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With the increasing demand for high speed reliable communications, smart antennas, such as the Butler Matrix array, can be used to develop a system that increases the performance of a wireless system. The Butler matrix is a switched beam array system which can produce orthogonal uniform beams. The main objective is to improve the efficiency of the power in a 90-degree bend. Also, the double-mitered bend is particularly interesting since it provides a substantially lower reflection coefficient and a lower value of S
_{12} at a frequency of 2.4 GHz compared to an unmitered one. Therefore, this paper describes an optimum design using a double-mitered method with a 2 × 2 and a 4 × 4 Butler Matrix array, operating at 2.4 GHz which is used in wireless systems with an FR4 substrate.

A smart antenna system can be used to improve the performance of wireless communications [_{12}, S_{21}, and VSWR are achieved.

This paper is organized as follows. In Section 2, materials and methods are described. In Section 3, simulation results are shown to assess the validity of the proposed approach. Finally, conclusions are drawn in Section 4.

Designing 90-degree bends for transmission lines in a Butler-Matrix causes discontinuities near the bend. In the region of discontinuities, the wide line varies as the transition discontinuities change in the microstrip line. Consequently, these discontinuities will affect the power passing through the microstrip line, in the structure of the Butler matrix. Hence, to yield optimum transmission, different methods such as right-angled corners are required.

In the right-angled corner, the capacitance value increases and the area around the microstrip line will be charged; it will effectively act as a capacitance. Due to charge accumulation, particularly at the outer corner of a bend, an excess capacitance is created, while current interruptions rise because of the excessive inductances [

It has been demonstrated that the mitered has a better figure of merit than unmitered in terms of the S11 (the reflected power at the transmitter) parameter at a 2.45-GHz operating frequency [

electromagnetic waves to interface with the microstrip line and causes a loss of power in the transmission line of the Butler matrix network. In comparison, the right-angled bend provides negligible radiation loss, so that it can be used in Butler matrix systems [

The double-mitered case is particularly interesting, since it provides a substantially low reflection coefficient over the frequency range of 22 - 38 GHz [

To achieve better S-parameter coefficients, some parts of the microstrip line are added to the corner of a single mitered. It has been indicated that a mitered bend produces a performance at least as good as than curved bends at least up to a frequency of about 10 GHz. This applies to a wide range of bend angles, from 30˚ up to 120˚ [

The value of the capacitance of the optimal mitered is less than the unmitered. Therefore, the reflection coefficient is enhanced. To determine the value of h (height of substrate), the following values for different parameters are used at operating frequency of 2.4 GHz [

Z 0 = 120 π ε e f f [ ( W H ) + 1.393 + 2 3 ln ( W H + 1.444 ) ] ( o h m s ) when W H ≥ 1

ε e f f = ε r + 1 2 + ε r − 1 2 [ 1 + 12 ( H W ) ] − 1 2 when W H ≥ 1

ε e f f = the effective dielectric constant of microstrip

Z 0 = characteristics impedance = 50 Ω

W = width of substrate

377 Ω = characteristics impedance of free space

H = height of substrate = 1.44 mm

ε r = relative permittivity

As such, the value of w become 2.4 mm, and the initial value of the miter before adding substrate is 1. 99 mm. The value of w h will be 1.66.

In this section, the results for the design of butler matrices are presented in two cases: 2 × 2 Butler matrix and 4 × 4 Butler matrix.

To implement and design a 2-Port Butler Matrix, a hybrid coupler, two patch antennas and two micro strips transmission lines are required to connect the Hybrid and patch antenna to each other. Therefore, the optimum mitered bend in the transmission line is used to increase the S_{21}.

To design 90 degrees bending, the method of optimum mitered bend is utilized. Thus, the zero-phase shifter is required to connect the hybrid coupler and the patch antenna to each other, as shown in _{11} parameter is in length of λ/4, as shown in _{12} and S_{21} are about zero dB at the operated frequency 2.4 GHz (see

The Voltage standing wave ratio (VSWR) of the connection line between the Hybrid and the patch antenna is shown in

As it can be seen in

The S parameter magnitude and VSWR at the design frequency of 2 × 2 Butler matrix are shown in

The Beam radiations of 2 × 2 Butler matrices when Port 1 and Port 2 are fed to the source by designed frequency of 2.4 GHz are shown in

_{11} parameter increases by −6 dB and S_{12} (the power transferred from Port 2 to Port 1) or S_{21} (the power transferred from Port 1 to Port 2) decreases by −19 dB.

_{11} parameter increases by −5 dB and S_{21} decreases by −30 dB.

The 4-Port Butler Matrix provides four different phases with equivalent distances between each antenna by λ/2. Various combinations of ports can provide other beam locations and shapes. To design a 4 × 4 butler matrix, two 45 phase shifters, two crossovers, and four hybrids are required.

To determine the phase difference of the beam direction between antennas, the angles are set to: θ i = sin − 1 λ Δ φ 2 π d

Where Δ φ is the difference phase along antennas and i = 1 , 2 , 3 ⋯ , ( N − 1 ) . The corresponding d is λ 2 . The values of 1R, 2L, 2R, and 1L are shown in

To design 4 × 4 Butler matrices, a connection between the hybrid coupler and cross over with a zero-phase shifter with optimum power is required. Consequently, the phase shifter plays an important role in this case, and a double miter is used to get an optimum result for the S parameter, as shown in Figures 18-31. The maximum power can be transmitted or received using optimum mitered method of 4 × 4 Butler matrices, since the values of S12 and S21 are about zero dB at the operated frequency 2.4 GHz (see

The optimum mitered technique used for 45 degrees phase shifter connection line between two Hybrids of 4 × 4 Butler matrix (see

As shown in the results, isolation between adjacent beams is provided and different phase of radiation pattern are evaluated. Also, the narrow horizontal beam width capability is also achieved.

A | B | C | D | φ | θ_{i}_{ } | |
---|---|---|---|---|---|---|

1R | −45 | −90 | −135 | −-180 | −-45 | −14.47 |

2L | −135 | 0 | −225 | −90 | 135 | 48.59 |

2R | −90 | −225 | 0 | −135 | −135 | −48.59 |

1L | −180 | −135 | -90 | −45 | 45 | 14.47 |

This paper aims to optimize the bending area and to minimize power losses in Butler matrix network. In order to get an optimum power, the efficiency of power at the 90-degree bend in case enhances both the reflection and transmission coefficients. Therefore, a planar design, including the simulation and implementation of a transmission line with a 90-degree bend, 45 degrees phase shifter, zero phase shifter connection between patch, a hybrid coupler and a cross-over using a microstrip antenna array with Butler beam forming network

for wireless applications is presented for operation at 2.45 GHz. A linear antenna array is designed using the Computer Simulation Technology (CST) software. The beamforming feeder network is designed using an N × N Butler matrix, and realized using quadrature hybrids, phase shifters and crossover circuits. For simulation procedures, the main elements such as the patch antenna, hybrid, and cross-over are designed. Finally, the Butler matrix feed network is simulated and optimized to achieve the required parameters at 2.4 GHz.

The authors declare no conflicts of interest regarding the publication of this paper.

Kiehbadroudinezhad, S., Bousquet, J.-F., Cada, M., Shahabi, A. and Kiehbadroudinezhad, M.A. (2019) Analysis and Design of Different Methods to Reach Optimum Power in Butler Matrix. Int. J. Communications, Network and System Sciences, 12, 19-35. https://doi.org/10.4236/ijcns.2019.122003