Design and Implementation of a 4x4 Butler-Matrix Switched-Beam Antenna Array at the Microwave Communications and Electromagnetic

Applications Lab of the Technological Educational Institute of Crete

G.A. ADAMIDIS and I.O. VARDIAMBASIS Microwave Communications & Electromagnetic Applications Laboratory,

Telecommunications Division, Department of Electronics, Technological Educational Institute (T.E.I.) of Crete - Chania Branch,

Romanou 3, Chalepa, 73133 Chania, Crete, GREECE

Abstract: - A switched-beam array system, capable to produce four orthogonal uniform beams and some low side-lobe beams, is presented in this work. The system is consisted of a four-element linear phased array and a 4x4 Butler-matrix beamforming network. System’s design and optimization was based on experimental results and computer simulations. New, small and easy to fabricate microstrip layout topologies for the 4x4 Butler-matrix beamforming network have been designed and constructed relying on a low cost dielectric material, the well-known FR4. Finally, measurements are presented in detail, in order to prove the excellent system’s performance. Keywords: - Smart antennas, switched beam antenna arrays, Butler matrix networks, beamforming. 1. Introduction 1.1 Antenna engineering education The Technological Educational Institute of Crete Greece (TEI-C), as any other university, is considered to have three major objectives, i.e., the education of students, the generation and assignment of competent young engineers to industries, and the evolvement of basic and applied research. Combining these roles, our Microwave Communications & Electromagnetic Applications (MCEMA) Laboratory has comprehensive modern facilities for teaching and research activities in theoretical and computational electromagnetics,

antenna analysis and design, microwave theory and applications, advanced communication and radar systems, and electromagnetic compatibility issues. This work’s focus is on smart antenna education at TEI-C’s Electronic Engineering Dept., whose undergraduate curriculum includes an advanced elective course in antennas and communication systems engineering, called Smart Antennas & Wireless Communications. This course is fully supported by the MCEMA Lab, with exercises, simulations, measurements and lab projects, like the switched-beam antenna array presented herein.

Figure 1. The geometry and the desired beam-set of a four-element phased array.

1.2 Operation concepts Referring to the geometry of Fig. 1, let us assume a 4-

element linear array with identical elements, all of identical magnitude excitation. Furthermore all

elements are equally spaced with distance d and each succeeding element has a b progressive phase lead current excitation, relative to the preceding one. Assuming that the reference point is the physical center of the array, the normalized array factor AF(θ) of the above geometry can be expressed as [1]:

1 sin(2 )AF( )4 sin( / 2)

ψψ = ⋅

ψ (1)

with 12 d cos b−ψ = π λ θ+ . (2)

The array factor of (1) has one main maximum in the observation angle of θi which is function of the current bi progressive phase excitation:

1 ii

bcos2 d

− ⎛ ⎞λθ = ⎜ ⎟π⎝ ⎠

. (3)

2. Implementation and Measurements By designing a beam-forming network capable to produce n different bi, a set of n different beams can be easily implemented. Fortunately, such a network, better known as Butler-matrix, has been introduced in [2]-[3]. A 4x4 Butler-matrix beam-forming network implementation is presented in Fig. 2a, where the boxes

H

5 7

H

6 8

1211109

H

-45

24

H

5 7

H

6 8

1211109

H

-45

13 Figure 2a. A 4x4 Butler-matrix network.

with H notation, are 90o hybrid junctions [4], and the circles with -45 notation, are 45o phase sifters. By connecting ports 5, 6, 7 and 8 to the array elements -2, -1, 1, 2, respectively, switched beam steering can be achieved in θi direction, for i=1,2,3 and 4 by choosing excitation either to port 1,2,3 or 4, respectively. All ports are almost perfect isolated from each other and they are matched to the system impedance. Butler-matrix is an absolute passive network. Consequently it is very simple, there is no need for calibration and it can be used either in the output state of a transmitter or in the input state of a receiver.

Table 1. The 4x4 Butler matrix beam-forming network.

Output state Input port Port 5 Port 6 Port 7 Port 8

b Beam θi (d=λ/2)

1 o1 45∠ o1 180∠− o1 45∠− o1 90∠ o135+ 1 138.6o

2 o1 0∠ o1 45∠ o1 90∠ o1 135∠ o45+ 2 104.5o

3 o1 135∠ o1 90∠ o1 45∠ o1 0∠ o45− 3 75.5o

4 o1 90∠ o1 45∠− o1 180∠− o1 45∠ o135− 4 41.4o

1

3 5

7

4

28

6

1

3

5 7

4

2

86 A B

1

3 5

7

4

28

6

3

1

6

8 2

4

5

7

C D

Figure 2b. Layouts for a 4x4 Butler-matrix.

Four possible microstrip layout topologies of a 4x4 Butler matrix have been designed and optimized using HP-Libra software [5]. Those layouts are presented under scale in Fig. 2b. Designs optimized for operation at 2.44GHz and fixed to 50 Ohm system impedance. They were fabricated in FR4 substrate ( r 4.35ε = , tan 0.013δ = , 1.5mm thickness) [6]-[7]. Particular effort was made in order to design those layouts in as small size as possible so that losses from dielectric are avoided. SMA connectors have been soldered to all ports, according to the indicated in Fig. 3 technique.

Figure 3. Layout design technique

The overall typical characteristics of the Butler-matrices in Fig. 2, are presented in Table 2. Those characteristics arise from S-parameters measurements

that were realized via network analyzer. Some of those measurements are presented in Figs. 4-8.

Table 2. Typical characteristics of the Butler-matrices in Fig. 2 (“p” referred to ports).

Freq. (MHz)

Output amplitude (typical)

Loss (typical)

Max amplitude

error

Max phase error

Max input SWR

(ports p.)

Minimum inter-port isolation

(db) 2250 -7.3db 1.3db 1.3db 7% 1.62 /p2,3 -16.0 /p32,41 2275 -7.3db 1.3db 1db 5% 1.56 /p2,3 -17.0 /p32,41 2300 -7.2db 1.2db 0.8db 3% 1.49 /p2,3 -17.5 /p32,41 2325 -7.1db 1.1db 0.6db 2% 1.40 /p2,3 -18.5 /p32,41 2350 -7.0db 1db 0.4db 2% 1.20 /p1,4 -19.0 /p32,41 2375 -7.0db 1db 0.4db 3% 1.20 /p1,4 -20.0 /p32,41 2400 -6.9db 0.9db 0.3db 4% 1.19 /p1,4 -20.0 /p32,41 2425 -6.9db 0.9db 0.3db 5% 1.18 /p1,4 -21.0 /p32,41 2450 -6.9db 0.9db 0.3db 6% 1.18 /p1,4 -22.0 /p32,41 2475 -6.9db 0.9db 0.3db 7% 1.19 /p1,4 -22.0 /p32,41 2500 -6.9db 0.9db 0.3db 8% 1.20 /p1,4 -22.0 /p32,41 2525 -6.9db 0.9db 0.3db 10% 1.21 /p1,4 -21.0 /p32,41 2550 -7.0 db 1db 0.3db 13% 1.24 /p1,4 -21.0 /p32,41 2575 -7.1db 1.1db 0.3db 14% 1.28 /p1,4 -21.0 /p32,41 2600 -7.1db 1.1db 0.3db 17% 1.30 /p1,4 -20.0 /p32,41

Figure 4. S parameters (magnitude) for beam 2.

Figure 5. S parameters (phase) for beam 2.

Figure 6. S parameters (magnitude) of beam 1.

Figure 7. S parameters (phase) for beam 1.

db

deg

db

deg

Figure 8. S parameters (return loss & isolation).

Our 4x4 Butler-matrices have been connected via coaxial cables to 4-element arrays in order to implement the overall system. Those arrays were designed to operate in almost all the available useful bandwidth with SWR less than 1.3 and they were optimized for possible simplicity and excellent electrical and radiation characteristics [6]-[7]. The geometries of these arrays are presented in Figs. 9-10.

Figure 9. Printed-dipole array with plain reflector [d= 6.1cm/ 0.5λ @ 2.44GΗz, α= 3.6cm/ 0.3λ @

2.44GHz, Reflector: 28x15cm, FR4: 23.5 x 5cm x 1.5mm, Dipole: 0.5λg @ 2.44GHz].

Figure 10. Monopole array with plain reflector [d=6.1cm / 0.5λ @ 2.44GΗz, α=3.6cm / 0.3λ @

2.44GHz, Reflector: 30x13,5cm, Monopole: 0.25λ @ 2,44GHz, Ground plane: 7x30cm].

0 20 40 60 80 100 120 140 160 180-35

-30

-25

-20

-15

-10

-5

0

db

Theta (deg.)

Theoretical Measured

(a)

0 20 40 60 80 100 120 140 160 180-35

-30

-25

-20

-15

-10

-5

0

db

Theta (deg.)

Theoretical Measured

(b)

0 20 40 60 80 100 120 140 160 180-35

-30

-25

-20

-15

-10

-5

0

db

theta (deg.)

Theoretical Measured

(c)

0 20 40 60 80 100 120 140 160 180-35

-30

-25

-20

-15

-10

-5

0

db

theta (deg.)

theoretical Measured

(d) Figure 11. Normalized total factor’s power graphs at

2.44 GHz for beams 1 (a), 2 (b), 3 (c), and 4 (d).

db

Reflector

Ground plane

Monopole

d

α 900

SMA connector

1 2 3 4

d

α

FR4 Printed dipole

Reflector

1 2 3 4

We chose to fabricate and test those two arrays among many solutions. They are both vertical polarized. The first one (Fig. 9) is consisted of four printed dipoles in front of a plain reflector, and the second one (Fig. 10), is consisted of four λ/4 monopoles, also in front of a plain reflector [6]-[7]. In order to reveal overall system’s performance we have measured radiation patterns of the four possible uniform beams, which can be achieved with our Butler-matrices connected to our antennas. Some of those measurements are presented in Fig. 11, along with theoretical values. Theoretical values have been calculated by making use of image theory [1].

Beams 1, 2, 3 and 4 are orthogonal [2]. This interesting characteristic was exploited so that we create cosine-illumination beams from the linear combination of two adjacent uniform beams [2]. The appropriate linear combination can be achieved with simultaneous equal magnitude excitation of two adjacent Butler-matrix’s input ports with the appropriate phase. The three possible low side-lobe beams that can be achieved by those combinations [6]-[7] are presented in Table 3.

Table 3. Low side-lobe level beams on a 4x4 Butler-matrix array.

Input state Beam Port 1 Port 2 Port 3 Port 4

α 0 1 1 0 b o1801 ±∠ 1 0 0 c 0 0 1 o1801 ±∠

Figure 12. Low side-lobe beams (calculated).

0 20 40 60 80 100 120 140 160 180 200-40

-30

-20

-10

0

db

theta (deg)

Theoretical Measured

Figure 13. Low side-lobe beam a (measured).

3. Conclusion A laboratory project on antenna array beamforming was presented. It was designed, implemented, and measured at the MCEMA Lab of TEI-C, aiming to develop our students’ knowledge and abilities to advanced antenna systems. This project demands the activation, concentration and study of every participating student, cultivating the full skills and advanced qualifications of the future engineers. Acknowledgment This work was supported by the Greek Ministry of National Education and Religious Affairs and the European Union under the ΕΠΕΑΕΚ ΙΙ project “Archimedes – Support of Research Groups in TEI of Crete – Smart antenna study & design using techniques of computational electromagnetics and pilot development & operation of a digital audio broadcasting station at Chania (SMART-DAB)”. References [1] C.A. Balanis, Antenna Theory, Analysis and

Design, 2nd edition, Wiley 1997.

Output state Beam Port 5 Port 6 Port 7 Port 8

b

α o038.0 ∠ o092.0 ∠ o092.0 ∠ o0.38 0∠ 0o b o5.6738.0 −∠ o5.2292.0 ∠ o5.11292.0 ∠ o5.15738.0 −∠ +90o c o5.15738.0 −∠ o5.11292.0 ∠ o5.2292.0 ∠ o5.6738.0 −∠ -90o

dB

[2] J.L. Butler, Chapter 3 in Microwave Scanning Antennas edited by R.C Hansen, vol. 3, Academic Press 1966.

[3] J. Butler and R. Lowe, “Beamforming matrix simplifies design of electronically scanned antennas”, Electronic Design, vol. 9, pp. 170-173, 1961.

[4] R.E. Collin, Foundations for Microwave Engineering, 2nd edition, McGraw-Hill 1992.

[5] Libra® for Windows, Hewlett-Packard Co. [6] G.A.Adamidis and E.Vafiadis, “Development of

simple smart array systems”, Technical Report, no.89, Aristotle Univ. of Thessaloniki, 2002.

[7] G.A. Adamidis, “Development of simple smart array systems”, Diploma Thesis, Physics Dept., Aristotle Univ. of Thessaloniki, 2002.