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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 1

A Novel Compact Butler MatrixWithout Phase Shifter

Ge Tian, Jin-Ping Yang, and Wen Wu

AbstractA novel compact 4 4 Butler matrix using only mi-crostrip couplers and a crossover is proposed in this letter. Com-paredwith the conventional Butlermatrix, the proposed one avoidsthe interconnecting mismatch loss and imbalanced amplitude in-troduced by the phase shifter. The measurements show accuratephase differences of and with an ampli-tude imbalance less than 0.4 dB. The 10 dB return loss bandwidthis 20.1%.

Index TermsButler matrix, coupler, phase shifter.

I. INTRODUCTION

M ULTIPLE-BEAM antenna technology is an attractivecandidate for mobile and satellite communication sys-tems [1]. The Butler matrix is used as beam-forming networkfor a multiple-beam antenna system due to its simplicity andlow power loss [2][5]. A lumped-element unit cell is used torealize a compact Butler matrix with a strong size reduction in[2]. In [3], a Butler matrix is proposed using slotline technologyand lumped elements. However, the phase and amplitude per-formance of these Butler matrices are influenced by the effectof the lumped elements. In [4], a classical branch-line couplerand a Schiffman phase shifter are used to build a Butler ma-trix. A composite right/left handed transmission line is appliedto engineer a Butler matrix in [5]. This novel transmission lineis composed of a Wunderlich-shaped dentiform capacitor and ameandered-line short-circuited stub inductor.However, phase shifters and lumped elements in the above

Butler matrices usually degrade the performance. In order to geta better performance, a novel 4 4 Butler matrix employingonly microstrip couplers and a crossover is proposed in thisletter. With the help of a phase difference coupler, thephase shifter is not needed in this Butler matrix. Cross-slot patchcouplers are used because they have advantages of miniatur-ized size and lower radiation loss [6]. This Butler matrix is de-signed, fabricated, and measured for verification. Further more,it is connected to a patch array antenna to demonstrate its per-formance as a beam-forming network.

Manuscript received October 22, 2013; accepted February 01, 2014.G. Tian andW.Wu are with the Ministerial Key Laboratory of JGMT, School

of Electronic Engineering and Optoelectronic Technology, Nanjing Universityof Science and Technology, Nanjing, China.J.-P. Yang is with the Key Lab of Radio Astronomy, Purple Mountain Obser-

vatory, CAS, Nanjing, China.Color versions of one or more of the figures in this letter are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LMWC.2014.2306898

Fig. 1. Block diagram of the proposed Butler matrix.

TABLE IPHASE RELATIONS OF COUPLERS WITH AND

PHASE DIFFERENCES BETWEEN OUTPUTS

II. DESIGN OF NOVEL BUTLER MATRIX

The 4 4 Butler matrix has four input ports and four outputports. As different input ports are excited, the Butler matrix pro-vides four output signals with equal amplitude and phase differ-ences of 45 , , 135 , and , respectively. As a conse-quence, four beams with different directions are obtained, onefor each input.The proposed Butler matrix is shown in Fig. 1. It contains

couplers with and phase difference and a crossover.The phase relations of the couplers are listed in Table I. It isnoted that, this novel Butler matrix employs a coupler re-placing the combination of quadrature coupler and phase shifterin the conventional Butler matrix.When the signal is excited on Port1, it goes through the path

of A-B-C-D to Port5 with 135 phase shift.Similarly, a phase shift of 90 is realizedbetween Port1 and Port6, when the signal goes through the pathof A-F-G-H. Also the signal goes through the path of A-B-C-Eto support a phase shift of 45 betweenPort1 and Port7. The phase shift between Port1 and Port8 is 0

, when the signal goes through the path of

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2 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS

TABLE IITHE PHASE RELATIONS OF THE BUTLER MATRIX

Fig. 2. (a) Structure of coupler with phase difference between outputs.(b) Structure of coupler with phase difference between outputs.

TABLE IIIPHYSICAL DIMENSIONS OF COUPLERS WITH

AND PHASE DIFFERENCES

A-F-G-I. Thus the phase difference between the output ports is45 . When thesignal is excited on other input ports, the phase shifts betweenthe input ports and output ports can be calculated in the similarway. The phase relations of the proposed Butler matrix are listedin Table II.

III. RESULTS AND DISCUSSIONS

The Butler matrix is fabricated on Rogers RO4003 substratewith a dielectric constant of 3.55 and a thickness of 0.813 mm.Simulations are carried out with CST Microwave Studio andthe target frequency is 6 GHz. A cross-slot patch coupler anda crossover in [7] are used to compose this Butler matrix. Asshown in Fig. 2(a), the structure of the coupler takes theform of a chamfer patch, which is etched by a pair of dumb-bellslots. A square patch with crossed slots for the coupleris shown in Fig. 2(b). Their physical dimensions are listed inTable III. As shown in Fig. 1, the input Port3 and Port2 aresymmetric, and so are input Port4 and Port1. Thus, only the

Fig. 3. Simulated and measured S-magnitudes of the proposed Butler matrix.

characteristics for exciting Port1 and Port2 are shown in thisletter.Fig. 3 shows the simulated and measured S-magnitudes of

the Butler matrix. When Port1 is excited, the transmissioncharacteristics are , ,

and at the target frequency.When Port2 is excited, the transmission characteristics are

, , and. The return loss is greater than 24.1 dB and

isolation is greater than 21.4 dB at the target frequency. The

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TIAN et al.: A NOVEL COMPACT BUTLER MATRIX WITHOUT PHASE SHIFTER 3

Fig. 4. Simulated and measured phase differences of the Butler matrix.

TABLE IVCOMPARISON OF PERFORMANCE OF BUTLER MATRICES

Fig. 5. Photograph of the fabricated Butler matrix.

10 dB return loss bandwidth is 20.1% and the 3 dB transmissionbandwidth is 24.4% (bandwidth with transmission character-istic between 6 dB and 9 dB).Fig. 4 shows the simulated and measured phase differences

of the Butler matrix. By feeding signal at Port1 and Port2, themeasured phase differences of and areobtained with an amplitude imbalance of less than 0.4 dB. Thus,the overall phase error is less than 0.9 at the target frequency.

Fig. 6. Radiation pattern of the proposed Butler matrix connected to a patcharray antenna.

Table IV compares the performance of the proposed Butlermatrix with several previous Butler matrices. The proposed onehas the widest 10 dB return loss bandwidth among the Butlermatrices, with minimum phase error and amplitude imbalance.Fig. 5 shows the photograph of the fabricated Butler matrix.The proposed Butler matrix is connected to a patch array an-

tenna to demonstrate its performance as a beam-forming net-work. Four patches of the array antenna are placed with a dis-tance of ( is wavelength at ). The simulatedand measured radiation patterns are shown in Fig. 6. The mea-sured beam directions are at , , 43.8 ,(theoretical beam directions are 14.5 , , 48.6 , ).

IV. CONCLUSION

In this letter, a novel 4 4 Butler matrix is proposed byemploying couplers with and phase differences. Aphase shifter is not needed in this Butler matrix as in conven-tional ones. As expected, this novel Butler matrix allows for sig-nificant improvement of phase and amplitude performance in acompact topology.

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unit cell for beam-forming networks and its application to a miniatur-ized Butler matrix, IEEE Trans. Microw. Theory Tech., vol. 61, no. 4,pp. 14771487, Apr. 2013.

[3] T. A. Denidni and M. Nedil, Experimental investigation of a newButler matrix using slotline technology for beamforming antenna ar-rays, IET. Microw. Antennas Propag., vol. 2, pp. 641649, Oct. 2008.

[4] C. R. Liu, S. Q. Xiao, Y. X. Guo, M. C. Tang, Y. Y. Bai, and B. Z.Wang, Circularly polarized beam-steering antenna array with Butlermatrix network, IEEE Antennas Wireless Propag. Lett., vol. 10, pp.12781281, 2011.

[5] H. X. Xu, G. M. Wang, and X. Wang, Compact Butler matrix usingcomposite right/left handed transmission line, Electron. Lett, vol. 47,no. 19, pp. 10811082, Sep. 2011.

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