Broadband single-layered 3 × 3 Butler matrix (ABFN)

Figure 1(b) shows a 3 × 3 Butler matrix ABFN with three inputs (port-C, port-L, and port-R) and three outputs (port-1, port-2, and port-3), in which there are two quadrature hybrids Q ₁, one quadrature hybrid Q ₂, and three fixed phase shifters β ₁, β ₂, and β ₃. As we know, the ideal quadrature hybrid couplers can be expressed by an orthogonal transmission matrix Q through the coupling coefficient of the quadrature hybrid. The phase difference between two output ports for any input is 90° due to the orthogonal property of the quadrature hybrid.

T_b is the transmission block of Q ₁ and Q ₂ with 90° phase shifter β ₃, and T_o is the transmission block of two phase shifters β ₁ and β ₂ at outputs (i.e. β ₁ = 180° and β ₂ = 90°). For Q ₁ and Q ₂, their corresponding coupling coefficients a are $1/\sqrt 2$ and $1/\sqrt 3$, respectively. Giving the value of quadrature hybrid Q ₁, Q ₂, β ₁, β ₂, and β ₃, the transmission block T _3×3 can be expressed as following:

(1)$$\eqalign{T_{3 \times 3} &= T_b \times T_o \cr & = \left[{\matrix{ {\displaystyle{{\sqrt 2 } \over 2}} & {\displaystyle{{\sqrt 2 } \over 2}j} & 0 \cr {\displaystyle{{\sqrt 2 } \over 2}j} & {\displaystyle{{\sqrt 2 } \over 2}} & 0 \cr 0 & 0 & 1 \cr } } \right]\left[{\matrix{ j & 0 & 0 \cr 0 & {\displaystyle{{\sqrt 3 } \over 3}} & {\displaystyle{{\sqrt 6 } \over 3}j} \cr 0 & {\displaystyle{{\sqrt 6 } \over 3}j} & {\displaystyle{{\sqrt 3 } \over 3}} \cr } } \right] \cr & \times \left[{\matrix{ {\displaystyle{{\sqrt 2 } \over 2}} & {\displaystyle{{\sqrt 2 } \over 2}j} & 0 \cr {\displaystyle{{\sqrt 2 } \over 2}j} & {\displaystyle{{\sqrt 2 } \over 2}} & 0 \cr 0 & 0 & 1 \cr } } \right]\left[{\matrix{ 1 & 0 & 0 \cr 0 & j & 0 \cr 0 & 0 & {-1} \cr } } \right]}$$

For depiction correlations between amplitudes and phases, transmission block T _3×3 in (1) could be represented by Euler's formula as following:

(2)$$T_{3 \times 3} = \displaystyle{{\sqrt 3 } \over 3}\left[{\matrix{ {e^{\,j{{2\pi } \over 3}}} & {e^{\,j{{4\pi } \over 3}}} & {e^{\,j2\pi }} \cr {e^{\,j{{5\pi } \over 6}}} & {e^{\,j{\pi \over 6}}} & {e^{\,j-{\pi \over 2}}} \cr {e^{{-}j\pi }} & {e^{{-}j\pi }} & {e^{{-}j\pi }} \cr } } \right]$$

Based on (2), the phase increment for the C/L/R ports of 3 × 3 Butler matrix are 0°, +120° (2π/3), and −120° (−2π/3), respectively, and signals at four outputs are ideally equal in amplitude of 4.77 dB.

To achieve the wide bandwidth and reduce the size of the quadrature hybrid, a cascaded three-section branch line coupler (BLC) with three-pair coupled line is adopted [Reference Wu and Shen19, Reference Wu and Shen20]. The initial impedance of quarter-wavelength branch lines is given by Z ₁ = 54 Ω, Z ₂ = 58 Ω, Z ₃ = Z ₄ = 143 Ω and the phase of quarter-wavelength is θ ₁ = θ ₂ = θ ₃ = θ ₄ = 90° [Reference Chun and Hong21]. In order to solve the problem of PCB manufacturing difficulty and high impedance affection caused by manufacturing tolerance, a single-layered layout with defected ground structure (DGS) [Reference Lim, Kim, Ahn, Jeong and Nam22] is conducted into the BLC design. DGS structures are used to give the increased equivalent inductance (L) and produce transmission lines with high impedance. The characteristic impedance of high impedance transmission line can be derived by $Zo = \sqrt {L/C}$.

The proposed 3 × 3 Butler ABFN is designed based on the Rogers RO4534 substrate with a relative dielectric constant of 3.50 and a thickness of 0.82 mm as shown in Fig. 2. It is simulated by Mentor Graphics IE3D. The width of 50 Ω microstrip line is 1.80 mm, and the high impedance microstrip line's width of 3 dB and 4.77 dB BLC is 0.5 mm (W ₁) and 0.6 mm (W ₂), respectively. In Figs 3(a)–3(c), the simulated amplitude distribution values at full frequency band of 1.69–2.69 GHz are −5.3 ± 1.5 dB when port-R is excited; −5.3 ± 1.5 dB when port-L is excited; and −5.3 ± 0.7 dB when port-C is excited. The simulated worst-case return loss is 15 dB, and the simulated worst-case isolation among port-C, port-L, and port-R are 17, 23, and 17 dB, respectively. In Fig. 3(d), the averaging simulated phase difference between two neighboring ports at the center frequency of 2.19 GHz is −122° of port-R, +118° of port-L, and −2° of port-C.

Fig. 2. PCB layout of proposed BLC.

Fig. 3. Simulated and measured response of proposed 3 × 3 Butler network (ABFN): (a) port-L excited. (b) Port-C excited. (c) Port-R excited. (d) Transmission phase difference.

Dual-polarized radiation element configuration

To achieve wide bandwidth and ±45° polarizations, the antenna radiation element comprises two cross-dipole arms, four parasitic strips, two perpendicular baluns, and a square bent ground reflector. Compared with the traditional dipole antenna element, a pair of parasitic strips with width W ₁ and gap S ₃ are added to extend the frequency bandwidth and improve the radiation performance [Reference Tao, Feng and Liu23, Reference Tao, Feng, Vandenbosch and Volskiy24]. By adjusting the lengths, widths, and gaps between the dipole arms and parasitic strips (W ₁, W ₂, S ₁, S ₂, S ₃, and their corresponding lengths), the operating frequency band of the antenna can be adjusted flexibly. For impedance matching, two PCB baluns are designed for broadband application [Reference Ye, Zhang, Gao and Xue25–Reference Li, Wu, Pan, Lim, Laskar and Tentzeris28]. The configuration of the balun is displayed in Fig. 4(a) and its equivalent circuit is shown in Fig. 4(b). The matching steps are listed as following:

(3)$$\left\{{\matrix{ {Z_1 = Z_s\displaystyle{{Z_d + jZ_s\tan \beta_sl_t} \over {Z_s + jZ_d\tan \beta_sl_t}}} \cr {Z_b = Z_{0s}\displaystyle{{\,jZ_1Z_s\tan \beta_sl_s} \over {Z_1 + jZ_s\tan \beta_sl_s}}} \cr {Z_a = rZ_b} \cr {Z_3 = {-}jZ_c\cot \beta_cl_c + Z_a\;} \cr } } \right.$$

where Z_d is the input impedance of the printed dipole without the integrated balun; Z_s, β_s, and l_t are the characteristic impedance, phase constant, and the length of the slot line; l_s is the length of the shorted stub; r is the impedance transformer coefficient; Z_c, β_c, and l_c are the characteristic impedance, phase constant, and the length of open stub, respectively. Z_d could be obtained by giving the excitation to the input port of dipole. According to the impedance matching theory, Z ₃ can be deduced from (4).

(4)$$Z_3 = Z_k\displaystyle{{Z_h + jZ_k\tan \beta _hl_h} \over {Z_k + jZ_h\tan \beta _hl_h}}$$

where Zk is defined by the input port impedance with 50 Ω. For simplifying the calculation, the turn ratio of transformer, r could be set to be 1:1 initially. The initial dimensions of the balun can be estimated through above equations and the microstrip line formula. The cross-dipole is printed on the top of a substrate of dielectric constant 3.50 and thickness 0.82 mm. The height of its substrate is selected as 0.238λ ₀ for high gain. By applying parameter optimization in Ansys HFSS, the wideband dual polarization dipole element with W ₁ = W ₂ = 10 mm, S ₁ = S ₂ = 2 mm, and S ₃ = 9 mm is obtained. The size of the proposed antenna element is 81.0 × 49.0 mm². The simulated results of proposed dipoles are shown in Figs 4(c)–4(d). The worst VSWR is less than 1.4 at full operating band and horizontal half-power beamwidth varies from 79° to 83°.

Fig. 4. Geometry of a printed cross-dipole with adjusted integrated balun (a), equivalent circuit of the proposed printed dipole with adjusted integrated balun (b), simulated input impedance/VSWR of proposed elements (c), simulated radiation pattern of horizontal plane at 1690, 2190, and 2690 MHz (d), geometry of dual-polarized panel antennas fed by EBFN (e).

Dual-polarized panel array fed by EBFN

To realize the dual-polarized omni-directional antenna, a medium gain array with three elevation panels working at the full frequency band of 1.69–2.69 GHz is considered. In each elevation panel shown in Fig. 4(e), there are four broadband antenna elements connected by EBFN with 4° electrical down tilt (EDT). By minimizing the mutual coupling between elements, a 0.86λ _o spacing is applied, where λ _o is the wavelength in air of the center frequency of 2.19 GHz. The EBFN is designed based on Chebyshev distribution, and the ideal power levels of four antenna elements are −4.77, 0, 0, and −4.77 dB, respectively. The ideal phases of four antenna elements with 4° EDT are 0°, −21.2°, −42.4°, and −63.5°, respectively.

Dual-polarized omni-directional antenna fed by BFNs

Through connecting output ports of ABFN boards to the input ports of EBFN boards with three identical dual-polarized panel arrays formed in a cylinder as shown in Fig. 1(a), the Butler-based dual-polarized omni-directional antenna is achieved. The input signal flows to the each dual-polarized panel through both ABFN and EBFN. There are six ports in which three ports produce +45° (L+/C+/R+) polarized radiation and other three ports produce −45° (L−/C−/R−) polarized radiation. The whole antenna structure is investigated by Ansys HFSS. The simulation results show that, for port-C with 0° phase increment, gain is 9.1–10.7 dBi and the azimuth null is 5.1 dB; for port-L/R with ±120° phase increment, gain is 9.3–10.8 dBi and the azimuth null is 12.5 dB.