd line shows FigureFigure 6.6. LengthsLengths ofof shortenedshortened dipolesdipoles inin thethe modifiedmodified antennaantenna structure.structure. TheThe redred dottedottedd lineline showsshows the line from Figure1 1 with with thethe angleangle ofof α.. thethe lineline fromfrom FigureFigure 11 withwith thethe angleangle ofof .. In Figure 66,, thethe lengthslengths ofof thethe firstfirst fivefive dipoles dipoles have have been been presented. presented. DistanceDistance x identifiesidentifies the In Figure 6, the lengths of the first five dipoles have been presented. Distance x identifies the dipoleIn positions Figure 6, along the lengths the antenna. of the For Forfirst this this five case, case, dipoles the the values valueshave been of of parameter parameter presented τ . wereDistancewere shown shown x identifies in in Figure Figure 7the .7. dipoledipole positionspositions alongalong thethe antenna.antenna. ForFor thisthis case,case, thethe valuesvalues ofof parameterparameter  werewere shownshown inin FigureFigure 77..

Figure 7. 7. ValuesValues of scaling of scaling constant constant for the for proposed the proposed antenna antennastructure structurewith optimized with optimizedshortened FigureFigure 7.7. ValuesValues ofof scalingscaling constantconstant forfor thethe proposedproposed antennaantenna structurestructure withwith optimizedoptimized shortenedshortened elements.shortened elements. elements.elements. Comparing values ofof τ forfor anan antennaantenna withwith linearly linearly shortened shortened elements elements (simplest (simplest case) case) (Figure (Figure4) ComparingComparing valuesvalues ofof  forfor anan antennaantenna withwith linearlylinearly shortenedshortened elementselements (simplest(simplest case)case) (Figure(Figure 4)and and an an antenna antenna in which in which dipole dipole geometry geometry is based is based on the on ratio the factorratio (Figurefactor (Fi7),gure one can7), one notice can that notice the 4)4) andand anan antennaantenna inin whichwhich dipoledipole geometrygeometry isis basedbased onon thethe ratioratio factorfactor (Fi(Figuregure 7)7),, oneone cancan noticenotice proposedthat the proposed method resultsmethod in results a smoother in a smoother curve of dipolecurve of lengths. dipole Anlengths. LPDA An antenna LPDA hasantenna been designedhas been ththatat thethe proposedproposed methodmethod resultsresults inin aa smoothersmoother curvecurve ofof dipoledipole lengths.lengths. AnAn LPDALPDA antennaantenna hashas beenbeen designedand developed and developed using the proposedusing the technique,proposed technique and a view, and of the a view manufactured of the manufactu antennared is depictedantenna inis designeddesigned andand developeddeveloped usingusing thethe proposedproposed techniquetechnique,, andand aa viewview ofof thethe manufactumanufacturedred antennaantenna isis depictedFigure8. Thein Figure value 8. of The VSWR value is presentedof VSWR is in presented Figure9. in Figure 9. depicteddepicted inin FigureFigure 8.8. TheThe valuevalue ofof VSWRVSWR isis presentedpresented inin FigureFigure 9.9.

Figure 8. IllustrationIllustration of of the the manufactured, manufactured, proposed LPDA antenna. FigureFigure 8.8. IllustrationIllustration ofof thethe manufactured,manufactured, proposedproposed LPDALPDA antenna.antenna.

Figure 9. SimulatedSimulated and and measured measured VSWR VSWR of of the proposed LPDA antenna with first ﬁrst three dipoles Figure 9. Simulated and measured VSWR of the proposed LPDA antenna with first three dipoles shortenedFigure 9. Simulatedusing the proposedand measured method. VSWR of the proposed LPDA antenna with first three dipoles shortenedshortened usingusing thethe proposedproposed method.method. The LPDA antenna with the first three shortened dipoles shows good matching properties, The LPDA antenna with the first three shortened dipoles shows good matching properties, from The760 MHz LPDA up antenna to a frequency with the of first18 GHz. three The shortened simulated dipoles results shows match goodwith the matching measured properties data. , from 760 MHz up to a frequency of 18 GHz. The simulated results match with the measured data. fromThe 760 MHz enlarged up to range a frequency for higher of 18 GHz. frequencies The simulated presented results in Figurematch with9, despite the measured the truncated data. The enlarged range for higher frequencies presented in Figure 9, despite the truncated structureThe , eisnlarged due to the range optimal for dipole higher shortening frequencies of thepresented shortest indipoles. Figure Such 9, despitean optimal the shorteningtruncated structure, is due to the optimal dipole shortening of the shortest dipoles. Such an optimal shortening functionstructure , was is due obtained to the optimal using the dipole ratio shortening factor. It shouldof the shortest be also dipoles. emphasized Such anthat o ptimal the conventional shortening function was obtained using the ratio factor. It should be also emphasized that the conventional scalingfunction constant was obtained allows using us to the calculate ratio factor the . length It should of be any also dipole emphasized based on that the the length conventional of one scaling constant allows us to calculate the length of any dipole based on the length of one neighboringscaling constant dipole allows, according us to to calculate Equation the (1) length. The p ofroposed any dipole ratio factor based takes on the into length account of two one neighboring dipole, according to Equation (1). The proposed ratio factor takes into account two neighboring dipoles dipole,— accordingone longer to and Equation one shorter (1). The than p theroposed analyzed ratio dipole. factor takes into account two neighboringneighboring dipolesdipoles——oneone longerlonger andand oneone shortershorter thanthan thethe analyzedanalyzed dipole.dipole.

Electronics 2020, 9, 1300 8 of 11

The LPDA antenna with the first three shortened dipoles shows good matching properties, from 760 MHz up to a frequency of 18 GHz. The simulated results match with the measured data. The enlarged range for higher frequencies presented in Figure9, despite the truncated structure, is due to the optimal dipole shortening of the shortest dipoles. Such an optimal shortening function was obtained using the ratio factor. It should be also emphasized that the conventional scaling constant allows us to calculate the length of any dipole based on the length of one neighboring dipole, according to Equation (1). The proposed ratio factor takes into account two neighboring dipoles—one longer and oneElectronics shorter 2020 than, 9, x FOR the analyzedPEER REVIEW dipole. 8 of 11 It also worth noting that such a good value of VSWR was obtained with a FR-4 substrate, It also worth noting that such a good value of VSWR was obtained with a FR-4 substrate, even even though this substrate is typically not recommended for higher frequencies. We decided to though this substrate is typically not recommended for higher frequencies. We decided to investigate this material anyway, considering that many laboratories use this dielectric substrate. investigate this material anyway, considering that many laboratories use this dielectric substrate. Figures 10 and 11 report the frequency relationship of the directivity and gain. Gain was measured Figures 10 and 11 report the frequency relationship of the directivity and gain. Gain was according to the ANSI/IEEE standard. The simulated directivity and measured gain of the proposed measured according to the ANSI/IEEE standard. The simulated directivity and measured gain of the antenna with modified first three dipoles are presented in Figure 10. A comparison of the measured proposed antenna with modified first three dipoles are presented in Figure 10. A comparison of the gain of the proposed modified antenna and reference antenna is shown in Figure 11. measured gain of the proposed modified antenna and reference antenna is shown in Figure 11.

Figure 10. Simulated directivity and measured gain of the proposed antenna. Figure 10. Simulated directivity and measured gain of the proposed antenna. In this work, directivity and gain are presented in Figures 10 and 11, with reference to direction θ = 90In◦. thisThis work, allows directivity us to reveal and the gain directivity are presented or non-directivity in Figures of10 theand antenna 11, with at reference different frequencies.to direction Figureθ = 90°. 10 Thisshows allows that, us in frequenciesto reveal the higher directivity than 13 or GHz, non-directivity both directivity of the and antenna gain areat reduced.different Thisfrequencies. means thatFigure such 10 ashows structure that is, in more frequencies akin to anhigher omni-directional than 13 GHz, antenna.both directivity On the and other gain hand, are whenreduced. directivity This means has athat negative such a value structure (above is more 16.5 GHz akin forto an discussed omni-directional antennas), antenna. the antenna On the radiates other significantlyhand, when indirectivity different has directions a negative to θ value= 90◦ .(above In fact, 16.5 a similar GHz tendencyfor discussed for LPDA antennas antennas), the antenna at high frequenciesradiates significantly was reported in different in [17,18 directions]. to θ = 90°. In fact, a similar tendency for LPDA antennas at highA comparison frequencies of was measured reported gains in [1 of7, the18]. reference and proposed antennas is presented in Figure 11. FigureA comparison 11 shows of thatmeasured the gains gains of of reference the reference and proposed and proposed antennas antennas have is a similarpresented tendency in Figure at frequencies11. below 6 GHz. In this frequency range, VSWR values of both antennas are lower than 2 (see also Figure2). At higher frequencies, the proposed antenna exhibits better gain. Obtained values show that modification of shorter dipole lengths in truncated LPDA antennas yields better antenna properties.

Figure 11. Comparison of the measured gains of the reference and proposed antennas.

Figure 11 shows that the gains of reference and proposed antennas have a similar tendency at frequencies below 6 GHz. In this frequency range, VSWR values of both antennas are lower than 2 (see also Figure 2). At higher frequencies, the proposed antenna exhibits better gain. Obtained values show that modification of shorter dipole lengths in truncated LPDA antennas yields better antenna properties. The normalized radiation patterns of both antennas (reference and proposed) in the “xy” plane are depicted in Figure 12. Presented diagrams refer to three representative frequencies: 5 GHz

Electronics 2020, 9, x FOR PEER REVIEW 8 of 11

It also worth noting that such a good value of VSWR was obtained with a FR-4 substrate, even though this substrate is typically not recommended for higher frequencies. We decided to investigate this material anyway, considering that many laboratories use this dielectric substrate. Figures 10 and 11 report the frequency relationship of the directivity and gain. Gain was measured according to the ANSI/IEEE standard. The simulated directivity and measured gain of the proposed antenna with modified first three dipoles are presented in Figure 10. A comparison of the measured gain of the proposed modified antenna and reference antenna is shown in Figure 11.

Figure 10. Simulated directivity and measured gain of the proposed antenna.

In this work, directivity and gain are presented in Figures 10 and 11, with reference to direction θ = 90°. This allows us to reveal the directivity or non-directivity of the antenna at different frequencies. Figure 10 shows that, in frequencies higher than 13 GHz, both directivity and gain are reduced. This means that such a structure is more akin to an omni-directional antenna. On the other hand, when directivity has a negative value (above 16.5 GHz for discussed antennas), the antenna radiates significantly in different directions to θ = 90°. In fact, a similar tendency for LPDA antennas at high frequencies was reported in [17,18]. ElectronicsA comparison2020, 9, 1300 of measured gains of the reference and proposed antennas is presented in Figure9 of 11 11.

Figure 11. Comparison of the measured gains of the reference and proposed antennas. Figure 11. Comparison of the measured gains of the reference and proposed antennas. The normalized radiation patterns of both antennas (reference and proposed) in the “xy” plane are depictedElectronicsFigure 20 in20 Figure11, 9, showsx FOR 12 PEER. Presentedthat REVIEW the gains diagrams of reference refer to and three proposed representative antennas frequencies: have a similar 5 GHz tendency (frequency9 of at11 offrequencies good matching below for6 GHz. both In antennas), this frequency 7 GHz range (with, VSWR values higher of than both 2 forantennas the reference are lower antenna), than 2 and(see(frequency 16also GHz Figure of (range good 2). At ofmatching higher frequencies).frequencies for both antennas), the proposed, 7 GHz antenna (with VSWR exhibits higher better than gain 2. forObtained the reference values showantenna) that, andmodification 16 GHz (range of shorter of higher dipole frequencies). lengths in truncated LPDA antennas yields better antenna properties. The normalized radiation patterns of both antennas (reference and proposed) in the “xy” plane are depicted in Figure 12. Presented diagrams refer to three representative frequencies: 5 GHz

Figure 12. Normalized radiation patterns of reference and proposed antennas in the “xy” plane; at Figure 12. Normalized radiation patterns of reference and proposed antennas in the “xy” plane; at 5 5 GHz: (a) reference, (b) proposed antenna; at 7 GHz: (c) reference, (d) proposed antenna, and at 16 GHz: GHz: (a) reference, (b) proposed antenna; at 7 GHz: (c) reference, (d) proposed antenna, and at 16 (e) reference, (f) proposed antenna. GHz: (e) reference, (f) proposed antenna.

Diagrams in Figure 12a,b show that, at a frequency of 5 GHz, radiation patterns of the reference and proposed antennas are quite similar. However, at 7 GHz and 16 GHz, the proposed antenna with modified dipole lengths has better directional properties. Table 2 summarizes a comparision of the key features of the proposed antenna with other related work. It can be noticed that the proposed solution provides a novel LPDA antenna design, allowing us to obtain a broad frequency band with shorter overall antenna length.

Table 2. Comparison with other related work.

Truncated (Tr)/ Number of Overall Antenna Length Ref. VSWR * Not Truncated Bandwidth Elements (mm) (N-Tr) 380 MHz-35 [17] <2.5 N-Tr 44 590 GHz [12] <2 Tr 400 MHz-3 GHz 13 577 [18] <2 Tr 1.1–13.8 GHz 9 not mentioned [19] <2 Tr 3–6 GHz 9 117 This 760 MHz-18 <2 Tr 12 168 work GHz * VSWR: voltage standing wave ratio.

Electronics 2020, 9, 1300 10 of 11

Diagrams in Figure 12a,b show that, at a frequency of 5 GHz, radiation patterns of the reference and proposed antennas are quite similar. However, at 7 GHz and 16 GHz, the proposed antenna with modiﬁed dipole lengths has better directional properties. Table2 summarizes a comparision of the key features of the proposed antenna with other related work. It can be noticed that the proposed solution provides a novel LPDA antenna design, allowing us to obtain a broad frequency band with shorter overall antenna length.

Table 2. Comparison with other related work.

Truncated (Tr)/ Number of Overall Antenna Ref. VSWR * Not Truncated Bandwidth Elements Length (mm) (N-Tr) [17] <2.5 N-Tr 380 MHz–35 GHz 44 590 [12] <2 Tr 400 MHz–3 GHz 13 577 [18] <2 Tr 1.1–13.8 GHz 9 not mentioned [19] <2 Tr 3–6 GHz 9 117 This work <2 Tr 760 MHz–18 GHz 12 168 * VSWR: voltage standing wave ratio.

5. Conclusions The aim of this work was to design an LPDA antenna which would be more eﬀective at higher frequencies. The proposed antenna is composed of 12 dipoles based on a FR-4 substrate, with a thickness of 1.5 mm. A new design methodology was presented in the work, based on analyzing the newly introduced parameter, which is the ratio factor. This is a very useful parameter, as it allows us to optimize antenna performance and ensures good return loss. Using the proposed technique, the designed and manufactured antenna operates at a frequency range of 760 MHz to 18 GHz. It was possible to obtain such good performance by shortening the ﬁrst three dipoles with the optimization technique described in the work. The proposed antenna, despite its truncated structure, can be treated as a frequency-independent antenna in the upper-frequency range.

Author Contributions: Conceptualization, R.K., M.C., D.L.; methodology, R.K., D.L.; Software, M.C., D.L.; validation, M.C., D.L.; Formal analysis, R.K., M.C.; Writing—original draft preparation, R.K., M.C.; writing—review and editing, M.C., D.L. 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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