Dual Radial-Resonant Wide Beamwidth Circular Sector Microstrip Patch Antennas

I.   Introduction

Wide beamwidth microstrip patch antennas (MPAs) are often highly demanded for various applications, such as wireless communication, broadcasting, and navigation [1]–[3]. Ordinary microstrip square patch antennas suffer from limited half-power beamwidths (HPBWs), which are usually 60° [4]. In the past few decades, various techniques have been developed to broaden HPBWs of MPAs. These approaches can be basically divided into five distinct types in terms of their operation principles. As the most common way, the reflector-shaping method is presented in references [5]–[12]: Herein, the size and shape of a ground plane is employed to control the radiation characteristics of MPAs [9]. MPAs with different-shaped reflectors, such as square and tapered-elliptical cavity [5]–[8], cylindrical [9], [10] and tapered reflectors [11], can realize a much wider HPBW than their ordinary ones, at the cost of higher antenna height. To maintain the inherent low-profile merit, the following four methods have been proposed. The first one is the use of rotational elements [13]–[16]. As seen, a low-profile backed cavity with crossed slits can yield a widened beamwidth [13]. With identical elements being symmetrically rotated to form an array, a wide beamwidth characteristic can alternatively be obtained [14]–[16]. The second type is to use the complementary dipole technique [17]–[20], e.g., combination of magnetic dipole and electric dipole toward stable unidirectional patterns with wide beamwidth [17]. The third way is the use of parasitic elements [21]–[25]. Parasitic elements such as L-probe [21], mushroom-shaped patch [22], metallic wall [23], [24], and shorting-pin [25] are included to design a wide beamwidth antenna. The final one is the material-based technique [26]–[30]. Meta-materials such as polarization rotation reflective surface [26], reactive impedance surface (RIS) [27], electromagnetic band gap structure [28] and frequency-selective surface (FSS) [30] can be effectively used as various beamwidth broadening techniques. Recently, a few innovative approaches based on self-balanced theory [31] and capacitive via fence [32], [33] have been advanced. Unfortunately, the planar self-balanced technology is strongly dependent on the size and shape of the ground plane of the antenna [31], and the blind bolt technique may incorporate geometrical complexity and narrow-band operation [32], [33]. Therefore, it is always a challenging task to develop a wide beamwidth antenna with simple structure, wideband operation, and low profile (i.e., height less than 0.1-guided wavelength) characteristics.

This article advances a novel design approach to dual radial-resonant, wide beamwidth, circular sector patch antenna. Firstly, the operation principle of radial-resonant patch antenna evolved from a U-shaped dipole is intuitively revealed. Then, key parameters are initially determined by mode synthesis table and dual radial-resonant, circular sector patch antennas with short-circuited circumference can be designed accordingly. Finally, the radial-resonant design approach is experimentally verified by prototype antennas fabricated on air and Teflon substrates.

II.   Theory and Design Approach

The radial-resonant circular sector patch antenna with short-circuited circumference is presented here with widened E-plane beamwidth, and it is basically evolved from a simplest, U-shaped dipole antenna with quasi-isotropic radiation pattern [34], as shown in Fig.1. Then, a mode synthesis method of patch antenna is revealed, and the key design parameters can accordingly be calculated and determined.

Figure  1.  Evolution of the proposed radial-resonant antenna.

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1   Evolution from a horizontal U-shaped dipole

The evolution of the proposed antenna is depicted in Fig.1. A horizontal, one quarter-wavelength, U-shaped dipole is used as the original prototype. The open aperture of the dipole coincides to the $z$-axis. By rotating the horizontal arms and short cross piece to a certain angle of $\alpha$, the prototype 1-D dipole can evolve into a 2-D circular sector cavity with short-circuited circumference, where its height is denoted as 2$h$. Equivalently, the evolved antenna can be recognized as a circumferentially short-circuited, circular sector antenna with flared angle of $\alpha$, height of $h$ and infinite ground plane according to the theory of image: As such, the antenna should only exhibit magnetic current distribution in the radial direction as shown in Fig.1.

The short-circuited circumference implies that the circumferential eigen-number must be zero, and the magnetic current should have only $\rho$ component that obeying the zero-order Bessel equation. By inserting the asymmetric boundary conditions at $\rho = 0$, $R_0$ into (1), the general solution can be attained to dominate the eigen-modes, where $R_0$ is the radius of circular sector patch, $A$ is an arbitrary, undetermined coefficient.

2   Dual-resonant design approach

The normalized radius of the patch can be estimated by the length of the equivalent magnetic dipole and the roots of the zero-order Bessel function [35], [36]: On one hand, according to the asymmetric boundary condition at $\rho = 0$, $R_0$ (i.e., $\rho = R_0$, $M = 0$; and $\rho = 0$, $\partial M/\partial \rho = 0$), the length of the prototype magnetic dipole should thus satisfy $L = 2R_0 = n\lambda_0/4$, as shown in (2a), where $L$ is the length of equivalent magnetic dipole [37]. The radius of the cavity model can be estimated by (2b). In the single-mode resonant case [38], the normalized radius can be calculated by (3). In the dual-resonant case, the radius of the circular sector patch can be alternatively estimated by (4) [37].

Using (3) and (4), a mode synthesis table (Table 1) can be attained. When $m = 1$, the difference between line 2 and line 4 of Table 1 is $0.01$, which corresponds to the single, fundamental TM$_{01}$ mode resonant case [38]. Values in line 3 and line 7 of Table 1 can be approximately regarded as equal with difference of $0.01$. It can be figured out that a dual, TM$_{01}$/TM$_{02}$ mode resonance can be excited in $L = 2R_0 = 1.25\lambda_0$ case.

Table  1.  Mode synthesis of the conceptual radial-resonant circular sector patch antennas

$2{\bar R_0} = \dfrac{n}{4}$	$n=1$	$0.25$
	${\boldsymbol{n=3}}$	0.75
	${\boldsymbol{n=5}}$	1.25
$2{ {\bar R}_0} = \dfrac{ { {\chi _{0,m} } } }{\pi }$	${\boldsymbol{m=1}}$	0.76
	$m=2$	$1.76$
	$m=3$	$2.75$
$2{ {\bar R}_0} = \dfrac{ { {\chi _{0,1} } + {\chi _{0,2} } } }{ {2\pi } }$		1.26

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In order to maintain a pure radial-mode resonance and suppress the circumferential ones, circumference of the circular sector patch ($R_0\alpha$) should be less than the length of prototype magnetic dipole ($L = 2R_0$), thus the flared angle $\alpha$ should be satisfied with

Therefore, the flared angle $\alpha$ of the radial-resonant circular sector patch antenna should be no more than 115° (i.e., 2-radian). In practical engineering design, such constraint can be slightly modified to $\alpha \le 120°$.

Fig.2 qualitatively illustrates the surface electric, magnetic current density and Electric-field distributions of the first two radial-resonant modes (TM$_{01}$ and TM$_{02}$ modes) within a conceptual microstrip circular sector radiator with short-circuited circumference.

Figure  2.  Radial surface electric/magnetic current density distributions and cross-sectional electric-fields of TM$_{01}$ and TM$_{02}$ modes within a circular sector radiator.

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As shown in Fig.2, a nodal line exhibits on the patch surface and its position $R_s$ can be determined by

In order to disturb the TM$_{02}$ mode properly, twin arc slits with length $L_s$ and width $W_s$ are introduced at $R_s$ [39]. According to the empirical equations [40], the length $L_s$ and the width $W_s$ of slits can be determined by $(7)$ and $(8)$

where $\lambda_H$ is the corresponding wavelength of the high order resonant mode. Therefore, when the center frequency is $3.6$ GHz, the radius of the circular sector patch should be approximately determined as $R_0 = 52.4$ mm. Thus, the initial value of slits can be approximately set as $L_s = 12.6$ mm and $W_s = 2.5$ mm.

A shorting pin is introduced between the feed and the shorting wall, aiming to perturb radial-resonant modes and attain dual-mode resonance [41]. Empirically, the distance between the pin and the center of the circular sector can be set as one-fourth to one-third of the patch radius [42], [43], thus the shorting pin should be set at $(x_1, 0) = (17.5$ mm, 0). Based on this analysis, most of design parameters can be initially determined. Hence, the dual radial-resonant circular sector patch antenna is resulted as shown in Fig.3, and parametric studies are then performed as shown in Fig.4.

Figure  3.  Geometry of the proposed dual radial-resonant antenna.

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In simulation, better impedance is obtained by placing the feeding probe at $(x_0, 0)$ = (12.5 mm, 0) [4], [44] and $\alpha = 90°$. In addition, the radius of the ground plane is set as $R_g = 70.0$ mm, which is larger than one half-wavelength. As shown in Fig.4(a), TM$_{01}$ and TM$_{02}$ modes can be simultaneously excited at 2.3 and 4.85 GHz in the unloaded case. When a pin is loaded, both TM$_{01}$ mode and TM$_{02}$ mode can be perturbed and tuned upward to 3.52 and 5.02 GHz. When slits are incorporated at the nodal line position, TM$_{02}$ mode can be tuned down to 3.91 GHz. When both pin and slits are incorporated, dual radial-resonant characteristic can be yielded at 3.6 GHz band. In Fig.4(b), both TM$_{01}$ and TM$_{02}$ modes are sensitive to the position of the pin. Fig.4(c) and Fig.4(e) indicate that the position and the width of slits have little effect on the two resonant frequencies, but play important roles in impedance matching. Therefore, wider bandwidth can be obtained by properly adjusting the position and width of those slits. As can be seen from Fig.4(d), the length of slits should be a critical parameter for impedance matching, so it should be finely tuned according to formula (7). Based on the above step-by-step numerical studies, the final key parameters can be determined, compared and tabulated in Table 2. It is found that the theoretical and simulated results agree well with each other, with discrepancy less than 6.5%. The correctness and effectiveness of the design approach have been thus numerically validated.

Table  2.  Key parameters of the dual-mode antenna (unit: mm)

Parameter	Theoretical	Simulated
$R_0$	$52.4$	$52.4$
$R_s$	$22.5$	$23.0$
$L_s$	$12.6$	$12.9$
$W_s$	$2.5$	$2.5$
$x_1$	$17.5$	$18.6$
$R_g$	70.0
$x_0$	12.5

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  4.  Parametric studies on the pin, slits and the position of pin and slits. (a) Reflection coefficients: comparison between unloaded, load pin, load slits and load pin and slits cases; (b) $x_1$ ($R_s$ = 23.0 mm, $L_s$ = 12.9 mm, $W_s$ = 2.5 mm); (c) $R_s$ ($x_1$ = 18.6 mm, $L_s$ = 12.9 mm, $W_s$ = 2.5 mm); (d) $L_s$ ($x_1$ = 18.6 mm, $R_s$ = 23.0 mm, $W_s$ = 2.5 mm); and (e) $W_s$ ($x_1$ = 18.6 mm, $R_s$ = 23.0 mm, $L_s$ = 12.9 mm).

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3   Experiment validations

Further experimental validations of the dual radial-resonant design approach are performed herein. Fig.5 shows the photograph of the fabricated dual radial-resonant antenna on air substrate with height $h$ = 3.0 mm. As shown in Fig.6, the measured central frequency is $3.72$ GHz and it matches well with the simulated one with a discrepancy less than 0.1%. The measured −10 dB reflection coefficient bandwidth is 17.4% in a range from $3.4$ to $4.05$ GHz, and the simulated one is 15.3% in a range from $3.43$ to $3.99$ GHz. It is obvious that the antenna under dual radial-resonant operation exhibits a tripled wider impedance bandwidth than that of a conventional circular patch antenna (approximately 6.0%) [4].

Figure  5.  Photograph of the fabricated dual-mode antenna on air substrate.

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Figure  6.  Simulated and measured reflection coefficients of a dual-mode antenna designed on air substrate.

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Fig.7 presents the simulated electric field at 3.63 and 3.9 GHz. As compared to the theoretical analysis in Fig.2, it can be seen that the proposed antenna should operate under TM$_{01}$ and TM$_{02}$ modes at 3.63 and 3.9 GHz. It indicates that the two radial-resonant modes are simultaneously excited under dual-mode resonance. The successful dual-mode excitation reveals the correctness of the dual radial-resonant design approach.

Figure  7.  Simulated E-field distributions at 3.63 GHz and 3.9 GHz.

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Fig.8 demonstrates the measured radiation patterns with the simulated ones in $zx$-plane and $zy$-plane at $f$ = 3.63, 3.78 and 3.9 GHz. As seen, measured and simulated radiation patterns all match well with each other. At $f$ = 3.63, 3.78 and 3.9 GHz, the antenna exhibits measured beamwidths of 128°/72°, 122°/66° and 107°/52° in $zx$-plane and $zy$-plane, respectively. As such, the proposed antennas can exhibit a stable, wide E-plane beamwidth within impedance bandwidth.

Figure  8.  Simulated and measured radiation patterns in $zx$- and $zy$-plane at different frequencies. (a) and (b) at 3.63 GHz; (c) and (d) at 3.78 GHz; (e) and (f) at 3.9 GHz.

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As shown in Fig.8, due to the fully-excited TM$_{02}$ mode, the radiation patterns present slight tilt beams with peak gain occurred at $\theta$ = ±45°. Fortunately, the difference between the measured peak and bore-sight gains is smaller than 2 dB, and the in-band bore-sight gain varies less than 3 dB. The measured average radiation efficiency within impedance bandwidth is about 87.9% and it matches well with the simulated one, as shown in Fig.9. These results validate the dual radial-resonant approach to wide beamwidth, circumferentially short-circuited circular sector patch antenna to be correct and effective.

Figure  9.  Simulated and measured radiation gains and efficiencies.

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Fig.10 shows a printed prototype on a modified Teflon substrate with $h$ = 2.0 mm and $\epsilon_r$ = 2.65, aiming at further verifying the dual-resonant design approach’s versatility. Refer to the case of air substrate, the key parameters of the fabricated antenna can be adjusted to $R_0$ = 35.3 mm, $R_g$ = 50.0 mm, $R_s$ = 17.4 mm, $x_0$ = 5.0 mm, $x_1$ = 18.0 mm, $L_s$ = 12.5 mm, and $W_s$ = 2.1 mm [4].

Figure  10.  Photograph of the printed patch antenna prototype on modified Teflon substrate.

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Fig.11 shows the reflection coefficients of the antenna (simulated and measured) and a reference, circular patch antenna (simulated only) on the same substrate. The center frequency is designed at 3.65 GHz, where a slight discrepancy between the measured and simulated ones is about 0.4%. The fabricated antenna exhibits a dual-resonant characteristic as its simulated counterpart and measured impedance bandwidth (for $|S_{11}| \lt -10$ dB) is 7.1% covering a range from 3.54 to 3.8 GHz, while the simulated one of the reference antenna is 2.3% only. Therefore, the advanced dual radial-resonant design approach should be effective for printed antennas, too.

Figure  11.  Simulated and measured reflection coefficients of dual radial-resonant antenna designed on modified Teflon substrate.

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Fig.12 depicts the simulated and measured radiation patterns of the printed antenna in $zx$- and $zy$-plane at $f$ = 3.55, 3.65, and 3.75 GHz. All measured and simulated patterns are in good agreement with each other, as shown in Fig.12. Wide beamwidths can be found in Fig.12(a), (c), and (e). The measured E-plane beamwidths are 117°, 100° and 120° at $f$ = 3.55, 3.65, and 3.75 GHz, respectively. In H-plane, the corresponding beamwidths are 77°, 68° and 58°. As TM$_{02}$ mode is fully excited, the radiation patterns at all frequencies are slightly titled but still hold stable broadside radiation patterns as like its air-substrate counterpart.

Figure  12.  Simulated and measured radiation patterns in $zx$- and $zy$-plane at different frequencies. (a) and (b) at 3.55 GHz; (c) and (d) at 3.65 GHz; (e) and (f) at 3.75 GHz.

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Fig.13 shows the radiation efficiencies, bore-sight gains and peak gains of the proposed printed dual radial-resonant antenna. Within the impedance bandwidth, both measured and simulated bore-sight gains exhibit a stable characteristic with a minor fluctuation less than 3.0 dB and the maximum measured one can reach to 7.3 dBi. Similar to the air-substrate case, although the peak gain deviates slightly from the +z-direction, the differences between the peak gains and the bore-sight gains are less than 3.0 dB. In addition, as its air-substrate counterpart behaves, the measured and simulated efficiencies agree well with each other and the measured in-band average efficiency is up to 85.7%. Again, these results convince the correctness and effectiveness of the advanced design approach.

Figure  13.  Simulated and measured radiation gains and efficiencies.

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III.   Comparisons and Discussions

Table 3 presents systematical comparisons between the proposed antennas and the latest counterparts in the aspects of operation principle, impedance bandwidth, patch electrical size, HPBW in E-plane, complexity (number of design parameters) and operational mode. Compared to its counterparts, the proposed antennas exhibit the lowest configuration complexity with only 6 key design parameters and an extremely low profile, which makes the proposed one more promising to conformal design [21]–[46]. Compared to the wideband counterparts [21], [31], the advanced antenna have a wider beamwidth, and can be flexibly implemented on the ultra-slim substrate. Compared to the designs with identical height and wider bandwidth [24], the advanced antenna can exhibit a more compact size of less than 1.0-wavelength. Such merit makes the advanced antenna more useful for array designs than its counterpart [24]. Comparing to the low-profile designs in [32], [33], the advanced antenna’s bandwidth is nearly tripled to the counterparts’. In addition, the proposed antennas can be easily implemented and fabricated without introducing additional cavity [25], multiple elements [32], or special blind bolt fence [33]. Compared with the self-balanced counterparts [31], [45], the proposed antennas are independent to the size and shape of the ground plane and more suitable for various applications mounted above a bulky ground plane. Besides, the wider impedance bandwidth and HPBW can also be obtained by adjusting the flared angle α or cooperating with other methods. Therefore, the comparative results evidently prove the effectiveness and advantages of the radial-resonant design approaches.

Table  3.  Wide beamwidth magnetic-type antennas for comparisons (N.A. =Not Available)

References	Principle of operation	Impedance bandwidth	Patch electrical size	HPBWs E-plane	Number of design parameters	Operational modes
[21]	Parasitic elements	34.8%	0.9$\lambda_g$ × 0.9$\lambda_g$ × 0.4$\lambda_g$	101°	13	N.A.
[24]	Parasitic elements	12.0%	0.45$\lambda_g$ × 1.02$\lambda_g$ × 0.029$\lambda_g$	140°	11	TM$_{10}$/TM$_{12}$
[25]	Metallic cavity	9.9%	0.49$\lambda_g$ × 0.49$\lambda_g$ × 0.07$\lambda_g$	116°	7	N.A.
[31]	Self-balanced magnetic dipole	20.0%	0.29$\lambda_g$ × 0.049$\lambda_g$	90°–100°	6	TM$_{11}$/TM$_{3/4, 1}$
[32]	Parasitic elements	2.7%	0.52$\lambda_g$ × 0.52$\lambda_g$ × 0.03$\lambda_g$	132°	8	TM$_{11}$
[33]	Blind bolt fence	3.0%	0.19$\lambda_g$ × 0.19$\lambda_g$ × 0.07$\lambda_g$	107°	11	TM$_{10}$
[45]	Self-balanced magnetic dipole	16.0%	0.29$\lambda_g$ × 0.049$\lambda_g$	115°–130°	7	TM$_{11}$
[46]	Parasitic elements	13.4%	1.15$\lambda_g$ × 4.95$\lambda_g$ × 0.1$\lambda_g$	126°	16	N.A.
This work	Dual radial-resonant	17.4%/7.1%	0.625λg × 0.03λg	100°–128°	6	TM01/TM02

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IV.   Conclusions

In this article, a novel design approach to radial-resonant MPAs has been systematically advanced. Dual ${\rm{TM}}_{0m}\;(m=1,\,2)$ modes resonant, wide beamwidth MPAs have been successfully designed and implemented on both air and dielectric substrates. As experimentally demonstrated, advanced antennas exhibit wide beamwidth characteristics within $zx$-plane (i.e., approximately 128°). Compared to existing design approaches, the advanced radial-resonant one can maintain the inherent low-profile characteristic of the MPAs, offer broader bandwidth and wider beamwidth, exhibit simpler configuration in geometry, etc. Therefore, the proposed design approaches would be promising in development of a variety of other low-profile wide beamwidth microstrip antennas in the future.