3x3 Microstrip Beam Forming Network forMultibeam Triangular ArrayAitor Novo Garcıa∗, Marıa Vera Isasa∗, Manuel Sierra Perez†

∗Grupo de Radiacion y Propagacion. Dpto. de Teorıa de la Senal y Comunicaciones. Universidad de Vigo.ETSI de Telecomunicacion. Lagoas-Marcosende. 36310 Vigo. Spain

anovo@grp.tsc.uvigo.es, mirentxu@tsc.uvigo.es

†Grupo de Radiacion. Universidad Politecnica de Madrid.ETSI de Telecomunicacion. Av. Complutense 30. 28040 Madrid. Spain.

m.sierra.perez@gr.ssr.upm.es

Abstract—The design of a beam forming network (BFN) for atriangular cell of three elements is considered. A useful relationbetween phase excitation of the elements of the cell, beamdirection, wavelength and distance is given. The BFN is studiedbased on a Butler matrix, using balanced and unbalanced hybridcouplers to obtain a three inputs and three outputs networkwhich is used to develop a multibeam structure. A system ofthree equations is also presented to calculate the lengths of thetransmission lines which connect the couplers of the network.These equations allow a flexible design of the network dependingon the needed specifications. Finally, a microstrip BFN circuitthat demonstrates the utility of the design has been developed.

I. INTRODUCTION

Classical antennas for satellite communications are thereflector antennas fed by horns. These antennas can receivesatellite signals in any direction with a mechanical procedure.In the case of low orbit satellites, the antennas must have atracking system so that the antenna can be accurately movedin a short time. The mechanical nature of the movementfor reflector antennas is a drawback when tracking suchsatellites. Also, more than one horn must be used to obtain amultibeam antenna, and the physical size of these horns limitsthe performance of the system.

Planar arrays can be used to obtain multiple beams workingsimultaneously. This system must be designed using a set ofcircuit elements, such as phase shifters, power dividers oramplifiers in order to built the proper BFN to obtain the desiredmultiple beams. The size and complexity of the system willgrow proportionally to the number of desired beams.

The GEODA antenna [1]–[3] is a dome antenna whichconsists of several planar arrays, allowing multiple beams inseveral directions in the 1.7 GHz working band. These planararrays are also subdivided in subarrays of three elements, fedby a beam forming network based on Butler matrix.

In this paper, the relation between the phase relation ofthe elements of the circular arrays and the beam direction isstudied, and a BFN is designed in order to obtain that phaserelation. There exist a few papers studying beam formingnetworks with three inputs and three outputs [5]–[7] whichuse non-standard Butler matrix. In this work, we present a set

Fig. 1. Dome antenna

of equations which provide a relation between the length of theconnecting transmission lines in the network. These equationsallow a flexible calculation of the transmission lines, and so amore flexible design of the BFN.

The last section shows a specific design made with the helpof the equations calculated. This circuit was developed to fitbelow the triangular array of antennas of the GEODA and toplace the outputs just below each antenna in order to improvethe use of space.

II. TRIANGULAR ARRAY

The GEODA antenna is subdivided in triangular flat panels,building a dome structure as can be seen in Fig.1. Each oneof these panels is also formed by 15 triangular arrays of threecircular patches referred to as cells, which must be fed toobtain a proper phase relation so that a specific beam directioncould be obtained. In this case, we want to design a networkto achieve a multibeam structure with three or even six beams.

A. Phase excitation and beam direction

The triangular array can be seen as a circular array of threeelements, separated a distance d between each other, and adistance a to the center of the circular array. In these conditionsthe array factor is

AF (θ, φ) =3∑

n=1

Anej[k a sinθ cos(φ−φn)+αn] (1)

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Fig. 2. Cell of three circular patches

where k is the wave number, θ is the elevation angle, φ isthe azimut angle, φn=2π(n/3) is the angular position of theelement n in the plane which contains the three patches andAn and αn are the amplitude and the phase of the excitationfor this element [4].

To direct the peak of the main beam in a direction (θ0, φ0),the phase of the excitation for the element n will be given by

αn = −k a sinθ0 cos(φ0 − φn) (2)

With (2) a phase relation for a specific main beam directioncan be obtained. This relation for three elements can beexpressed as

1

2(α1 + α2)− α3 =

3

2k a sinθ0 cosφ0 (3)

B. Cells phase relation

The patches which constitute each cell, shown in Fig.2, willbe excited with the phase relation given in Table I, obtainingthe main beam directions given in that table for a distanced=100 mm. This phase relation, studied by Shelton [5], [6]and used in [7], provides a group of three beams. In Fig.3 thissituation is shown for the case of φ0=0o radians with the cutsin the planes φ=0o, φ=120o and φ=240o.

III. BEAM FORMING NETWORK

The group of patches which constitute the cell must befed with an appropriate beam forming network that allowsto excite each patch with the phase shift in order to obtainan oriented beam in a fixed direction. This network shouldbe composed of phase shifting elements which combinedcan show a suitable response. A proper feeding network forour case must also show an uniform amplitude for the threeantennas of the cell, so that the incident power in the cell isdistributed evenly.

There are different methods and devices to implement thisscheme [8]. Phase shifters can be implemented by digitally

TABLE IRELATIVE PHASE SHIFT

Phase Relation θ0 φ0

α1=α2=α3+120 42.784o 0o

α2=α3=α1+120 42.784o 120o

α3=α1=α2+120 42.784o 240o

Fig. 3. Normalized array factor for φ0=0o

Fig. 4. Beam forming network with hybrid couplers

switched phase shifters, which change the length of a trans-mission line to approximate the desired phase relation. Diodephase shifters can also be implemented, combined with hybridcouplers or loaded lines, especially useful because of their veryrapid switching. Other methods, as the ferrimagnetic phaseshifters, Reggia-Spencer phase shifters or Latching ferritephase shifters, can be consulted in [8].

One of the most used schemes to obtain a BFN wasdescribed by Butler and Lowe [9] and studied in depth byShelton [5], [6], [10]. This network, theoretically lossless, useshybrid couplers along with fixed phase shifters, connected bytransmission lines of fixed length, to form with N inputs Ncontiguous beams from an N element array. However, theButler network, in its original design, only allows N=2p inputsand N=2p outputs, with p an integer, so that it can not be useddirectly in our three elements array.

In 1965 Shelton [6] published a scheme for feeding a trian-gular array, based on a Bulter matrix, where not only hybridcouplers were used, but also unbalanced hybrid couplers, asshown in Fig.4. Balanced hybrid couplers, represented in blacksquares, divide the incident power in one port between thetwo opposite ports, with a phase shift of -π/2 radians in thefirst and -π radians in the second, keeping the contiguous portisolated. On the other hand, unbalanced hybrid couplers splitthe power given in one port in an unequal manner between theopposite ports, with the adjacent port isolated. In this device,represented in white squares, the power in the opposite portsis 2/3 and 1/3 of the incident power, with a phase shift of -π/2and -π radians, respectively.

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TABLE IIRELATIVE PHASE SHIFT

Phase Relation θ0 φ0

α1=α2=α3-120 42.784o 180o

α2=α3=α1-120 42.784o 300o

α3=α1=α2-120 42.784o 60o

In the design of the network the hybrid couplers are con-nected by transmission lines, denoted by tli in Fig.4. Theselines introduce a phase shift of -2πli/λ, where li is the length ofthe transmission line i and λ is the wavelength in the substrate.When one of the inputs of the network (denoted by I1, I2 andI3) is fed with a signal, its power is equally divided at theoutputs of the network (O1, O2 and O3), and a different phasedistribution will be obtained depending on the excited input(α1 at O1, α2 at O2 and α3 at O3).

In the design in [6] and in [7] there was no explicitcalculation of the transmission lines lengths and a phase shifterof -30o was used. In our design, the lengths of the transmissionlines needed to obtain the response shown in Table I has beenstudied. When input 1, 2 or 3 is excited, the main beam shouldbe oriented in φ0=4π/3, 2π/3 or 0 radians, respectively. Inorder to obtain such response, a system of three equationshas been calculated. These equations give the needed relationamong all the lengths of the lines to achieve the desired phaserelation.

l1 − l2 + l3 = λ4

l4 − l3 − l5 = 2λ3

l5 − l6 = 7λ12

(4)

Six beams can be provided with the use of two boards:one is the structure Fig.4 and the other is the same designwith a fixed phase shifter of 4π/3 radians in one of the outputports. With this second design beams oriented in φ0=π/3, πor 5π/3 radians can be obtained. In Table II phase relationsand pointing direction of the beams are shown in the case of aphase shifter in the output of port 4. This way two boards willbe used, one for each group of three beam directions. Thesecircuits can be combined in a single structure with the helpof Wilkinson dividers, obtaining a design with six inputs andthree outputs.

IV. DESIGN AND RESULTS

The simultaneous equations (4) show that there is somedegree of freedom in the design of the BFN. This flexibilityallows to set three lengths with fixed values, and the otherlengths will be given by these equations. This way severaldifferent approaches are possible to start the design of thenetwork. We can design the BFN to obtain the minimum lengthor equal length for some transmission lines, or we can eventry to maximize the length of some lines, which can be usefulwhen considering the position of the ports.

In this section the board to obtain the beams given in TableI will be studied. The fixed values for the lengths were chosen

TABLE IIITRANSMISION LINES LENGTHS

Transmision line Length Transmision line Lengthtl1 λ tl4 7λ/6tl2 λ tl5 λ/4tl3 λ/4 tl6 2λ/3

Fig. 5. Beam forming network layout

TABLE IVDESIGN SIMULATION RESULTS

Input 1 Input 2 Input 3Return loss (dB) -24.44 -24.76 -30.02Output 1 (dB) -5.52 -5.71 -6.71Output 1 (deg) 103o 99.15o 8.07o

Output 2 (dB) -5.39 -6.19 -5.92Output 2 (deg) -13.41o -139.5o 9.84o

Output 3 (dB) -5.78 -6.33 -5.72Output 3 (deg) 104o -139.9o -108.1o

to be l1=λ, l2=λ and l5=λ/4. Whith this constraints, the givenlengths for the design are the values shown in Table III.

The network was designed in microstrip technology usingthe electromagnetic simulator IE3D. The substrate used forthis simulations was FR-4 with εr=4.25 and thickness h=1.5mm. Hybrid couplers and transmission lines were studied andoptimized separately, and then connected according to thedesign presented in Fig.4. It has been also considered the ideaof obtaining a network with the outputs in a common plane,in order to facilitate the fabrication of the board. The layoutof the final circuit is shown in Fig.5, where the input ports aredesigned as I1, I2 and I3, and the output ports as O1, O2 andO3.

The results of the simulation for this circuit are shown inTable IV for the frequency of f0=1.7 GHz. The module of thepower at the outputs for every input is slightly lower than -4.77 dB with respect to the incident power at that input, whichis the ideal power obtained with an equal distribution betweenthe three output ports. Return losses are below -24 dB for thethree inputs, and the phases obtained at the outputs fulfil therelations of Table I as desired.

A prototype of the board was constructed with the substrateFR-4 and measured. This prototype is shown in Fig.6, whereasmeasurements of magnitude and phase with respect to the

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Fig. 6. Beam forming network prototype

Fig. 7. Board measurements for input 1

Fig. 8. Board measurements for input 2

Fig. 9. Board measurements for input 3

incident power are plotted in Fig.7, Fig.8 and Fig.9 whenthe input port is I1, I2 and I3, respectively. It can be seenthat power at the outputs is near equal around 1.7 GHz, with

the desired phase relation. Power reflected in the input portand transmitted to the isolated ports are below -17 dB in thefrequency of interest.

V. CONCLUSION

A beam forming network design for the three patches cellof the GOEDA antenna was studied. This feeding networkmust provide three simultaneous beams in given directionsfor what a proper phase relation must be achieved for eachelement of the cell. A relation between this phase relation andbeam direction is given, depending on position of elements ofthe circular array and working wavelength.

A BFN based on Butler matrix was presented with threeequations to provide the lengths to achieve the desired phaserelation at the outputs of the network for each input. Theserelations allow a certain degree of freedom in the design,and so a more appropriate design can be developed for eachparticular situation. An example of the use of these equationswas presented and the results obtained in the simulationscorroborate the developments achieved.

ACKNOWLEDGMENT

This work was supported by MCI under TEC2008-06736-C03-02.

REFERENCES

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[2] Montesinos, I.; Masa, J.L.; Sierra-Perez, M.; Fernandez-Jambrina, J.L.; ,Geoda: Conformal adaptive antenna of multiple planar arrays for satel-lite communications, Antennas and Propagation Society InternationalSymposium, 2008. AP-S 2008. IEEE , vol., no., pp.1-4, 5-11 July 2008.

[3] Montesinos, I.; Sierra-Perez, M.; Fernandez, J.L.; Martinez, R.; Masa,J.L.; , GE.ODA: Adaptive antenna of multiple planar arrays for satellitecommunications, Antennas and Propagation, 2009. EuCAP 2009. 3rdEuropean Conference on , vol., no., pp.773-777, 23-27 March 2009

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[6] J. P. Shelton, Multibeam, hexagonal, triangular-grid, planar arrays,Antennas and Propagation Society International Symposium, 1965 ,vol.3, no., pp. 90- 97, Aug 1965.

[7] Shi Lei and M. Sierra-Perez, Triangular Grid Multibeam Array andBeam Forming Networks Antennas and Propagation, 2007. EuCAP 2007.The Second European Conference on , vol., no., pp.1-4, 11-16 Nov.2007.

[8] Merrill I. Skolnik, Introdution to radar systems, 2nd ed., Ed. McGraw-Hill, 1981.

[9] Jesse Butler and Ralph Lowe, Beam-forming matrix simplifies design ofelectronically scanned antennas, Electronic Design, Vol. 9, pp. 170-173,1961.

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