Design Approach to a Novel Dual-Mode Wideband ... - IEEE Xplore

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 10, OCTOBER 2017

Design Approach to a Novel Dual-Mode Wideband Circular Sector Patch Antenna Wen-Jun Lu, Member, IEEE, Qing Li, Sheng-Guang Wang, and Lei Zhu, Fellow, IEEE

Abstract— A design approach to a novel wideband circular sector patch antenna is proposed. Design guidelines are laid down based on an approximate 1.5-wavelength, multimode magnetic dipole, and the cavity model. Then, the flared angle of the circular sector patch and the corresponding usable resonant modes for wideband radiation are determined. It is demonstrated that the resonant TM4/3,1 and the TM8/3,1 modes within a 270° circular sector patch radiator can be simultaneously excited, perturbed, and employed to form a wideband unidirectional radiation characteristic with two resonances. Prototype antennas are designed and fabricated to experimentally validate the dualresonant wideband property on a single-layered substrate. It is further demonstrated that the antenna designed on a 5-mm-thick air substrate exhibits an available radiation bandwidth (ARB) of 14.5%, while the printed one designed on a 2-mm-thick modified Teflon substrate exhibits an ARB of 6.5%. It is evidently validated that the proposed approach can be employed to effectively enhance the operational bandwidth of microstrip patch antennas without increasing antenna profile, inquiring multiple radiators or employing reactance compensation techniques. Index Terms— Dual-mode resonance, patch antenna, wideband antenna.

I. I NTRODUCTION

C

ONCEPTUAL design of microstrip antennas was presented in the 1950s [1] and had been intensively studied since the 1970s [2]–[6]. In the past few decades, various wideband techniques of microstrip antennas had been intensively developed [7]. These techniques can be basically categorized into three distinctive types. The first type is the multipleradiator technique. One or more parasitic patches with comparable size are stacked to the primary patch radiator, thus lead to an overall wideband response [8], [9]. The second one is the enhanced-coupling feed technique. In this aspect, the feed line is applied to electromagnetically feed a patch radiator by either coupling in proximity [10] or through an aperture [11]. The third one is the reactance compensation technique. For a patch antenna designed on thick substrates, the equivalent inductance caused by the long probe can be compensated

Manuscript received May 1, 2017; revised June 28, 2017; accepted July 25, 2017. Date of publication July 31, 2017; date of current version October 5, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61471204 and Grant 61427801 and in part by the Top-Level Talent’s Project in Jiangsu Province under Grant 2013-XXRJ-020. (Corresponding author: Wen-Jun Lu.) W.-J. Lu, Q. Li, and S.-G. Wang are with the Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing 210003, China (e-mail: [email protected]). L. Zhu is with the Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau 999078, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2017.2734073

by capacitive plate/gap [12]–[14], U-slot [15], L-probe [16], 3-D-tapered transition [17], E-shape patch [18], backed cavity [19], and parallel-plate disc capacitor [20], leading to emergence of one or more additional, less-radiative resonances near the primary, radiation-caused resonance. Basically, these broadband techniques share one common characteristic that only the dominant resonant mode is excited within a single patch radiator and utilized for the purpose of radiation. If multiple resonant modes with broadside radiation properties (e.g., the odd-order modes such as TM01 and TM03 in a rectangular patch radiator) can be excited in a single patch radiator and then properly tuned to be in proximity, a wideband microstrip patch antenna can be expected to be developed [21]. When the undesired modes within the patch radiator are not sufficiently suppressed, unstable broadside radiation performance [21] or dual-band characteristics will be obtained instead [22]. Recently, a series of wideband design approaches using multiple resonant modes within a patch radiator has been developed: A pair of orthogonal modes of TM10 and TM01 with a square patch radiator is used to realize wideband performance at the cost of high resultant crosspolarization level and low gain [23]. In [24] and [25], the TM10 and TM20 modes within a triangular patch radiator, and the TM01 and TM02 within a circular patch radiator, are, respectively, employed to realize wideband, low-profile antennas with omnidirectional, conical beams. More recently, the TM01 and TM03 modes within a rectangular patch radiator have been utilized to realize stable wideband radiation in the broadside direction [26], [27]. Although the undesired evenorder modes [21] can be fully suppressed, these antennas have an inherent length larger than one wavelength and inevitably exhibit high grating lobe levels [26], [27]. In addition, an airgap layer is required in these designs [26], [27] for bandwidth enhancement, and this may increase the height and configurational complexities. Therefore, it is a challenging task to design a wideband patch antenna with two resonant modes with stable unidirectional radiation, while to further reduce its size, sidelobe level and complexity. In this paper, a novel design approach to a dual-mode, wideband circular sector patch antenna is presented. At first, design criteria are laid down and tabulated, based on an approximate 1.5-wavelength magnetic dipole model [28], and employed to determine the flared angle of the circular sector patch radiator, and the corresponding operational modes. Then, the radiation behaviors of the usable resonant modes within the circular sector patch radiator are theoretically analyzed and numerically validated. A pair of tuning stubs is then employed to perturb the two resonant modes in proximity, resulting

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LU et al.: DESIGN APPROACH TO NOVEL DUAL-MODE WIDEBAND CIRCULAR SECTOR PATCH ANTENNA

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TABLE I F LARED A NGLE , N ORMALIZED R ADIUS , AND P OSSIBLE O PERATIONAL M ODES OF THE C ONCEPTUAL C IRCULAR S ECTOR PATCH A NTENNAS

as clearly described in Fig. 1 α · 2π R0 L ≈ 1.5λ0 = 2π χν1 nπ R0 = λ0 , ν = , n = 1, 2, . . . 2π α R0 1.5 R¯ 0 = ≈ λ0 α nπ R χ 0 ν1 , ν= , n = 1, 2, . . . R¯ 0 = = λ0 2π α

Fig. 1. Conceptual evolution from an approximate 1.5-wavelength magnetic dipole to a circular sector patch radiator.

in a wideband, dual-resonant antenna. Finally, the developed design approach is experimentally verified on thin, single-layer air substrate and modified Teflon substrate, respectively. II. P RINCIPLE AND T HEORY A. Conceptual Design and Operation Principle Basically, a wideband patch antenna with multiple resonant modes for radiation can be initially evolved from a straight, multiresonant magnetic dipole antenna having an approximate length of 1.5λ0 (λ0 is the wavelength of the corresponding center frequency in free space) as those discussed in [28] and [31]. For simplicity, all conceptual designs are performed on an air substrate with relative permittivity of εr = 1. As intuitively demonstrated in Fig. 1, a multiresonant, microstrip circular sector patch antenna would be equivalently resulted in by circumferentially fitting the basic straight, magnetic dipole to the arc periphery of a circular sector with a flared angle α. Therefore, the resonant frequency of the magnetic dipole can be estimated by (1). On the other hand, the resonant and radiation behavior of the resultant microstrip patch antenna would be dominated by the nonstatic, resonant TMν,1 modes within a circular sector patch radiator having the minimum radius [32], [33], as denoted by (2), where ν is the circumferential Eigen number determined by the flared angle α and χν1 is the first root of the first-order derivative of the v-order Bessel function of the first kind, respectively [34]. In this way, the resonant frequency of the magnetic dipole, and the operational mode of the circular sector patch antenna can be automatically associated with each other by (1) and (2),

(1) (2) (3) (4)

According to the basic theory of circular sector patch antennas [34] and using (1) and (2), the normalized radius R¯ 0 , flared angle α and the corresponding operational resonant mode can then be estimated by using (3) and (4). The predicted results for R¯ 0 by (3) and (4), and the possible operational modes, are tabulated in Table I. It is seen that (1) to (4) and Table I can provide the basic design guidelines for multimode circular sector patch antennas. There should be three constraints when determining the flared angle α and the possible operational modes: 1) first of all, it is noted that the normalized radius estimated by (3) and (4) should be approximately equal to each other; 2) the second high order resonant mode for radiation should share the identical polarization and the similar broadside radiation characteristics with its low-order counterpart [26], [27]; 3) to maintain the minimum radius [32], [33], only the TMν,1 modes can be employed for radiation, and the undesired, low-order TMν2 modes with n = 1 and ν = π/α should be sufficiently suppressed or detuned. Under the constraint 1 and as tabulated in Table I, it is known that the first even-order TMν,1 modes with n = 2 and ν = 2π/α should be used for primary radiation. It is also known that the flared angle of the circular sector patch should be chosen in a range between 2π/3(120°) to 3π/2(270°). To ensure that the second resonant mode share identical polarization with the first usable one (i.e., the constraint 2), the second mode should be an even-order TMν,1 mode with n = 4 and ν = 4π/α. As noted in Table I, for a circular sector patch with a small α, the resultant normalized radius is larger than the case of a large α. Especially for α ≤ π, the normalized radius is larger than or approximately equal to 0.5. In these cases, when the second even-order TM4π/α,1 mode is excited, the low-order TMπ/α,2 mode may tend to be simultaneously excited, too. To clearly demonstrate the possible excited modes within a circular sector patch radiator, the roots for TMπ/α,2 modes, TM2π/α,1 modes, and TM4π/α,1 modes are

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TABLE II ROOTS OF TMπ/α,2 , TM2π/α,1 , AND TM4π/α,1 M ODES

tabulated in Table II. In this way, the constraint 3 can be quantitatively expressed by (5) and (6): the roots of TMπ/α,2 modes should not fall between the roots of the two usable TM2π/α,1 and TM4π/α,1 modes, or they should be detuned to deviate from the latter one as possible, so that the undesired, redundant TMπ/α,2 modes could be removed outside the effective radiation bandwidth (5) / χ 2π ,1 , χ 4π ,1 χ πα ,2 ∈ α α χ π ,2 − χ 4π → max . (6) ,1 α α

As tabulated in Table II, it can be seen that the undesired TMν,2 modes could be evidently excited, and these redundant modes could be hardly suppressed for α ≤ π. Otherwise, configurational complexity is required for mode suppression. Therefore, the cases of α ≤ π are not satisfied with the constraint 3 and (5) and (6), and they are not suitable for dualresonant, wideband antenna designs with simple structures. As observed from Table II, the TMπ/α,2 modes can be gradually detuned to resonate outside the effective radiation band comprised by the TM2π/α,1 and TM4π/α,1 modes, and then moved far away from the TM4π/α,1 mode with the increasing of α. Thus, the constraint 3 can be automatically satisfied by employing α > π. Therefore, a circular sector patch antenna with flared angle of 3π/2 (270°), and an approximate radius varied from 0.318- to 0.359-wavelength can be determined as the initial prototype in further designs accordingly, to minimize the size of the antenna as much as possible [32], [33]. Due to its relatively small size (i.e., normalized radius is significantly smaller than 0.5), such an antenna should provide great potential for application in array antennas without grating lobes [26], [27]. Based upon these design guidelines, and to further verify whether the high-order resonant mode should satisfy the broadside radiation condition in constraint 2, radiation behavior of the two usable resonant modes within a microstrip circular sector radiator with a flared angle of 270° should be studied in a more rigorous and precise way.

Fig. 2. Surface electric and virtual magnetic current density distributions of the first four nonstatic, resonant modes within a circular sector radiator with flared angle α = 270°.

B. Analysis of Resonant Modes The surface electric and virtual magnetic current density distributions of the first four, nonstatic resonant modes within a microstrip circular sector radiator are shown in Fig. 2. The circumferential dependencies with respect to the source coordinate ϕ of the equivalent magnetic current distributions are also presented in Fig. 2. According to the equivalent surface electric and magnetic current distributions of the TM4/3,1 and the TM8/3,1 modes, they should share identical

natural boundary conditions [28], [30] within two principal cut planes, and thus exhibit an infinite electric wall (E. W.) and an infinite magnetic wall (M. W.) within x y and zx planes, respectively. For a z-oriented coaxial probe placed along the x-axis (i.e., the angular bisector of the patch), an infinite E.W. boundary condition within the x y plane, and an infinite M. W. one within the zx plane should be exhibited [35]. Owing to the boundary condition matching between the patch and the


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probe within the x y and zx planes, the TM4/3,1 and TM8/3,1 modes can be sufficiently excited by a z-oriented probe placed along the x-axis. While for the orthogonal TM2/3,1 and TM2,1 modes exhibiting an infinite E.W. boundary condition within the zx plane, they should be automatically suppressed due to the mismatching of natural boundary conditions in the zx plane. Hence the radiation pattern of the usable even-order resonant modes, i.e., TM4/3,1 and TM8/3,1 modes, can be theoretically calculated by (7)–(12), as intensively discussed in [6] and [36] ⎧

χ 4 ,1 ρ ⎪ 4 ⎪ 3 ⎪ −2E cos ϕ J , for TM 4 ,1 4 ⎪ 0 ⎨ 3 3 R0 3 Mϕ (ρ , ϕ ) =

ρ χ 8 ⎪ 8 ⎪ 3 ,1 ⎪ cos ϕ , for TM 8 ,1 ⎪ ⎩2E 0 J 83 3 R0 3 Fϕ =

ε0 h R0 4π

Fρ2 =

Eθ =

Eϕ =

3π/4

Mϕ (R0 , ϕ )e j k R0 sin θ cos(ϕ −ϕ) dϕ

−3π/4

(8) 3π ε0 3π j kρ sin θ cos 4 +ϕ h Mϕ ρ , − dρ e 4π 0 4 (9)

0 3π ε0 3π j kρ sin θ cos 4 −ϕ e h Mϕ ρ , dρ 4π 4 R0 (10) 3π 3π −ϕ − Fρ1 sin +ϕ − j ωη0 Fρ2 sin 4 4 + Fϕ cos ϕ − ϕ (11) 3π +ϕ + Fρ2 +j ωη0 cos θ Fρ1 cos 4 3π −ϕ − Fϕ sin(ϕ −ϕ) × cos 4 (12)

Fρ1 =

(7)

R0

where ε0 is the permittivity in vacuum, h is the thickness of the substrate, η0 is the wave impedance in free space, k is the wavenumber, ω is the operational angular frequency, R0 is the radius of the circular sector, E 0 is the magnitude of the peripheral E-field, Jv (·) is the v-order Bessel function of the first kind, Mϕ denotes the virtual magnetic current density distribution, Fϕ is the magnitude of the vector potential generated by Mϕ , Fρ1 and Fρ2 are the magnitudes of the vector potentials dominated by the virtual magnetic currents along the two radius, and E θ and E ϕ denote the magnitudes of the radiated far-field components. As numerical validations, the normalized, E-plane (i.e., zx plane) radiation patterns of the two modes are simulated by employing Zeland’s IE3D [37]. In the simulation, the ground plane of the circular sector patch antenna is supposed to be ideal and infinity. To sufficiently excite the usable modes, the z-oriented probe is placed at the edge of the patch on the x-axis as previously discussed. As observed from Fig. 3, it is seen the analytical and numerical results agree well with each other, especially within the main beam. The TM4/3,1 mode

Fig. 3. Radiation behaviors of the two usable resonant modes within a circular sector patch radiator with a flared angle of 270°. (a) TM4/3,1 mode and (b) TM8/3,1 mode.

Fig. 4.

Proposed dual-resonant wideband circular sector patch antenna.

exhibits a good, broadside radiation pattern with |E ϕ | = 0. Although the broadside radiation level tends to reduce about 5 dB than the peak one, the TM8/3,1 mode still exhibits a stable broadside pattern with an identical polarization and a low cross-polarization level (i.e., |E ϕ | = 0) as the TM4/3,1 mode behaves. It is concluded that the TM8/3,1 mode still potentially exhibits a usable broadside radiation characteristic, just behaves as those high-order modes within a circular sector patch radiator presented in [3], and thus, the broadside radiation condition in constraint 2 is evidently satisfied. Using the results shown in Tables I and II and basing upon the mode analyses, a circular sector patch antenna with flared angle of 270°, radius of about 0.35-wavelength, and an exciting probe along the angle bisector of the sector can be designed.

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Fig. 5. Parametric studies on the tuning stub. (a) Comparison between initially loaded (L s = 14 mm, Ws = 5.5 mm, and β = 67.5°) and unloaded cases. (b) L s (Ws = 5.2 mm and β = 75°). (c) Ws (L s = 15.4 mm and β = 75°). (d) β (L s = 15.4 mm and Ws = 5.2 mm).

C. Dual-Mode Design Suppose the antenna is designed on an air substrate with height h = 5 mm, at the center frequency of 3.25 GHz. Using (1)–(4), the radius of the circular sector can be approximately determined as R0 = 32 mm. As discussed in [28] and [38], [39], a pair of open-circuited, tuning stubs with length of L s , width Ws can be introduced to a certain position ϕ = ±β on the periphery of the circular sector radiator to perturb the two desired resonant modes in proximity to form a wideband operation under dual-mode resonance. Hence, the resultant dual-mode circular sector patch antenna is shown in Fig. 4. Using the empirical equations in [38], the length L s of the tuning stub can be set to approximately equal to one-quarter wavelength of the TM8/3,1 mode (which should resonate at about 5.51 GHz). Therefore, the initial value of stub length can be approximately chosen as L s = 14 mm. According to the empirical values presented in [39], the width of the stub

Fig. 6.

Photograph of the fabricated antenna prototype on an air substrate.

can be set to approximately equal to one-tenth wavelength of the TM8/3,1 mode. Therefore, the initial value of stub width can be chosen as Ws = 5.5 mm. The stubs should be placed near the E-field’s null of the first resonant mode, so that only the high order mode is perturbed and moved downward its low order, rarely perturbed counterpart [22], [26]–[28]. Therefore,


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Fig. 7. Simulated and measured input impedances and reflection coefficients. (a) Input impedances and (b) reflection coefficients.

the initial position of the stubs should be symmetrically placed at β = 67.5° and β = 292.5° (or, β = −67.5°, alternatively), as denoted in Fig. 2. In this way, all the design parameters of the antenna can be initially determined. For the comparison, the unloaded case with Ws = L s = 0 is also considered. To suppress the undesired TM0,m modes (m = 1, 2, 3, . . .), the center of the circular sector is electrically shorted to the ground plane by a metallic post as presented in [6] and [39]. Parametric studies are carried out by employing the Zeland’s IE3D simulator with the relevant results as shown in Fig. 5. In the simulation, the feeding probe is placed at (x 0 , 0) = (18, 0) for better impedance matching as discussed in [6] and [40], and the radius of the ground plane is set as Rg = 60 mm. In this way, the diameter of the ground plane is set to be slightly larger than one wavelength centered at 3.25 GHz, as conventionally used in microstrip antennas [6]. As seen from Fig. 5(a), the TM8/3,1 mode is insufficiently excited in the unloaded case. As an evident, this mode exhibits a large inductive reactance [6]. When a pair of stubs is loaded near the E-field’s null of the TM4/3,1 mode, the TM8/3,1 mode can be sufficiently excited and moved downward the rarely perturbed TM4/3,1 resonant mode. In this way, a dual-resonant, wideband characteristic can be potentially realized, just as those presented in [26] and [28]. As further demonstrated in Fig. 5(b)–(d), the dual-resonant wideband characteristic is more sensitive to the positions of the tuning stubs than to their lengths and widths. With the aid of these parametric studies, the final design parameters of the antenna can be determined as R0 = 32 mm, Rg = 60 mm, Ws = 5.2 mm, L s = 15.4 mm, x 0 = 18 mm, and β = 75°.

Fig. 8.

Simulated surface current density. (a) 3.15 GHz and (b) 3.45 GHz.

III. N UMERICAL AND E XPERIMENTAL VALIDATIONS Prototype antennas are then designed, fabricated, and measured to verify the design approach. According to the design parameters presented in Section II, the photograph of one of the fabricated prototypes is shown in Fig. 6. To suppress the undesired TM0,m modes (m = 1, 2, 3, . . .), the center of the patch is electrically shorted to the ground plane by a metallic post with radius of 1.25 mm. The antenna prototype is measured by employing an Agilent’s N5230A vector network analyzer and a Satimo’s Starlab near-field antenna measurement system. As can be seen from Fig. 7, the fabricated antenna exhibits a wideband characteristic with two resonances from 3.07 to 3.55 GHz (for |S11 | lower than −10 dB). The measured frequency responses for both the input impedance and the reflection coefficient agree well with the simulated ones. For the comparison, the simulated impedance and reflection coefficient frequency responses of a conventional TM11 mode circular patch antenna (i.e., the reference antenna) designed on the same substrate with an identical ground plane size are also displayed. It is seen that the proposed antenna exhibits an impedance bandwidth of 14.5%, while the one of the singlemode reference antenna is 8.2% only. Therefore, it is verified that the proposed approach should be effective and useful

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Fig. 10.

Fig. 9. Simulated and measured radiation patterns at different frequencies. (a) and (b) x z and y z plane at 3.3 GHz. (c) and (d) x z and y z plane at 3.4 GHz. (e) and (f) x z and y z plane at 3.5 GHz.

for impedance bandwidth enhancement of microstrip patch antennas. The simulated surface current density distributions at 3.15 and 3.45 GHz are demonstrated in Fig. 8. As compared to Fig. 2, it is clearly seen that the proposed antenna is simultaneously operating under TM4/3,1 mode at 3.15 GHz and TM8/3,1 mode at 3.45 GHz for dual-mode resonating radiation. Therefore, the two resonant modes have been evidently excited and employed for wideband radiation as expected. The revealed design guidelines and theoretical analysis in the previous section are numerically validated to be correct. The radiation patterns of the proposed antenna are measured and compared with the simulated ones. As can be observed from Fig. 9, all of the measured patterns agree very well with the simulated ones. The antenna exhibits a stable unidirectional beam with low cross-polarization level within most of its impedance bandwidth. It is noted that the simulated cross-polarization level within the E-plane (i.e., zx plane) is lower than −40 dB at all frequencies, hence

Simulated and measured radiation gains and efficiencies.

the numerically simulated cross-polarized E ϕ -components rarely appear in all zx planes. The radiation patterns at all frequencies agree well with the simulated ones. At 3.5 GHz, the radiation pattern exhibits a slightly tilt beam with its peak gain deviated from the boresight direction (i.e., +z-direction), due to the sufficient excited TM8/3,1 mode. However, it still exhibits a stable broadside radiation pattern without grating lobes, and the difference between the peak gain and boresight gain is smaller than 1.5 dB. The maximum sidelobe level at θ = 60° is 12 dB lower than the main one, as shown in Fig. 9(e). As can be seen from Fig. 10, the measured boresight gain varies less than 3 dB within the impedance bandwidth from 3.07 to 3.55 GHz. The antenna exhibits a stable, high boresight gain up to 10.7 dBi, and an in-band average boresight gain (ABG) of 10 dBi. The measured average radiation efficiency is about 88% and matches well with the simulated one. The measured efficiency exhibits a flat, dual-resonant characteristic, just as the simulated one behaves. These experimental results evidently validate the design approach of the dual-mode circular sector patch antenna to be correct and effective. Thus, the available radiation bandwidth (ARB) of the antenna should be determined as the same value of its impedance one. The design approach is then validated on a modified Teflon substrate with relative permittivity εr = 2.65, loss tangent tan δ = 0.002, and thickness h = 2 mm, as shown in Fig. 11. According to the empirical results of the air substrate case, the printed prototype centered at 3.55 GHz is designed by using Zeland’s IE3D with parameters of R0 = 18.5 mm, Rg = 50 mm, Ws = 4 mm, L s = 11 mm, x 0 = 7 mm, and β = 70°. The center of the patch is shorted to the ground plane by a metallic via-hole with radius of 0.7 mm for undesired TM0,m modes (m = 1, 2, 3, . . .) suppression. As can be seen from Fig. 12, the fabricated antenna exhibits a wideband characteristic with two resonances from 3.44 to 3. 67 GHz (for reflection coefficient smaller than −10dB). The measured input impedance and reflection coefficient agree perfectly well with the simulated ones. For comparison, the simulated impedance and reflection coefficient of a conventional TM11 mode circular patch antenna (i.e., the reference antenna) designed on the same substrate with an identical ground plane size is also displayed. It is seen


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Fig. 11. Photograph of the printed patch antenna prototype on modified Teflon substrate.

Fig. 13. Simulated surface current density. (a) 3.50 GHz and (b) 3.65 GHz.

Fig. 12. Simulated and measured input impedances and reflection coefficients. (a) Input impedances and (b) reflection coefficients.

herein that the impedance bandwidth of the proposed antenna is 6.5%, while the one of the single-mode, reference antennas is 2.3% only. Again, the proposed design approach has been evidently verified to be effective for impedance bandwidth enhancement of printed patch antennas. The simulated surface current density distributions at 3.50 and 3.65 GHz are demonstrated in Fig. 13. As compared to Figs. 2 and 8, it is clearly seen that the proposed antenna is operating under both of TM4/3,1 mode at 3.50 GHz, and TM8/3,1 mode at 3.65 GHz. Therefore, the two resonant modes have been excited and employed for wideband radiation. Once again, the design approach and theoretical analysis in the previous section are numerically validated on a single-layered, thin dielectric substrate with a height of 0.023-wavelength in free space at the center frequency.

The radiation patterns of the printed patch antenna with dual resonances are measured and compared with the simulated ones. As can be observed from Fig. 14, the measured patterns agree reasonably well with the simulated ones. The antenna exhibits a stable unidirectional beam with low cross-polarization level within its impedance bandwidth, as conventional microstrip patch antennas behave. Similar to the air substrate case, it is also noted that the simulated cross-polarization level within the E-plane (i.e., zx plane) is lower than −40 dB at all frequencies, so the simulated cross-polarized E ϕ -components do not appear in all zx planes. The measured radiation patterns at all frequencies agree well with simulated ones. At 3.66 GHz, the radiation pattern exhibits a slightly tilt, asymmetrical beam with its peak gain deviated from the boresight direction (i.e., +z-direction), due to the sufficient excitation of TM8/3,1 mode. However, it still exhibits a stable broadside radiation pattern without grating lobes and side lobes, and the difference between the peak gain and boresight gain is smaller than 1 dB.

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TABLE III PATCH A NTENNAS W ITH D UAL R ESONANCE FOR C OMPARISONS

Fig. 14. Simulated and measured radiation patterns at different frequencies. (a) and (b) x z and y z plane at 3.46 GHz. (c) and (d) x z and y z plane at 3.56 GHz. (e) and (f) x z and y z plane at 3.66 GHz.

average radiation efficiency is equal to about 82%, and it matches reasonably well with the simulated one. These results have evidently validated again that the proposed design approach is correct and effective for wideband, printed circular sector patch antennas. Therefore, the ARB of the printed antenna should be determined as the same value of its impedance one. Finally, the proposed antennas are comprehensively compared with typical microstrip patch antennas with dual resonance in terms of ARB, ABG, height and operational modes, as tabulated in Table III. It is demonstrated that the proposed antennas are distinctive from their counterparts in terms of operational modes. It is also seen that the proposed antennas have higher boresight gains to all of its counterparts. Even though the antenna’s height is reduced to 0.023λ0 (λ0 is the wavelength of the corresponding center frequency in free space), its ABG is still maintained as high as 7.4 dBi, and the ARB is still kept up to 6.5%. Hence the proposed approach can be directly realized on a thin, single-layered substrate, without introducing additional feed accessories (i.e., directional coupler with 180° phase shift for differential feed [26], capacitive coupled plate [41]) and multilayered configurations (i.e., air-gap or feed-line layer [26], [27]). Since the dual-resonant characteristic of the proposed antennas is realized by incorporating two resonant modes sharing identical polarization, rather than the orthogonal ones [23], [41], they exhibit a much higher gain and a better polarization purity than their counterparts [23], [41]. In addition, the proposed antennas have stable unidirectional beam without grating lobes. Therefore, they should be more promising for array applications than their counterparts in [23], [26], [27] and [41]. In general, the proposed antennas should exhibit superior performance and lower configurational complexity to most of the existing wideband patch antennas with dual-resonant characteristics, while maintaining the inherent low-profile merit of the microstrip patch antennas. IV. C ONCLUSION

Fig. 15. Simulated and measured radiation gains and efficiencies of the printed wideband patch antenna.

As can be seen from Fig. 15, the measured boresight gain varies less than 3 dB within the impedance bandwidth from 3.44 to 3.67 GHz. The antenna exhibits a stable boresight gain as high as to 8.1 dBi, and the in-band ABG is 7.4 dBi. The measured radiation efficiency exhibits a dual-resonant characteristic, just as the simulated one behaves. The measured

In this paper, a new design approach to a novel dualmode wideband patch antenna is systematically developed by simultaneously exciting and merging the TM4/3,1 and TM8/3,1 modes within a single circular sector radiator with flared angle of 270°. The circular sector patch antenna is conceptually evolved from an approximate 1.5-wavelength magnetic dipole. In this way, the operational modes can be determined by employing the cavity model, and the dualresonant operation principle can be revealed by utilizing mode analyses. The design approach to the proposed antenna has


been experimentally validated on both single-layered air and modified Teflon substrates with thin profiles. The proposed design approach has provided clear physical insights into its wideband operation under dual-mode resonance, and it can be easily incorporated with other wideband patch antenna design techniques (e.g., using stacked patches [8], [9], utilizing thick substrates and capacitive compensation [12], [16]). Therefore, it would be a promising design approach to the development of novel, broadband microstrip antennas. ACKNOWLEDGMENT The authors would like to thank Y. Yu, C.-Y. Yuan, C. Gao, and H.-Q. Yang from the Nanjing University of Posts and Telecommunications, Nanjing, China, for their help in prototype fabrication and test. They also would like to thank Prof. Y.-M. Bo and Prof. W. Cao from the Nanjing University of Posts and Telecommunications, for their beneficial suggestions on this paper. R EFERENCES [1] G. Deschamps and W. Sichak, “Microstrip microwave antennas,” in Proc. 3rd Symp. USAF Antenna Res. Develop. Prog., Monticello, IL, USA, Oct. 1953, pp. 1–21. [2] R. Munson, “Conformal microstrip antennas and microstrip phased arrays,” IEEE Trans. Antennas Propag., vol. AP-22, no. 1, pp. 74–78, Jan. 1974. [3] Y. T. Lo, D. Solomon, and W. Richards, “Theory and experiment on microstrip antennas,” IEEE Trans. Antennas Propag., vol. -AP-27, no. 2, pp. 137–145, Mar. 1979. [4] S. A. Long and M. Walton, “A dual-frequency stacked circulardisc antenna,” IEEE Trans. Antennas Propag., vol. AP-27, no. 2, pp. 270–273, Mar. 1979. [5] D. M. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. New York, NY, USA: Wiley, 1995. [6] R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook. Boston, MA, USA: Artech House, 2001. [7] K.-F. Lee and K.-F. Tong, “Microstrip patch antennas-basic characteristics and some recent advances,” Proc. IEEE, vol. 100, no. 7, pp. 2169–2180, Jul. 2012. [8] R. Q. Lee, K. F. Lee, and J. Bobinchak, “Characteristics of a two-layer electromagnetically coupled rectangular patch antenna,” Electron. Lett., vol. 23, no. 20, pp. 1070–1072, Sep. 1987. [9] D. M. Pozar and F. Croq, “Millimeter-wave design of wide-band aperture-coupled stacked microstrip antennas,” IEEE Trans. Antennas Propag., vol. 39, no. 12, pp. 1770–1776, Dec. 1991. [10] P. B. Katehi, N. Alexopoulos, and I. Y. Hsia, “A bandwidth enhancement method for microstrip antennas,” IEEE Trans. Antennas Propag., vol. AP-35, no. 1, pp. 5–12, Jan. 1987. [11] D. M. Pozar, “Microstrip antenna aperture-coupled to a microstripline,” Electron. Lett., vol. 21, no. 1, pp. 49–50, Jan. 1985. [12] P. S. Hall, “Probe compensation in thick microstrip patches,” Electron. Lett., vol. 23, no. 11, pp. 606–607, May 1987. [13] M. J. Alexander, “Capacitive matching of microstrip patch antennas,” IEE Proc. H Microw., Antennas Propag., vol. 136, no. 2, pp. 172–174, Apr. 1989. [14] G. A. E. Vandenbosch and A. R. Van de Capelle, “Study of the capacitively fed microstrip antenna element,” IEEE Trans. Antennas Propag., vol. 42, no. 12, pp. 1648–1652, Dec. 1994. [15] K. F. Lee, K. M. Luk, K. F. Tong, S. M. Shum, T. Huynh, and R. Q. Lee, “Experimental and simulation studies of the coaxially fed U-slot rectangular patch antenna,” IEE Proc.-Microw., Antennas Propag., vol. 144, no. 5, pp. 354–358, Oct. 1997. [16] K. M. Luk, C. L. Mak, Y. L. Chow, and K. F. Lee, “Broadband microstrip patch antenna,” Electron. Lett., vol. 34, no. 15, pp. 1442–1443, Jul. 1998. [17] N. Herscovici, “A wide-band single-layer patch antenna,” IEEE Trans. Antennas Propag., vol. 46, no. 4, pp. 471–474, Apr. 1998. [18] F. Yang, X.-X. Zhang, X. Ye, and Y. Rahmat-Samii, “Wide-band E-shaped patch antennas for wireless communications,” IEEE Trans. Antennas Propag., vol. 49, no. 7, pp. 1094–1100, Jul. 2001.

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Wen-Jun Lu (M’12) was born in Jiangmen, Guangdong, China, in 1978. He received the B.E. and Ph.D. degrees in communication engineering and electronic engineering from the Nanjing University of Posts and Telecommunications (NJUPT), Nanjing, China, in 2001 and 2007, respectively. He was a Lecturer from 2007 to 2009, an Associate Professor from 2009 to 2013, and has been a Professor Since 2013 with the Jiangsu Key Laboratory of Wireless Communications, NJUPT. In 2013, he joined University College London, London, U.K., as a Visiting Scholar. In 2014, he joined the University of Macau, Macau, China, as a Guest Research Fellow. In 2016, he joined National Sun Yat-sen University, Kaohsiung, Taiwan, as a Visiting Professor. He has authored or coauthored over 120 technical papers published in peer-reviewed international journals and conference proceedings. He is the Translator of the Chinese version “The art and science of ultrawideband antennas”(by H. Schantz). He has authored the book “Antennas: concise theory, design and applications” (in Chinese). He is the Inventor or Co-Inventor of 20 granted Chinese patents. His current research interests include antenna theory, wideband antennas, and antenna arrays. Dr. Lu was a recipient of the Exceptional Reviewers Award for the IEEE T RANSACTIONS ON A NTENNAS AND P ROPAGATION in 2016. He was also a co-recipient of other six Scientific and Technological Awards granted by the Jiangsu Province, Chinese Institute of Electronics, and Chinese Institute of Communications, respectively. He received the Award of New Century Excellent Talents in Universities from the Ministry of Education of China in 2012, and the Nomination Award of Top-100 Outstanding Ph.D. Dissertation of China in 2009. He has been an Editorial Board Member of International Journal of RF and Microwave Computer-Aided Engineering since 2014. He currently serves as a regular reviewer for 15 international journals (including the four IEEE and three IET journals) and many international conferences.

Qing Li was born in Xuzhou, Jiangsu, China, in 1993. She received the B.Sc. degree in electronics and information engineering from the Nanjing University of Posts and Telecommunications, Nanjing, China, in 2015, where she is currently pursuing the M.Eng. degree in communication engineering. Her current research interests include the microtrip antennas theory and design approach.

Sheng-Guang Wang was born in Zhangye, Gansu, China, in 1993. He received the B.S. degree in information and computational science from the Nanjing University of Posts and Telecommunications, Nanjing, China, in 2015, where he is currently pursuing the M.Eng. degree. His current research interests include the multimode antenna theory and design approach.

Lei Zhu (S’91–M’93–SM’00–F’12) received the B.Eng. and M.Eng. degrees in radio engineering from the Nanjing Institute of Technology, Nanjing, China, in 1985 and 1988, respectively, and the Ph.D. degree in electronic engineering from the University of Electro-Communications, Tokyo, Japan, in 1993. From 1993 to 1996, he was a Research Engineer with Matsushita-Kotobuki Electronics Industries Ltd., Tokyo. From 1996 to 2000, he was a Research Fellow with the École Polytechnique de Montréal, Montréal, QC, Canada. From 2000 to 2013, he was an Associate Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. In 2013, he joined the Faculty of Science and Technology, University of Macau, Macau, China, as a Full Professor, and has been a Distinguished Professor since 2016. Since 2014, he has been the Head of the Department of Electrical and Computer Engineering, University of Macau. He has authored or coauthored more than 380 papers in international journals and conference proceedings. His papers have been cited more than 4650 times with the H-index of 38 (source: ISI Web of Science). His current research interests include microwave circuits, guided-wave periodic structures, planar antennas, and computational electromagnetic techniques. Dr. Zhu was a recipient of the 1997 Asia–Pacific Microwave Prize Award, the 1996 Silver Award of Excellent Invention from Matsushita-Kotobuki Electronics Industries Ltd., and the 1993 First-Order Achievement Award in Science and Technology from the National Education Committee, China. He was the Associate Editors of the IEEE T RANSACTIONS ON M ICROWAVE T HEORY AND T ECHNIQUES from 2010 to 2013, and the IEEE M ICROWAVE AND W IRELESS C OMPONENTS L ETTERS from 2006 to 2012. He served as the General Chair of the 2008 IEEE MTT-S International Microwave Workshop Series on the Art of Miniaturizing RF and Microwave Passive Components, Chengdu, China, and a Technical Program Committee Co-Chair of the 2009 Asia–Pacific Microwave Conference, Singapore. He served as a member of the IEEE MTT-S Fellow Evaluation Committee from 2013 to 2015, and the IEEE AP-S Fellows Committee from 2015 to 2017.