# A New Design of Compact4×4 Butler Matrix for ISM Applications

Authors: Mbarek Traii; Mourad Nedil; Ali Gharsallah; Tayeb A. Denidni
Journal: International Journal of Microwave Science and Technology
 (2008)

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## Abstract

A novel design of a compact4×4 Butler matrix is presented. All the design is based on the use of a Lange coupler with certain geometrical characteristics. This matrix occupies only 20% of the size of the conventional Butler matrix at the same frequency (80% of compactness). To examine the performance of the proposed matrix, the Lange coupler and the Butler matrix were simulated using Momentum (ADS) and IE3D softwares. Simulation results of magnitude and phase show a good performance. Furthermore, a four-antenna array was also designed at 2.45 GHz and then connected to the matrix to form a beamforming antenna system. As a result, four orthogonal beams at −45∘, −15∘, 15∘, and 45∘ are produced. This matrix is suitable for wireless application at ISM band of 2.45 GHz.


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## Body

## 1. Introduction

Smart antenna systems have been introduced to improve wireless
performance and to increase system capacity by spatial filtering, which can
separate spectrally and temporally overlapping signals from multiple users. Switched
beam systems are referred as antenna-array systems that form multiple-fixed
beams with enhanced sensitivity in a specific area. This antenna system detects
signal strength, selects one of the several predetermined fixed beams, and
switches from one beam to another as the user moves. One of the most widely known
of switched beam networks is Butler matrix [1]. It is an N×N passive feedingnetwork with beam steering capabilities for phased array antennas with N outputs and N inputs. Feeding an N-element
antenna array using an N×N Butler matrix, N
orthogonal beams can be generated, and each beam has a gain of the whole array.In most cases, circuits are designed using branch-line directional
couplers [2]. However, in single-layer Butler matrix, hybrid coupler takes up over 50% of the area. It has a dimension of a quarter wavelength square
and occupies a significant amount of the board area. For reducing the area, some
techniques such as the use of lumped-element [3] have been proposed. However,
lumped inductors and capacitors with the required values are not always
available and their tolerance is quite larger. Thus, the need for compact
circuits with simple structure and low cost is more and more attractive.The problem of miniaturization was reported in [4], where semilumped branch-line
couplers have been proposed. The broadband 3 dB coupled line directional
couplers were used in [5]. In this case, a small size has been achieved but the
bandwidth of the Butler
matrix is limited by differential phase characteristics. In [6], the authors
have proposed a stripline Butler
with broadband differential phase matrix. However, the stripline technique presents
high manufacturing costs and complexity [7]. The most attractive technique for
designing and manufacturing microwave circuits is a microstrip technique since
it uses a single laminate layer and allows easy mounting of surface mount
devices and components.In this contribution, a new design
of a compact Butler matrix based on Lange coupler and Lange crossover is
proposed and described. This
matrix is advantageously used to offer a compact structure with low cost. In addition, the significant size reduction
achieved with high performances with low loss compared to the conventional Butler
matrix design. To
have a prevalidation of the proposed design, the proposed Butler matrix has
been simulated with using two softwares Momentum (ADS) and IE3D. Simulation results including
return loss and insertion loss are presented and discussed. Furthermore, to
examine the performance of the proposed matrix in terms of beamforming, a four-antenna
array was connected to this matrix to form a multiple beam antenna system at 2.45 GHz. Simulations were carried out on this beamforming system and the
obtained results are also presented and discussed.


## 2. Butler Matrix Design

A standardN×N Butler matrix
has N input and N output
ports. Matrices with 90° hybrids are symmetrical networks, whereas those with
180°
hybrids are asymmetrical [8]. For each input port, the network will produce
signals with progressive phase shifts at the output ports with equal power. As
a result, this matrix produces N orthogonal beams at its outputs.The Butler  matrix system also
works in a reverse manner. An incident plane wave from a specific direction
produces the appropriate phase difference that will give RF power only at one
input port [9]. This can lead to the implementation of various algorithms that derive the direction of
arrival of the incident signal. Butler
matrices operate like an FFT algorithm. If the linear array of the Butler matrix is on the z axis, the
beams produced are directed [10] as follows: (1)θp=sin−1(ψpβd), where (2)ψp=2p−1Nπ,  where p is the beam number, p∈{0,…,N−1}, and N is the maximum number of beams.Figure1 shows the proposed
4×4 Butler matrix that
uses microstrip Lange couplers
(directional couplers), Lange crossovers, and phase shifters. The key components of the proposed
compact Butler
matrix are the directional Lange coupler and Lange crossover. Using the EM
simulators, the design procedure of the Lange coupler, Lange crossover, and the 4×4 Butler matrix were carried out. In the following sections, the
design  and the performance of each component of this matrix are presented and
described in more detail.Figure 1
Schematic
diagram of the proposed4×4 Butler matrix.


### 2.1. Lange Coupler Design

The proposed Lange coupler with symmetric structure is composed of several parallel lines with
alternate lines tied together as shown in Figure2. It is necessary to bond
directly, via very short wires, between alternate lines of the coupler. The
bond wires should be as close as possible to a short circuit to minimize the
lumped inductance. Therefore, in designing this coupler, emphasis was made to
minimize the effect of bonding-wire inductance and to maintain electrical
symmetry [11]. In this section, the designed −3 dB microstrip Lange coupler
structure is composed of four interdigitated fingers. In the coupler design,
the Duroid substrate of RT/Duroid 6006 with εr=6.15 and thickness of 1.27 mm is used.Figure 2
Layout of proposed Lange coupler
using ADS.Using the ADS-Momentum EM simulator [12], the even- and odd-mode impedances
were calculated and then  the effective dielectric constant for Lange couplers
structure was determinate. The lines dimensions are calculated by using the LineCalc software of Agilent, Cal, USA. As a result, the line width (W) of 350 μm, the conductor spacing (S=96 μm), and the width of 50 Ω transmission line (W1=1.85 mm) are obtained. The physical length of the Lange
coupler is approximately equal to one quarter wavelength at the operating center frequency on the
host substrate (L=15.11 mm). The coupling between
the coupler ports is controlled by the interfinger distance. The effective
dielectric constant is computed from the length (L) of the coupler used in the
simulation.The initial dimensions
of the coupler were computed by using both the even- and the odd-mode analyses and LineCalc software. The
optimum Lange coupler parameters are obtained by using Momentum and IE3D software. Simulation
results of the return loss and insertion loss are shown in Figure3.Simulated scattering
parameters of a 3 dB Lange
coupler, (a) with ADS and (b) with IE3D.
(a)(b)Figure 4
Simulation results of Lange coupler phase difference.The average
value of the coupling for the direct port and the coupled port is 3.12 dB, the
return loss and isolation is better than −16 dB and −19 dB. It can be seen that
a 0.5 dB of amplitude imbalanced is achieved. The authors think that this value
is due to the accuracy of the software.The phase difference between the direct
and coupled ports is approximatively 90° across the operating band, which
supports the proposed approach. Data comparisons of the simulated results show
a good agreement. It can be concluded that the Lange is suitable
for building Butler
matrix circuits.


### 2.2. Lange Coupler Crossover

In the uniplanar
implementation of Butler matrix, crossovers are one of the main drawbacks. They may add undesired effects,
such as increased insertion loss, mismatched junctions, additional line cross-couplings,
and poor power handling [12]. They could cause difficulty in manufacturing using
conventional photolithography.To overcome this
problem, different characteristic techniques are available for the crossover design,
such as in CPW designs [13], an
expensive laminate is usually needed, and there is also an overhead in the
fabrication and measurement processes [14]. The planar implementation is made
here as a cascade of two hybrid couplers to work as a crossover. However, this
structure takes more space. In our study, we use the Lange coupler reported in
[15] to reduce the occupied space compared to the conventional crossovers. The
Lange crossover is designed abandoned the classical form of a four- or
six-finger Lange coupler. The layout of Lange crossover is shown in Figure 5.Figure 5
Layout of proposed Lange coupler crossover
using ADS.In the design of the Lange
coupler crossover, the number of fingers was reduced to three, and the number
of bond wires to two [15]. The two outer fingers had a width equal to w=0.617 mm, while the width of the center finger was w=1.85 mm. It can be noted that the microstrip line has the same width of Lange
coupler design. The interfinger distance of the coupler is equal to 3.341mm. The bond wires are made of copper,
having a width w=0.308 mm. In this case,
two wires are used instead of one in order to make the two paths more
symmetrical [16].The broadband Lange coupler crossover was designed and optimized to have
good isolation and to keep the return loss at an acceptable level. From the simulation
results, the coupling
is almost constant over the band and close to −0.08 dB, while the cross-coupling between isolated ports is
less than −19 dB. Moreover,
the return loss is less than −36 dB in the band of interest, as illustrated in Figure6.Scattering parameters of Lange coupler
crossover, (a) simulation with ADS and (b) with IE3D.
(a)(b)


## 2.1. Lange Coupler Design

The proposed Lange coupler with symmetric structure is composed of several parallel lines with
alternate lines tied together as shown in Figure2. It is necessary to bond
directly, via very short wires, between alternate lines of the coupler. The
bond wires should be as close as possible to a short circuit to minimize the
lumped inductance. Therefore, in designing this coupler, emphasis was made to
minimize the effect of bonding-wire inductance and to maintain electrical
symmetry [11]. In this section, the designed −3 dB microstrip Lange coupler
structure is composed of four interdigitated fingers. In the coupler design,
the Duroid substrate of RT/Duroid 6006 with εr=6.15 and thickness of 1.27 mm is used.Figure 2
Layout of proposed Lange coupler
using ADS.Using the ADS-Momentum EM simulator [12], the even- and odd-mode impedances
were calculated and then  the effective dielectric constant for Lange couplers
structure was determinate. The lines dimensions are calculated by using the LineCalc software of Agilent, Cal, USA. As a result, the line width (W) of 350 μm, the conductor spacing (S=96 μm), and the width of 50 Ω transmission line (W1=1.85 mm) are obtained. The physical length of the Lange
coupler is approximately equal to one quarter wavelength at the operating center frequency on the
host substrate (L=15.11 mm). The coupling between
the coupler ports is controlled by the interfinger distance. The effective
dielectric constant is computed from the length (L) of the coupler used in the
simulation.The initial dimensions
of the coupler were computed by using both the even- and the odd-mode analyses and LineCalc software. The
optimum Lange coupler parameters are obtained by using Momentum and IE3D software. Simulation
results of the return loss and insertion loss are shown in Figure3.Simulated scattering
parameters of a 3 dB Lange
coupler, (a) with ADS and (b) with IE3D.
(a)(b)Figure 4
Simulation results of Lange coupler phase difference.The average
value of the coupling for the direct port and the coupled port is 3.12 dB, the
return loss and isolation is better than −16 dB and −19 dB. It can be seen that
a 0.5 dB of amplitude imbalanced is achieved. The authors think that this value
is due to the accuracy of the software.The phase difference between the direct
and coupled ports is approximatively 90° across the operating band, which
supports the proposed approach. Data comparisons of the simulated results show
a good agreement. It can be concluded that the Lange is suitable
for building Butler
matrix circuits.


## 2.2. Lange Coupler Crossover

In the uniplanar
implementation of Butler matrix, crossovers are one of the main drawbacks. They may add undesired effects,
such as increased insertion loss, mismatched junctions, additional line cross-couplings,
and poor power handling [12]. They could cause difficulty in manufacturing using
conventional photolithography.To overcome this
problem, different characteristic techniques are available for the crossover design,
such as in CPW designs [13], an
expensive laminate is usually needed, and there is also an overhead in the
fabrication and measurement processes [14]. The planar implementation is made
here as a cascade of two hybrid couplers to work as a crossover. However, this
structure takes more space. In our study, we use the Lange coupler reported in
[15] to reduce the occupied space compared to the conventional crossovers. The
Lange crossover is designed abandoned the classical form of a four- or
six-finger Lange coupler. The layout of Lange crossover is shown in Figure 5.Figure 5
Layout of proposed Lange coupler crossover
using ADS.In the design of the Lange
coupler crossover, the number of fingers was reduced to three, and the number
of bond wires to two [15]. The two outer fingers had a width equal to w=0.617 mm, while the width of the center finger was w=1.85 mm. It can be noted that the microstrip line has the same width of Lange
coupler design. The interfinger distance of the coupler is equal to 3.341mm. The bond wires are made of copper,
having a width w=0.308 mm. In this case,
two wires are used instead of one in order to make the two paths more
symmetrical [16].The broadband Lange coupler crossover was designed and optimized to have
good isolation and to keep the return loss at an acceptable level. From the simulation
results, the coupling
is almost constant over the band and close to −0.08 dB, while the cross-coupling between isolated ports is
less than −19 dB. Moreover,
the return loss is less than −36 dB in the band of interest, as illustrated in Figure6.Scattering parameters of Lange coupler
crossover, (a) simulation with ADS and (b) with IE3D.
(a)(b)


## 3. The Proposed4×4 Butler Matrix

The block diagram of the proposed4×4 Butler matrix is presented in Figure 1 and its layout is shown in Figure 7. Combining the components presented in
Sections 2.1 and 2.2, the proposed Butler
matrix was designed using only Lange coupler device. From the dimensions of
both matrices shown in Figure 7, it can be seen that the proposed structure is more
compact compared to the conventional one with 80% of compactness. To demonstrate our approach, the proposed Butler
matrix was designed at a frequency range of 2.45 GHz using Rogers
substrates RT/Duroid 6006 (εr=6.15, and h=1.27 mm) as shown in Figure 7. Copper
metallization for the conductive layers is 17.5 μm thick. In this configuration,
signals incident at input ports (no. 1, no. 2, no. 3, or no. 4) are divided into four output
ports (no. 5, no. 6, no. 7, and no. 8) with equal amplitude and specified
relative phase differences.(a) Layout of conventional4×4 Butler matrices.
(b) Layout of the proposed 4×4 Butler matrix.
(a)(b)Figure8 show simulation
results of the insertion and return loss for port 1 with two softwares (ADS and IE3D) when
the other ports are matched.Simulated
results of magnitude S parameters of the4×4 Butler matrix, (a) simulation with
ADS and (b) with IE3D.
(a)(b)These results illustrate
that the return loss is better than 15 dB and the coupling to the output ports is well equalized (around
6.5 dB). It can be concluded that the obtained results are very promising.Figure9  illustrates a good agreement between the
simulated results of the phase shift of adjacent output ports, where (3)Phasedifference1=Phase(S(5,1)−Phase(S6,1)),Phasedifference2=Phase(S(6,1)−Phase(S7,1)),Phasedifference3=Phase(S(7,1)−Phase(S8,1)). It can be seen that the phase differences are not perfectly flat in the
entire bandwidth which the theoretical values are in 45°. The phase errors are going from 4° (2.4 GHz) to 5° (2.5 GHz) in all the bandwidths compared to
desired value of 45°. These errors are due to the use of the narrowband transmission line phase
shifters and crossover. To
demonstrate the performance of the 4×4 Butler matrix using Lange coupler in
terms of beamforming, the proposed Butler matrix is connected to antenna array
[17]. This array structure has four
elements spaced by 0.5 λ0 at 2.45 GHz in order to minimize the mutual
coupling between elements and to obtain the minimum level side lobes. As a
result, the array has uniform amplitude distribution and constant phase shift
between adjacent elements to generate orthogonal beams.Simulated
results of Butler matrix phase signal at port 1, (a) simulation with ADS and (b)
with IE3D.
(a)(b)Figure10 shows the simulated results of radiation patterns in the H-plane of the
beamforming antenna array system at 2.45 GHz, these numerical results take into
account the mutual coupling between element arrays. With
this matrix, four beams are produced at −45°, −15°, 15°, and 45°. Simulation
results indicate a good agreement with the theoretical prediction. These
features make the proposed matrix suitable for beamforming applications.Simulated H-plane radiation pattern
with (a) ADS and (b) IE3D.
(a)(b)


## 4. Conclusion

A compact4×4 Butler matrix on a
single-layer with relatively negligible cost has been designed. The circuit is
compact with 80% of size reduction compared with conventional structure. In the
proposed design, Lange coupler and Lange crossover have been used as a key
component of new topology, which leads
to significant size reduction and loss minimization. Simulated results are
validated by using the software tools IE3D and Momentum. Furthermore, a
four-antenna array has also been designed and connected to the proposed Butler
matrix to form a beamforming system resulting in four-orthogonal beams −45°, −15°, 15°, and 45° at 2.45 GHz. The proposed system has the advantages of low cost, small volume, and
light weight. These features make the proposed Butler
matrix suitable for ISM applications
at 2.45 GHz.



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*Source: 784526-2009-02-25.xml*