Sk Rafidul, Debatosh Guha, Chandrakanta Kumar
IMAGE LICENSED BY INGRAM PUBLISHING
This article revisits the reasons behind the cross-polarized (XP) radiation in microstrip patches and focuses on alleviating a long-standing deficiency in terms of a comprehensive knowledge about the same. This study has a twofold objective. First, it explores all possible components of the surface fields as the correlating factors over all of the radiation planes, especially across the diagonal or skewed axes. An extensive study involving varied patch geometries along with different feed networks has been executed. The resulting huge volume of data has been analyzed to identify the ideal surface field requirements for the best possible XP performance.
In the second phase, a representative example proposing required modifications in the design has been demonstrated. A planar microstrip feed has been addressed, keeping its suitability in mind in realizing planar arrays. A C-band prototype comprising a circular patch geometry on an engineered ground plane (GP) experimentally ensures as much as 11 dB of XP suppression over the diagonal plane along with 16 dB over the H-plane. This study pinpoints the actual sources causing XP radiation as a function of radiation plane. It should also open topics for practicing engineers as well as antenna researchers in exploring further variants to handle XP issues.
The microstrip patch is now a common and widely applicable antenna element [1], [2]. It radiates due to the fundamental transverse magnetic (TM) resonant mode, but a part of the input power is coupled to orthogonally polarized ${\text{TM}}_{\text{mn}}$ modes and causes XP radiating fields [3], [4]. The variation of the XP characteristics of rectangular and circular patch antennas is studied in [5], [6], [7] for different feed positions, substrate thicknesses, permittivities, and resonance frequencies. A variety of techniques has been reported to suppress the XP issue, including balanced feeding [8], a dual-layer substrate [9], GP shaping [10], [11], probe shaping [12], and shorting of the patch [13], [14], [15]. These methods involved additional volume, cost, and complicated fabrications. Relatively simpler techniques employ defected ground structure (DGS) integration [16], [17], [18], [19], although all of them could address only the orthogonal plane (H-plane) XP levels.
Dubost [20] and Lee et al. [7] explicitly demonstrated that the XP field is a function of the azimuth angle ${(}{\varphi}{)}$ and is minimum at ${\varphi}\,{\approx}\,{0}^{\circ}$, maximum at ${\varphi}\,{\approx}\,{45}^{\circ} / {135}^{\circ}$, and maintains an intermediate value at ${\varphi}\,{\approx}\,{90}^{\circ}$. Recently, a couple of attempts have been made to address the diagonal plane or D-plane ${(}{\varphi}\,{\approx}\,{45}^{\circ}{)}$ XP issue using GP techniques [21], [22] based on a partial understanding. Oberhart et al. [3] and Lee et al. [6], [7], in their fundamental works, considered only the orthogonal modes in analyzing the XP radiation. They were revisited in [23] using a mathematical model involving only the near fields ${E}_{x}$ and ${E}_{y}$. In a recent work [15], the authors have deliberately discriminated the orthogonal mode by a set of shorting pins. That helps in suppressing ${E}_{y}$ but fails in improving the situation over the D-planes. This, in turn, indicates the existence of some additional sources other than ${E}_{x}$ and ${E}_{y}$ that are not yet known to the microstrip community.
This article aims to alleviate those lacunae and works with a twofold objective. In the first phase, it explores a deeper insight into identifying all possible sources as a function of azimuth ${\varphi}$. Such a holistic approach, to the best of our knowledge, is new. It tries to establish a correlation among the possible sources and the associated XP behavior. Three common microstrip elements, viz., rectangular, square, and circular patches with different feeding configurations, have been extensively examined and systematically documented. All significant findings have been carefully recorded and analyzed.
The second phase of this article demonstrates how the new gathered data could guide us in obtaining the required change in the surface fields. A representative example featuring targeted XP characteristics has been demonstrated by reconfiguring the GP current. The required GP engineering has been made as simple as possible and eventually comes near to that used in [21]. Such an engineered striped GP offers a huge challenge in realizing feed networks for a practical array. The coax-based design, as in [21], happens to be next to impossible in terms of array realization. Keeping that in view, a planar microstrip feed has been demonstrated as a more practical one in the present study. The analysis and inference drawn on the basis of simulated data have been successfully verified through experimental measurements. A set of C-band prototypes promises as much as 16 dB XP suppression over the ${\varphi} = {90}^{\circ}$ plane (H-plane) and about 11 dB over the ${\varphi} = {45}^{\circ}$ plane (D-plane), maintaining the primary radiation unperturbed. We also have extended the feasibility in array designs with a target of low XP over the 3D patterns. This investigation ensures the possibility of controlling the XP level by strategically handling the identified “source fields.” The eventual outcome is very promising and much improved compared to earlier works, e.g., [13], [14], [15], [16], [17], [18], [19], [21], and [22].
As predicted by Oberhart et al. in [3], the XP radiation in a microstrip antenna originates from the orthogonally polarized modes. For the strategic investigation in [15], these orthogonal modes in a rectangular microstrip have been blocked by inserting shorting pins across its nonradiating edges. An identical rectangular element [15] has been considered as the reference to start this present examination. The aim is to investigate whether any dependence of ${\text{XP}}{(}{\varphi}{)}$ lies on the surface fields ${E}{(}{\varphi}{)}$ and ${H}{(}{\varphi}{)}$. A set of data obtained using [24] has been extracted on the upper surface of the substrate, maintaining a constant radial distance S from the patch center, as shown in Figure 1(a). The value of S is arbitrary; it is ${S} = {1.25}\,{L}$ for the present study. At the beginning, only the y-polarized components have been considered since the known source for XP fields is the ${\text{TM}}_{02}$ mode [3], which is always polarized to the y-axis.
Figure 1. Geometry of the probe-fed conventional patches: (a) rectangular, (b) square, and (c) circular. Parameters: h = 1.575, ${\varepsilon}_{r} = {2.33}$, D = 50; rectangular: L = 15, W = 22.5, ${\rho} = {4}$, S = 1.25 L; square: L = W = 15, ${\rho} = {2.6}$, S = 1.25 L; circular: R = 9.5, ${\rho} = {2.7}$, S = 2 R. All dimensions are in millimeters. S is the radius of an observation arc.
A comparative study for both ${E}_{y}$ and ${H}_{y}$ occurring in a conventional patch as well as its shorting pin-loaded version [15] is shown in Figure 2. Over the ${\varphi} = {90}^{\circ}$ plane, ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$ in the pin-loaded version is reduced with a clear evidence of considerable reduction of both ${E}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ and ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$. But here is an important observation: a huge reduction of ${E}_{{y}_{{(}{\varphi}\,{\sim}\,{60}^{\circ}{-}{70}^{\circ}{)}}}$ does not cause a similar reduction in ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{60}^{\circ}{-}{70}^{\circ}{)}}$. Thus, one may infer that ${E}_{y}$ has a predominant effect on XP over ${\varphi} = {90}^{\circ}$ (the H-plane) only, but not for other ${\varphi}$ values. For the D-plane ${(}\varphi = {45}^{\circ}{)}$, neither ${E}_{y}$ nor ${H}_{y}$ shows any change in their values or in the XP level. Thus, blocking of the ${\text{TM}}_{02}$ mode can help in reducing XP on ${\varphi} = {90}^{\circ}$ only, but not over the D-plane.
Figure 2. Source field components and resulting XP radiations of a pin-loaded patch [15] compared with those of a conventional configuration as a function of azimuth {: (a) Ey and (b) Hy. Parameters: L = 10.15, W = 1.6 × L, ${\rho} = {3.1}$, D = 60, h = 1.575 (all dimensions are in millimeters), ${\varepsilon}_{r} = {2.33}$.
To figure out the unknown sources that cause XP radiations over the skewed radiation planes, we have executed a thorough investigation on ${E}_{x},{E}_{y},{H}_{x}$, and ${H}_{y}$ for three representative patch geometries, viz., rectangular, square, and circular at the C-band, each being fed by different known techniques. As mentioned earlier, the surface fields have been extracted as a function of ${\varphi}$ at a constant radial distance ${S} = {1.25}\,{L}$ for rectangular/square patches and ${S} = {2}\,{R}$ for a circular patch, as shown in Figure 1(c). A huge volume of data obtained for three sets of representative patches and feed networks has been processed and comprehensively represented through Figure 3. Indeed, this study is too extensive, involving multiple ${\varphi}$ values with 5° intervals between ${\varphi} = {0}^{\circ}$ to ${\varphi} = {90}^{\circ}$. But, for simplicity and ease of understanding, they have been plotted only over three representative planes, viz., ${\varphi} = {0}^{\circ},{45}^{\circ}$, and ${90}^{\circ}$, without losing any important information. They are critically discussed next.
Figure 3. Source field components and resulting XP radiations as a function of azimuth ${\varphi}$ of rectangular, square, and circular patches with different feeding mechanisms. (a) rectangular patch, (b) square patch, and (c) circular patch; feed #1 = probe fed, feed #2 = inset fed, feed #3 = edge fed, and feed #4 = aperture fed. Parameters of the antennas are as in Figure 1.
Figure 3(a-i) and (a-ii) depicts the variation of ${\text{XP}}{(}{\varphi}{)}$ and ${E}_{x}{(}{\varphi}{)}$, revealing no mutual correlation. A higher ${E}_{{x}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ for feed #4 corresponds to a low ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}$. But an increase in ${E}_{x}{}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{\text{ and }}{90}^{\circ}{)}}$ does not indicate any such decrement in ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{\text{ and }}{90}^{\circ}{)}}$. Thus, no definite relation between ${E}_{x}$ and XP could be established. Figure 3(a-iii) examines ${E}_{y}$ and endorses the observation in Figure 2(a). Also, from Figure 3(a-i) and (a-iii) one can observe that a somewhat lower ${E}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ produces a relatively lower ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$, which appears valid for all of the feed configurations. Also, a critical look into the XP values indicates that there must be some other sources apart from ${E}_{y}$ as the contributing factors. This becomes prominent from the studies in Figure 3(a-iv) and (a-v). The observation is as follows: feed #4 correlates the lowest ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$ with the lowest ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$, and feed #3 correlates the highest ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$ with the highest ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$. But no definite relation of ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{)}}}$ is found. There are two possibilities: 1) ${H}_{x}$ has no effect on XP over this plane, or 2) ${H}_{x}$ has a weak effect, and ${H}_{y}$ may have some influence. Keeping the contribution of ${E}_{y}$ in mind, one may comfortably examine Figure 3(a-v) in correlation with the XP values in Figure 3(a-i) and conclude two distinct features of ${H}_{y}$. First, ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ reveals inverse relations with ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{\text{ and }}{90}^{\circ}{)}}$. Second, ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ has a minimal relation with ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$. This is true for all feed configurations.
Feed #4 shows the highest ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ [Figure 3(a-v)] correlating with the lowest ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{)}}$ [Figure 3(a-i)]. This is endorsed by another observation where ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ for feed #3 is higher than those of feeds #1 and #2. The corresponding ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{)}}$ is found to be lower than that caused by feeds #1 and #2. Again, feed #4 causes the highest ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ but indicates almost no effect on the XP level, which is the lowest in that region. This is due to the minimal contribution of ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ along with the strong influence of ${E}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ and ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$.
The previous studies with a rectangular patch have been repeated for square and circular geometries as depicted through Figure 3(b) and (c), respectively. Here again, the impact of ${E}_{x}$ on XP level is found to be inconclusive. The magnitude of ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}$ in Figure 3(b-i) and (c-i) is directly related to their respective ${E}_{{y}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ except for feed #2 in Figure 3(b-iii). The reason can be viewed in terms of the contribution of ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ as observed previously. In the ${\varphi} = {45}^{\circ}$ plane, ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ in Figure 3(b-v) and (c-v) follows the same trend as observed for the rectangular patch, i.e., a strong correlation with their ${\text{XP}}_{{(}{\varphi}\,{\sim}\,{45}^{\circ}{)}}$.
The previous studies with three representative patch geometries, each with four commonly used feeding techniques, lead to identifying a relation between their XP levels and corresponding surface field components ${E}_{y},{H}_{y}$, and ${H}_{x}$. The overall inference is as follows:
The previous drawn inference guides a designer in controlling three specific source field components (e.g., ${E}_{y},{H}_{x}$, and ${H}_{y})$ to minimize the XP levels. The scheme is briefly sketched in Table 1, which clearly indicates that the required control of fields can be achieved by controlling the GP current components ${i}_{x}$ and ${i}_{y}$. Figure 4(a) shows a representative sketch of the typical current distribution on the GP caused by the primary resonance of the patch. As per the guideline in Table 1, our aim would be blocking of ${i}_{y}$ and facilitating ${i}_{x}$. Thus, a simple and logical way of achieving this is a striped GP surface, as sketched in Figure 4(b). This would cause minimum ${i}_{y}$ with maximum ${i}_{x}$. Although it resembles the GP intuitively conceived and used in [21], this configuration evolves on the basis of the present case study revealing some useful correlations. Moreover, unlike the work in [21], we prefer using a different microstrip element as a radiator (a circular patch) along with a different feed mechanism. We have adopted a fully planar microstrip feeding that is more realistic for realizing arrays. Indeed, the possibility of advanced array design has also been addressed in our study, which is unrealizable in [21]. Figure 4(c), therefore, shows some required adaptation on Figure 4(b) to accommodate a microstrip-fed circular patch as the radiator.
Figure 4. Design steps for GP engineering of the proposed antenna. (a) Conventional GP, (b) stripped GP, and (c) modified stripped GP to support the fields beneath the circular patch and the feeding line.
Table 1. The Requirements for the Source Fields to be Achieved.
Figure 5 shows the final configuration, which uses an RT/duroid 5870 substrate and operates at the C-band. The ${\text{S}}_{11}$ values have been studied using [24] in Figure 6 with ${d}_{1}$ and ${d}_{2}$ as parameters. The basis of optimization is to maintain the input impedance as well as gain values unchanged with respect to its conventional GP. The section bearing width ${d}_{3}{(} = {5}{\text{ mm}}{)}$ has to be optimized to accommodate a microstrip feed on top of this and to achieve the required feed impedance.
Figure 5. The geometry of the proposed antenna: (a) isometric top view and (b) isometric bottom view. Parameters: R = rg = 9.5, l = 6, w1 = 2, w2 = 2.2, d1 = d2 = 2.8, d3 = 5, h = 1.575, ${\varepsilon}_{r} = {2.33}$, D = 50 (all dimensions are in millimeters).
Figure 6. S11 versus frequency plots of the conventional and the proposed antenna with d1 and d2 as parameters. Other parameters: R = rg = 9.5, l = 6, w1 = 2, w2 = 2.2, d3 = 5, h = 1.575, ${\varepsilon}_{r} = {2.33}$, D = 50 (all dimensions are in millimeters).
Their radiation characteristics as a function of ${d}_{1}$ and ${d}_{2}$ are examined in Figure 7. It is important to note that we obtain no degradation in peak gain, unlike the cases observed in [21] and [22]. The E-plane radiations [Figure 7(a)] are comparable with the conventional case. The copolar radiations over the H-plane [Figure 7(b)] are also found to be comparable. But a significant improvement in XP level is evident. The value ${d}_{1} = {d}_{2} = {2.8}{\text{ mm}}$ is found to give the optimum response. It shows about 20–21 dB suppression in the peak XP values relative to that with a conventional ground. The radiation patterns over a diagonal plane [Figure 7(c)] are equally significant. The 3-dB beamwidth of the copolar pattern perfectly matches that of the conventional GP but reveals as much as 12 dB suppression in the XP level. Here also ${d}_{1} = {d}_{2} = {2.8}{\text{ mm}}$ is found to offer the optimum performance. Another observation embodies about 2 dB reduction in backside radiation. The effect of GP dimensions on both copolar and cross-polar gains is examined in Figure 8. The variation of D over a practical range of ${0.9}{\lambda}$ to ${1.1}{\lambda}$ indeed reveals a significant observation: relative suppression of the XP level over both the D- and H-planes attains optimum suppression when ${D}\,{\approx}\,{\lambda}$. The copolar gain remains consistent over the entire range. We, therefore, have chosen ${D} = {\lambda}$ for the present design. The final optimum parameters of the proposed antenna are shown in Table 2.
Figure 7. The radiation patterns of the conventional and proposed antennas with d1 and d2 as parameters. Other parameters are as in Figure 6. (a) E-plane, (b) H-plane, and (c) D-plane.
Figure 8. Variations of peak gain and peak XP over D- and H-planes for proposed and conventional antennas with GP dimensions. Parameters: d1 = d2 = 2.8 mm. Other parameters are as in Figure 6.
Table 2. Antenna Parameters/Dimensions (MILLIMETERS).
The improvements in Figure 7 are actually based on our acquired knowledge in Figure 3 followed by Table 1. Those specific parameters, e.g., ${H}_{x}$ and ${H}_{y}$, have now been further examined in Figure 9 using our newly proposed GP surface. As was done previously, here also the fields have been extracted on the surface of the substrate at a radial distance ${S} = {2}{R}$ from the patch center. ${H}_{x}$, as per the requirement in Table 1, is significantly decreased [Figure 9(a)]. The requirement is to increase ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$, which is perfectly satisfied in Figure 9(b). Ripples in the fields with a change of ${\varphi}$ are apparent. This is predominantly significant in Figure 9(b), specifically for ${d}_{1} = {d}_{2} = {3.8}{\text{ mm}}$. The reason behind this is the discontinuity between the GP stripes which lies along the y-axis, and Figure 9(b) addresses the y-component of the H-fields. The larger the gap ${(}{d}_{2}{)}$, the more prominent are the ripples. The numerical representations in Figure 9 can be visualized from the simulated field portrayals of Figure 10. The field magnitudes have been extracted exclusively over ${\varphi} = {0}^{\circ},{45}^{\circ}$, and ${90}^{\circ}$ planes from the simulated data [24], plotted as bar charts using [25], and displayed on the appropriate substrate areas in Figure 11. Here, ${H}_{{x}_{{(}{\varphi}\,{\sim}\,{90}^{\circ}{)}}}$ is found to decrease, whereas ${H}_{{y}_{{(}{\varphi}\,{\sim}\,{0}^{\circ}{)}}}$ increases compared to the conventional geometry. The surface impedance, as shown in Figure 12, indeed justifies the field variations. This striped ground surface thus satisfies the required surface impedance in favor of a reduction in XP level.
Figure 9. Comparison of the of the H-field components of the conventional antenna with the proposed antenna with d1 and d2 as parameters. Other parameters are as in Figure 6. (a) Hx and (b) Hy.
Figure 10. Magnitude plots of the field distribution on the surface of the substrate for the conventional and proposed antennas. (a) Hx and (b) Hy. Scales are in amperes/meter. Parameters are as in Table 2.
Figure 11. 3D bar graph plots of the field distribution over a quadrant of the conventional and proposed antenna. (a) Hx and (b) Hy. Scale: min (blue) = 0 A/m; max (red) = 0.3 A/m. Parameters are as in Table 2.
Figure 12. 3D bar graph plots of the impedance distribution over a quadrant of the conventional and proposed antennas. (a) ${Z}_{{S}1} = {\left\vert{E}_{x} / {H}_{y}\right\vert}$ [scale: min (blue) = 0, max (red) = 290 X]; (b) ${Z}_{S2}{\left\vert{E}_{y} / {H}_{x}\right\vert}$ [scale: min (blue) = 0, max (red) = 800 X]. Parameters are as in Table 2.
A set of prototypes bearing the newly conceived GP surface along with the conventional configuration is shown in Figure 13. Radiall SMA connectors have been used for the feeding purpose. The measurements were executed using Agilent’s E8363B network analyzer and an automated anechoic chamber provided with an MI-750 microwave receiver. There is more than 60 dB of dynamic range for the power level of operation used in the chamber. Thus, its contribution to noise is negligible, although the positioner could be a prominent contributor. However, the present system offers an accuracy of about 0.1; therefore, the XP values are repeatable within a maximum error of ±1 dB. Figure 14 compares the measured and simulated ${\text{S}}_{11}$ values, revealing excellent mutual agreement. This confirms our design strategy that the modified GP current should not affect the input impedance. Also, as per our design conjecture, it should not affect the primary radiation and antenna gain.
Figure 13. Bottom views of the fabricated prototypes. Top views are shown in insets. Parameters are as in Table 2.
Figure 14. S11 versus frequency plots of the fabricated prototypes. Parameters are as in Table 2.
Figures 15 and 16 examine those measured data. Figure 15 deals with the central frequency of the matching bandwidth and shows the patterns over three representative planes passing through ${\varphi} = {0}^{\circ},{90}^{\circ}$, and ${45}^{\circ}$. The measurement closely follows the simulated predictions maintaining a compatible 3-dB beamwidth. No change in peak gain is revealed. The XP level in the E-plane also shows no relative change. A truly significant change in the XP level is observed for both the H- ${(}\varphi = {90}^{\circ}{)}$ and diagonal ${(}\varphi = {45}^{\circ}{)}$ planes. The order of suppression follows the simulated predictions: about 16 dB in the H-plane ${(}\varphi = {90}^{\circ}{)}$ and 11 dB in the diagonal plane ${(}\varphi = {45}^{\circ}{)}$. Figure 16 actually confirms the reliability and consistency of the proposed XP suppression over the entire bandwidth. Two band edges, therefore, have been addressed here. Nearly 11–14 dB suppression is obtained over the H-plane and 7–10 dB over the diagonal plane.
Figure 15. Measured and simulated radiation patterns of the proposed and conventional antennas at resonant frequency. Parameters are as in Table 2. (a) E-plane, (b) H-plane, and (c) D-plane.
Figure 16. Measured and simulated radiation patterns of the proposed and conventional antennas at the band-edge frequencies. (a) H-plane at fL, (b) H-plane at fH, (c) D-plane at fL, and (d) D-plane at fH. fL: lower band-edge frequency; fH: upper band-edge frequency.
As mentioned earlier, the proposed configuration should handle the challenges of array realization, which is practically impossible using the geometry of [21]. A representative example has been furnished here. Figure 17 shows the layout for a 2 × 2 circular patch array viewed from the top and bottom faces (all parametric details are provided in the figure caption). It is designed to operate near the same frequency, i.e., around 6.2 GHz, as for a standalone element. The antenna performance has been examined using a set of simulated values as furnished through Figures 18 and 19. The ${\text{S}}_{11}$ characteristics have been compared with those of its conventional versions in Figure 18. An excellent mutual agreement is revealed. Figure 19 examines the simulated gain as a function of the elevation angle for ${\varphi} = {90}^{\circ}$ (the H-plane) and ${\varphi} = {45}^{\circ}$ (the D-plane). Compared to a conventional version, the proposed array promises a reduction in XP level by about 16 dB in the H-plane and as much as 5 dB in the D-plane. Compared to a single element, the H-plane value is comparable, but the D-plane performance decreases by 6 dB. The reason is ${i}_{x}$, which in the array platform loses its track of linearity due to the inclusion of multiple circular base regions on the GP [Figure 17(b)]. The primary pattern indeed remains unaltered except with the promise of a nominal increment in peak gain.
Figure 17. The geometry of the proposed array: (a) isometric top view and (b) isometric bottom view. Parameters: D1 = 85, D2 = 18, R = 9.5, S1 = 30, S2 = 27.5, l = 6, l1 = 32.45, l2 = 5.13, w1 = 2, w2 = 2.2, ltr = 22, wtr1 = 1, wtr2 = 1.3, c = 2.8, rg = 9, d1 = d2 = 2.5, d3 = 5, e1 = 32.5, e2 = 11.2. (All dimensions are in millimeters.)
Figure 18. Simulated S11 versus frequency of the proposed 2 × 2 array compared to its conventional version. Parameters are as in Figure 17.
Figure 19. Simulated radiation characteristics of the proposed 2 × 2 array compared with its conventional version. (a) H-plane and (b) D-plane. Parameters are as in Figure 17.
This article documents a set of case studies that finally suggests some useful inferences indicating comprehensive relations between the surface fields around a microstrip patch and its XP generation. It should find a wide range of applications, and one such example has been successfully demonstrated to control the “source” to minimize the XP value over all radiation planes. The development based on this new insight appears to be more useful and practical compared to the earlier ones, as documented in Table 3. In terms of mitigating the XP issues over the full azimuth, maintaining the primary radiation and gain undisturbed, the present mechanism qualifies as the most lucrative one. It also shows a noticeable improvement in backside radiation (by about 2 dB), which was absent in the work of [21] and [22]. Moreover, the adaptibility of the proposed design in planar arrays is also a significant aspect. This is probably the first example of an array that claims low XP simultaneously across the D- and H-planes.
Table 3. A Comparison with Earlier Reported Investigations.
This work is supported partially by the Council of Scientific and Industrial Research, Government of India, and the scheme of the Abdul Kalam Technology Innovation National Fellowship of the Indian National Academy of Engineering/Department of Science and Technology-Science and Engineering Research Board, Government of India.
The authors thankfully acknowledge the useful comments of the reviewers, which helped significantly in improving the technical content. They also acknowledge the help received from Dr. Koushik Dutta of Netaji Subhash Engineering College, Kolkata, and Debi Dutta of the University of Calcutta, India, during the work.
Sk Rafidul (rafidul100@gmail.com) is a Ph.D. student at the Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, 700009, India. His current research interests include antennas with engineered ground and metasurface. He is a Student Member of IEEE.
Debatosh Guha (dguha@ieee.org) is a professor in radio physics and electronics, University of Calcutta, Kolkata, 700009, India. His research interests include both printed and dielectric resonator antennas. He is a Fellow of IEEE and the Indian Academies of Sciences and Engineering.
Chandrakanta Kumar (kumarchk@ieee.org) is a scientist/engineer “SG” at U.R. Rao Satellite Centre, Bangalore, 560017, India. He has been involved in designing and developing antennas for the Indian Space Mission. He is a Senior Member of IEEE.
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Digital Object Identifier 10.1109/MAP.2022.3143434