# A Wideband Tightly Coupled Array for Omnidirectional Pattern Synthesis

Authors: Manuel Luciarini; Domenico Gaetano; Christian Canestri; Cosmo Mitrano; Walter Fuscaldo; Alessandro Galli
Journal: International Journal of Antennas and Propagation
 (2022)

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## Abstract

This work presents the design of a wideband circular tightly coupled array for omnidirectional pattern generation. The proposed array works over an 8:1 bandwidth, providing very high performance in terms of active reflection coefficient, realized gain, and omnidirectional patterns with reduced ripples. The array is composed of 32 low-profile, self-complementary, bow-tie elements displaced around a metallic mast. The capacitive coupling between neighbouring elements and the implementation of a properly designed frequency selective surface allow for increasing the electrical length of each antenna while compensating for the inductive effect of the metallic mast, according to the tightly coupled and connected arrays theory. A cover layer is then inserted to improve the average gain on the azimuthal plane. Time-domain simulation results confirm the validity of the proposed approach and implementation.


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## Body

## 1. Introduction

During the last years, tightly coupled arrays (TCAs) attracted a lot of interest owing to their advantages, such as wide bandwidth and good radiative performance [1, 2]. Devices based on TCAs are expected to find applications in various contexts such as radar systems, 5G mobile communications, and the Internet of Things (IoT) [3]. The concept of TCAs was originated from Wheeler’s (and then Munk’s) idea of the current sheet [3], which consists in placing the adjacent radiating elements close enough to deliberately generate a strong capacitive coupling. The latter effect is able to counteract the inductive effect of the ground plane (which is supposed to be close to the radiating elements) and increase their electrical length, resulting in a higher radiation resistance at low frequencies. Munk’s array achieved 9:1 bandwidth and has been regarded as a benchmark since 2009. Since that time, TCAs have been used in numerous applications in UHF and SHF bands with additional elements (substrates, superstrates, and coupling structures) to improve TCAs in terms of scan performance, costs, low cross-polarization, and easiness of fabrication.Numerous designs [3–5] have proven successful in providing all the above-mentioned features whilst ensuring proper matching (VSWR less than 2–3.5) in a rather wide bandwidth (from 1.6:1 to 21:1). In this regard, Table 1 shows a summary of the state of the art of TCAs (2018) in terms of achieved bandwidth (BW), voltage standing-wave ratio (VSWR), radiation efficiency (ηrad), and specific features. They have been sorted in ascending order by their bandwidth. Further details about the referred designs can be found in [6–20]. All of them incorporate specific structures to enhance the array bandwidth. The recently published papers [12, 15, 20] are an interesting reference for the work proposed in this manuscript, as they proposed similar bandwidths (from 5:1 to 9:1) achieved with similar coupling techniques. But, on the whole, [18] has been the most important reference because its extremely promising results showed a very large bandwidth achieved through an array of bow-tie elements located between an FSS (frequency selective surface) and a superstrate. The same techniques have been applied to this work too.Table 1
State of the art of TCAs.
BWVSWRηradFeaturesRef1.6:1<293% (B.S.)Shorted edge terminations[6]2.5:1<2N.M.Parasitic ring loading[7]3:1<2.1 (B.S.)N.M.PUMA[8]3.3:1<3N.M.Octagonal ring element[9]5:1<2.1 (B.S.)N.M.PUMA[10]5:1<2 (B.S.)N.M.[11]5:1>60%Metasurface6:1<385%Capacitive overlaps[12]6.1:1<3.265%–80%Maximum scan angle; FSS superstrate[13]7.35:1<2.65N.M.[14]9:1<3.4N.M.Resistive FSS[15]10:1<2 (B.S.)N.M.Spiral element[16]13.5:1<2.5 (B.S.)60%–70%Substrate loading[17]21:1<3 (B.S.)73%Resistive FSS substrate[18]∗B.S.: broadside scan. ∗∗N.M.: not mentioned. ∗∗∗PUMA: planar ultrawideband modular antenna.All the above-mentioned works describe the design of planar arrays with a ground plane, and their results have not been extended to more specific structures such as circular TCAs around a metallic mast. Here, the aim is to obtain similar results with these kinds of structures while satisfying further requirements, such as omnidirectional patterns with controlled gain ripples on the elevation plane over the operating bandwidth.The proposed work presents the design of an original architecture consisting of a circular tightly coupled array that works over an 8:1 bandwidth (from 1.1f0 to 9f0), defined as the frequency range where the average realized gain is greater than −5 dBi. This definition has been chosen because the realized gain (which includes the loss due to the impedance matching) was the relevant figure of merit for such an antenna. According to this definition, the actual bandwidth is presumably wider, as the average realized gain is still higher than 4 dBi at the upper edge frequency 9f0. However, the array performance for frequencies higher than 9f0 is beyond the scope of this work and thus has not been analyzed. It is worth stressing here that f0 can be any frequency in the microwave range subject to the availability of the thicknesses of the commercial laminates used in the antenna design. The dimensions of the array design are thus reported in terms of the operating wavelength and will scale accordingly. Still, the presented results have been obtained by choosing f0 in the licensed NATO E-Band, that is, within the 2–3 GHz frequency range.The device is expected to be mounted around a metallic mast, providing a modular solution that can be implemented on several platforms (naval or terrestrial). Omnidirectional patterns with controlled ripples are required to provide a 360° analysis of all incident signals in the azimuthal plane with half-power beamwidth (HPBW) higher than 20° on the elevation plane. A circular array consisting of 32 wideband horizontally polarized bow-tie antennas has been chosen to comply with the above-mentioned requirements.The paper is organized as follows. Section2 describes the circular array design. Section 3 illustrates the design of a proper frequency selective surface (FSS) to compensate for mast inductive effects and a superstrate to improve the average realized gain in the azimuthal plane. Section 4 shows the most relevant full-wave results. Concluding remarks are finally drawn in Section 5.


## 2. Array Design

The proposed array is composed of 32 self-complementary horizontally polarized bow-tie antennas placed on a TG24/2000 Trelleborg Eccofloat [21] (εr = 1.45 and tan δ = 0.002) circular substrate around a metal mast. The array is expected to be used at frequencies lower than 9f0 and has a bandwidth (average realized gain greater than –5 dBi on the azimuthal plane) ranging from 1.1f0 to 9f0 (8:1). Figure 1 shows the array structure with the relevant reference system.Figure 1
Tightly coupled array under analysis: 3-D model.The mast has a radiusRM = 0.58λmax (where λmax = c/f0, with c speed of light in vacuum) and a length of 4λmax (these are typical values for masts used in, e.g., naval platforms). The device can be adapted to masts with different radii by varying the number of elements in order to guarantee an omnidirectional pattern (low realized gain ripple in the elevation plane).Figure2 shows the realized gain ripple on the azimuth plane for 16 and 32 elements of the array. The ripple is evaluated as the difference between the maximum and the minimum realized gain for each fixed frequency and elevation plane. Considering 32 radiating elements of length 0.112λmax, a realized gain ripple lower than 8 dB for elevation 0° plane is obtained. It is seen that if, with the same mast radius, 16 bow-tie elements of double-length (0.224λmax) are used, the realized gain ripple in the azimuthal plane turns unacceptable for f > 3.5f0.Figure 2
Realized gain ripple in the azimuthal plane at different frequencies for 16 and 32 elements arrays. The array radius has been kept fixed to 0.58λmax.A self-complementary bow-tie antenna has been chosen as the radiating element. It consists of a pair of metal triangles printed on a dielectric substrate and achieves a good wideband performance while exhibiting lightweight and a simple planar conformable structure [22]. Each bow-tie antenna is λmax/9 long in order not to increase the realized gain ripple at high frequencies. A bow-tie flare angle equal to 77.3° has been chosen to guarantee, together with a low-permittivity substrate, a 200 Ω input impedance [23]. The distance between each bow-tie antenna and the mast has been optimized through various accurate simulations (time-domain simulation throughout the whole bandwidth f0−9f0 to analyze the behaviour of the overall structure and frequency-domain simulation at 3.215f0 to analyze the parallel LC resonance between the metal mast and the designed FSS) in order to provide a reduced inductive loading effect on each radiating element, which limits the bandwidth by lowering the radiation resistance, particularly in the low-frequency band (approximately from 1.1f0 to 3.5f0).Unfortunately, whilst long bow-tie antennas show wideband performance, the same does not occur if the antenna length is not much greater than the operating wavelength. Hence, in the case of our interest, only in the higher frequency band (3f0−9f0), good matching is achieved.Figure3 shows how the input reflection coefficient magnitude of a single bow-tie antenna gradually increases as its length L is reduced. If a bow-tie antenna with L = 0.56λmax ensures |S11| < −10 dB throughout the bandwidth, the same does not apply for the case with L = 0.11λmax, where |S11| < −5 dB occurs from 3f0 (and from 4f0 if a metallic mast close to the antenna is placed). This problem has been solved thanks to capacitive coupling between adjacent antennas aimed at increasing the single antenna electrical length and compensating for the mast loading effect. Each antenna has been supplied by a discrete port of 200 Ω that is equal to the average radiation resistance of a bow-tie antenna in free-space with a 77.3° flare angle. A 0.0136λmax thickness TG24/2000 substrate has been chosen to achieve an average input impedance of 200 Ω for each bow-tie element.Figure 3
Input reflection coefficient magnitude |S11| (dB) for an isolated bow-tie antenna with 77.3° flare angle supplied with a 200 Ω discrete source. Three different antenna lengths have been considered.An approximate transmission line model has been used to design an FSS able to compensate for the mast inductance. Assuming the metal mast to be in the antenna far-field region in the receiving mode (which is verified until 4.25f0) and focusing only on the wave propagation along the normal direction to each bow-tie antenna, the equivalent circuit shown in Figure 4 has been considered.Figure 4
(a) CAD model of a single bow-tie antenna with metal mast and (b) transmission-line equivalent model.
(a)(b)In this approximate model, each antenna sees an equivalent load equal to the parallel connection between the free-space impedance representing the upper space and the input impedance of the lower space transmission line loaded on the mast. In the considered device, through the previous transmission-line model, the mast can be shown to be an equivalent inductor of 13.6 nH. Its effect is to “short” the antenna output port in 1.1f0–3.5f0 approximately, causing an abrupt drop in radiation resistance at the antenna input port.In order to obtain a controlled omnidirectional pattern exploiting the TCA theory, the distance between the phase centres of the chosen bow-tie antennas should be less than 0.11λmax, according to circular array theory [24]. Therefore, the radiation resistance of the single bow-tie element is further reduced.Tight coupling is provided between adjacent elements in order to compensate for the mast inductive effect and increase the radiation resistance, according to Munk’s and Wheeler’s current sheet concept [25].In Section4, it is described how the low-frequency behaviour of the input active reflection coefficient can indeed be strongly improved through this technique [26]. The array is able to take advantage of the extra inductance from the metal mast to resonate with the capacitive impedance of the coupled radiating elements, resulting in a wider bandwidth.


## 3. FSS and Superstrate Design

A capacitive FSS [27] can be introduced to further compensate for the mast inductive effect in the low-frequency band. The FSS has been realized with properly displaced capacitive metal squares providing a good matching compensation in 1.1f0−3f0 at the expense of mitigating the higher frequency performances. An active VSWR <3.57 is achieved in 1.6f0−9f0 owing to TCA and FSS (see Section 4). Such a result has been obtained through time-domain simulation (from f0 to 9f0) of the entire structure. Moreover, the FSS allows us to control the destructive interference between the radiated waves and the reflected waves from the metal mast, especially around its central frequency.An FSS made of an array of square patches has been chosen (see Figure5). They have been designed with unit cell subwavelength period D = 0.03λmax and spacing w=0.0033λmax to achieve an equivalent input capacitance of 0.045 pF for TEM incidence according to the following equations [28]:(1)ZsTEM=−jη02αεeff,where εeff is the relative effective permittivity of the uniform host medium and α is the grid parameter and can be expressed as follows:(2)α=k0εeffπD⋅ln1sinπw/2D.Figure 5
A capacitive FSS made with square metal patches.Such a capacitance has been designed to compensate for the inductive behaviour of the metal mast until 4f0. Parallel LC resonance occurs at about 3.215f0.In order to increase the array average realized gain on the azimuthal plane, a superstrate has been inserted in front of the radiating elements at a distance of 0.059λmax. This well-known issue has been investigated in [29, 30] and shows how a properly designed high-permittivity superstrate can increase the antenna directivity at the expense of a reduction in bandwidth. More recently, the same phenomena have been analyzed for wideband applications [5, 18, 31, 32]. Therefore, the antenna directivity can be approximated as a function of the ratio between the dielectric permittivity of the superstate and that of the substrate (see, e.g., [24]). Moreover, it has recently been shown [33, 34] that when the FSS is lossy, the position that maximizes the gain at the broadside is no longer the substrate-superstrate interface but shifts towards the middle plane of the substrate. A higher permittivity superstrate (ROGERS TC350; εr = 3.5 and tan δ = 0.002 [35]) has been chosen, and by means of parametric time-domain simulations on CST MWS, it has been shown able to guarantee an improvement of 2 dBi of the average realized gain over the azimuthal plane.


## 4. Array Performance

The single element structure with the FSS designed in Section3 is depicted in Figure 6 in an array configuration. As described, each bow-tie antenna has been designed with a 77.3° flare angle to show an average input radiation resistance of 200 Ω throughout the bandwidth [23]. The bow-tie antenna length L has been fixed to 0.11λmax to guarantee a circular spacing between adjacent radiating elements small enough to keep the realized gain ripple below 8 dB (the overall spacing between array elements is d). A coupling distance G = 0.0027λmax has been shown to be the optimal trade-off for such a device between the increase of the electrical length and the increase of the transmission coefficients Sij, i ≠ j.Figure 6
Array front view with single bow-tie elements, FSS, and mast. The array’s main dimensions are shown.As shown in Figure7, the low-density synthetic foam TG24/2000 has been chosen as a substrate to provide a low effective permittivity and minimize unwanted coupling whilst guaranteeing the desired radiation resistance with the bow-tie dimensions previously chosen. The array main dimensions are indicated in Table 2. The distance u = 0.053λmax = 0.48λmin between each bow-tie antenna and the metal mast is slightly less than λmin/2 to avoid destructive interference at 9f0 whilst minimizing the inductive effect of the metal mast by keeping it far enough. Finally, the higher permittivity superstrate ROGERS TC3502 has been inserted to increase the antenna realized gain in addition to the array factor enhancement. Simulations have shown that a 2 dBi average increase of the realized gain in the azimuthal plane may be reached without compromising the bandwidth. This result is achieved through the reduction of the elevation beamwidth due to the added superstrate.Figure 7
Array view with single bow-tie element, substrate, superstrate, FSS, and mast. The array’s main dimensions are shown.Table 2
Array parameters.
Size (fraction ofλmax)Descriptiond = 0.1150Bow-tie centres spacingg = 0.0017Feed gapL = 0.1120Bow-tie lengthR = 0.090Bow-tie widthG = 0.0027Bow-tie edges spacingD = 0.03FSS sidew = 0.0033FSS spacinghsup = 0.0133Superstrate thicknesshsub = 0.0136Substrate thicknessRM = 0.5801Mast radiusWsub = 0.1067Substrate widthv = 0.1063Superstrate-mast distanceu = 0.0053FSS-Mast distanceFigure8 depicts the three main array configurations that have been considered in the simulations. The initial model consists of a simple TCA without additional elements. Then an FSS has been added, and the final structure with both FSS and superstrate has been considered. All the following simulation performances refer to those three configurations.Figure 8
Main array configurations compared in terms of simulated performances.The final array design achieves an active input reflection coefficient of |Гin| < −5 dB (i.e., active VSWR < 3.57) from 1.55f0 to 9f0, as illustrated in Figure 9 (see the yellow curve). The frequency response of the input reflection coefficient of a single bow-tie antenna close to the metallic mast (see the blue curve) presents a considerable mismatch around 1.1f0−3f0. Placing such an antenna in a TCA configuration increases its electrical length providing a good matching from 2.4f0 (see the red curve). The low-frequency performance is further improved by inserting the designed FSS for a greater compensation of the parasitic inductance of the metal mast (see the yellow curve).Figure 9
Frequency responses of the absolute value of the input reflection coefficient (dB).Figure10 illustrates the frequency response of the average realized gain over the azimuthal plane for the horizontal polarization (HP). The realized gain over the azimuthal plane Gr (Az, El = 0°) is defined as the realized gain pattern (function of the azimuth and elevation angles) evaluated at 0° elevation (azimuthal plane). Such a function of the azimuth angle is of great interest as our purpose was to design an omnidirectional antenna in the azimuthal plane (Gr (Az, El = 0°) = constant). Its average value, analyzed for each frequency of interest, is a good figure of merit for the design of such an antenna. The blue curve shows the performances achieved by the TCA made of 32 bow-tie elements. If a proper FSS is added, a significant increase in the mean realized gain is observed in 6.5f0−9f0 (see the orange curve). It is possible to explain this phenomenon from a theoretical viewpoint. The partial shielding of the wave reflected from the mast is a possible cause of this behaviour. In particular, in the upper-frequency band, it would destructively interfere with the wave radiated by each antenna as the distance from the mast approaches λ/2. In brief, the FSS suppresses the λ/2 resonance induced by the metal mast. Finally, the insertion of the aforementioned superstrate allows for increasing the mean realized gain up to 2 dBi (see the yellow curve). The resulting device provides an average realized gain in the azimuth plane between −4.1 dBi and +5.8 dBi over the whole band 1.2f0−9f0.Figure 10
Frequency response of the average realized gain (in dBi) in the azimuthal plane for different TCA solutions. Only the horizontal (azimuth) polarization has been considered.The frequency behaviour of the realized gain ripple in the azimuthal plane is shown in Figure11. The realized gain ripple in the azimuthal plane is defined as the deviation in dB between the maximum and minimum value of the realized gain in the azimuthal plane Gr (Az, El = 0°). The initial model of the TCA has a ripple peak higher than that of the final versions with the same (0.115λmax) circular spacing between adjacent bow-tie antennas. Those peaks are significantly lowered by the insertion of the FSS (red curve), which reduces the destructive interference, thus mitigating the minimum points in the radiation pattern. A small increase of the ripple (less than 3 dB) is observed for 4f0 < f < 6f0 and f > 8f0 when the superstrate is added. Nevertheless, the final device presents a realized gain ripple lower than 8 dB over the entire frequency band.Figure 11
Frequency response of the realized gain ripple in the Azimuth plane.The frequency response of the half-power beamwidth (HPBW) in the elevation plane for the horizontal polarization is shown in Figure12. The proposed final array achieves HPBW >20° over the desired bandwidth.Figure 12
Frequency response of the HPBW in the elevation plane.All previous results have been obtained by choosing an 18μm-thick copper layer as the metal conductor for each bow-tie antenna, the metal mast, and the FSS. These results perfectly overlap with those obtained with PEC materials. The insertion of low-loss materials to counteract parasitic effects results in a very high radiation efficiency compared to that achieved in several designs shown in Table 1 including RFSS (resistive FSS) [3]. Figure 13 shows the frequency response of the radiation efficiency for the proposed array. It is higher than 93% throughout the entire bandwidth.Figure 13
Frequency response of the radiation efficiency of the proposed array.


## 5. Conclusion

In this paper, an original architecture consisting of 32 bow-tie elements arranged in a circular array configuration surrounding a metallic mast has been proposed, providing a modular solution that can be implemented on several platforms (naval or terrestrial). We exploited the concepts of tightly coupled antenna theory to achieve satisfactory performance in terms of realized gain ripple and radiation efficiency over an 8:1 bandwidth. The novelty of this work consists in the application of the current sheet concept originated from Munk’s and Wheeler’s works to a circular array used for the synthesis of an omnidirectional radiation pattern around a metallic mast.The insertion of an FSS and a proper dielectric superstrate, together with an optimal degree of capacitive coupling, resulted in a good performance in the whole bandwidth of interest. Nonresistive compensations have been used to counteract the mast parasitic inductance and increase the radiation resistance, resulting in a very high radiation resistance throughout the bandwidth. The final antenna has provided an average realized gain in the azimuth plane between −5 dBi and +5.8 dBi, with ripple lower than 8 dB, an HPBW > 20°, and a radiation efficiency higher than 93% over the whole band 1.1f0−9f0, with f0 in E-Band. Future works include the design of a tapered wide-band microstrip BALUN with the purpose of matching the 200 Ω bow-tie input impedance to a 50 Ω microstrip line. In the final structure, 32 BALUNs, passing through 32 pre-drilled holes inside the mast, would supply the single elements of the array. Such a feed network would be contained almost entirely inside the metal mast already taken into account in the array design, hence with minimal effect on the overall radiation pattern and array performances.



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*Source: 5051710-2022-04-22.xml*