Koch Fractal Antenna Application in MonopulseAntenna Array

Vilmos Rosner, Tamas Peto, Rudolf SellerRadar Research Group

Broadband Infocommunications and Electromagnetic Theory DepartmentBudapest University of Technology and Economics

Budapest, Hungarye-mail:rosner@mht.bme.hu, peto@hvt.bme.hu, seller@mht.bme.hu

Abstract—This paper addresses the design and evaluationof monopulse antenna array used in UAV on-board collisionavoidance radar. The antenna array use the advantages of thefractal geometry. The inverted Koch square patch fractal antennahas been modified in order to gain more control over theefficiency degradation originating from production difficultiesand to meet the requirements of a monopulse collision avoidanceradar. Simulation and measurement results show the applicabilityof fractal geometry in antenna arrays.

Index Terms—monopulse radar, fractal antenna, inverted Kochfractal, fractal antenna array

I. INTRODUCTION

This paper addresses the application of Koch fractal geome-try in small sized antenna arrays. When it comes to designingantenna systems, it is essential to properly set the spacing be-tween antenna elements. The interelement spacing should notexceed one wavelength to avoid grating lobes (multiple mainbeam) [1]. However, the physical size of single elements arecommensurable with half wavelength or quarter wavelength ingeneral. Therefore, the realization of the antenna system couldeasily come up against problem. On of the possible solutionsto size reduction is the application of fractal antennas. Thegoal of this paper is to present the design and evaluation ofan antenna system that takes advantage of fractal antennas.The design considerations and the characterization of singleelement are discussed in detail. The efficiency of Koch fractalgeometry using in antennas has been widely proved so far[4],[5],[6],[3]. At the same time, proper fabrication of invertedKoch square patch antennas can be difficult due to the requiredsharp edges. In this paper we describe our fractal geometrywhich is a modification of the standard inverted Koch squarefractal. Design methodology has been presented along withthe simulation and measurement results comparison.

II. DESIGN CONSIDERATIONS

Collision avoidance radars can use the monopulse principleto detect nearby targets and determine those position. Accord-ing to the measurement results the UAV could execute thenecessary maneuvers to avoid the collision. In order to performthe right maneuvers the UAV must have three dimensionalinformation about the targets position, thus it is necessary tomeasure both azimuth and elevation angles. So the antenna

d>λ/2

Tx

Rx

Rx Rx

Rx

Figure 1. Schematic layout of the monopulse antenna array

system must consist of four receiver and a transmitter antennato produce the two delta and the sum channels. The distancebetween receiver antenna elements should be kept aroundhalf a wavelength to evaluate wide enough beams in themonopulse beampattern. However, receiver elements shouldbe placed maximum a wavelength away from each other toprevent grating lobes appear and measurements uncertainty.Since the separation of the transmitter and receiver antennasis not feasible due to the small space the layout presented onfigure 1 has been designed. Other benefit of this antenna layoutis the nearly symmetrical electromagnetic field distributionon the different antenna elements. The operating frequencyof the experimental radar is in the F-band, while the relativebandwidth of the system is approximately 4%.

W =1

2fr√µ0ε0

√2

εr + 1(1a)

L =1

2fr√εeff√µ0ε0

− 2∆L (1b)

εeff =εr + 1

2+εr − 1

2

(1 + 12

h

W

)− 12

(1c)

Figure 2. Koch fractal evolution

Using the well known equations above (1 a-c) [1] thephysical sizes of a conventional microstrip rectangular pathantenna can be calculated. For a standard FR4 substrate withε = 4.5 relative permittivity and h = 1.5 mm substrate heightwe get W = 30.13 mm for the width and L = 36.9 mmfor the length of the patch antenna. While the free-spacewavelength is λ0 = 100 mm. Figure 1 illustrates the structureof the designed antenna array. The interelement spacing ofthe receiver antennas is half wavelength. The dashed linesillustrates the previously calculated sizes of the antennaelements. As it can be seen from the layout the use ofstandard microstrip patch antennas is not possible becauseof inter element overlapping. Consequently the physical sizeof the antenna elements must be reduced. There are severalmethods to reduce the size of the microstrip patch antennasuch as using substrate with high dielectric permittivity orapplying slots. However, higher dielectric substrate can onlyused in the expense of reducing the antenna bandwidth as itis analyzed in [1]. In order to increase the bandwidth of theantenna the FR4 substrate was extended with 10 mm heightair gap (The height of the FR4 substrate is also decreasedfrom 1.5 mm to 0.5 mm). Figure 6 illustrates the stack up ofa single element.

Using fractal geometry the electrical size of the antennacan be increased without greatly affecting other antenna pa-rameters. Our main goal was to design the above describedantenna system using fractal geometry antennas thus theantenna system could meet the requirements.

III. FRACTAL ANTENNA GEOMETRY

Our antenna design utilizes the geometry of invertedKoch square patch. The Koch curve is one of the firstpublished fractal shapes proposed in 1904 by Niels FabianHelge von Koch [2]. Taking a segment of a straight lineas initiator, then substitute the middle third of it with anequilateral triangle, results the so called generator. Repeating

0th iteration 1st iteration 2nd iteration

Figure 3. inverted Koch square fractal evolution

0th iteration 1st iteration 2nd iteration

Figure 4. Modified inverted Koch square fractal evolution

the previous step for all the newly obtained segments againand again we get the Koch fractal curve depicted on figure 2.Applying the Koch generator to a regular polygon convergeto the Koch island fractal. In case of the base polygon isa square, the fractal is called Koch square fractal. InvertedKoch square fractal geometry can now be constructed withusing subtraction instead of complement the initiator withthe equilateral triangle in each iteration. Using the abovedescribed procedure the fractal illustrated on figure 3 can begenerated [3]. Effectiveness of the fractal antenna geometrygenerated in this manner has been proven so far.

At the same time this fractal shape has also some drawbacks.Symmetrical properties of the structure may easily damagedduring the etching process in PCB manufacturing. Toovercome this difficulty we are proposing a modified invertedKoch fractal geometry. To eliminate the sharp edges of thefractal structure we experimented with using rectangularnotches instead of sharp triangles. Figure 4 illustrates themodified inverted Koch fractal patch evolution until thesecond iteration.

IV. DESIGN METHODOLOGY

For designing the antenna we have developed an invertedKoch square fractal geometry generator program. This pro-gram is capable of generating the inverted Koch square patchantenna geometry both with triangle insets and with rectan-gular insets. The parameters of the insets such as the widthand height can be configured in the program. The output ofthe program is a ’.dxf’ file which can be used by an EMsimulator program. In order to facilitate the manufacturingwe only generated antenna geometries until the second fractaliteration.

Feeding of the antenna elements using microstrip trans-mission lines could not be carried out without affecting thesymmetry of the antenna system. L-probe feeding used in[3] was not advisable in our case because of low mechanicalstability. Thus, in order to prevent unwanted coupling effectsand to achieve stable feeding structure we are feeding theantenna directly with coaxial probe. Figure 6 shows the appliedfeeding method and the parameters of the antenna stack up.

After the fractal geometry generation the EM performanceof the fractal antenna has been evaluated using CST Mi-crowave Studio. Simulations are made using frequency domainsolver and tetrahedral mesh. Parameter optimization has also

done with CST, such as structure scaling and coaxial probefeeding position. Sweeping with the coaxial probe offset thereal part of the antenna radiating impedance can matched to50 Ω.

However, care must be taken when placing the coaxial probeclose to the center of the antenna. As the probe position isapproaching to the center the four main part of the antennatends to radiate each independently. This kind of radiationpattern can not be accepted in monopulse antenna systems asit may results in uncertainty during target detection.

V. RESULTS

The first experimental prototype of the antenna has designedto operate at 3.3 GHz. In order to gain good enough sizereduction and easy manufacturability we have designed thefractal geometry until the second iteration. The physical sizeof the designed fractal antenna element is 19 mm. Simulationresults including the farfield pattern, input reflection can beseen on figure 7, 8. After the simulations had made the antennaarray was fabricated (figure 11). Measured input reflection alsocan be seen on figure 7. The input reflection curve showssimilarity between measured and simulated result.

Calculating the standard rectangular patch antenna physicalsizes using equations 1 (a-c) with h = 10 mm and with airsubstrate we get W ' 50 mm and L ' 36 mm, while ourdesigned antenna physical sizes are 19 mm, thus we achieved62% size reduction.

During the course of optimization a trade-off must bemade between the input reflection and the radiation pattern.The better the input reflection is the more the major beamsplits into individual sections. To obtain better monopulselike characteristic, the splitting of the major beam can not beaccepted. Figure 8 and 9 shows the radiation pattern variationboth in E-Plane and H-plane for different feed positions,while figure 10 shows the input reflection for different feedingoffset. Thus to satisfy these conditions the radiation patternof the antenna system has been optimized in the expense ofinput reflection. The final feed offset has set to 6.8 mm. Thesimulated monopulse delta channel beampattern is illustratedon figure 12.

Figure 5. Developed fractal geometry generator program

Metal plane - ground

Air (10 mm)

Copper-ground planeFR4 (0.5 mm)Copper-antenna layout

Coaxial probe

10m

m

Figure 6. Single antenna element stack up

VI. CONCLUSION

With the presented modifications on inverted Koch fractalgeometry almost the same performance can be achieved aswith the original one. The achieved 60 percent size reductionproves the applicability of the proposed geometry in antennaarray where available space is an important factor. With carefuldesign a reasonable trade-off can be made between the inputreflection and the farfield pattern of the antenna.

ACKNOWLEDGMENT

The research reported here was supported in part by theNational Development Agency (KMR 12-1-2012-0008, NFU,Hungary) as part of the project Introduction of CognitiveMethods for UAV Collision Avoidance Using Millimeter WaveRadar, UWBSRR12, 2012-2015, by TUB, BHE, Astron andMTA-MFA, Budapest, Hungary.

REFERENCES

[1] Constantine A. Balanis Antenna Theory: Analysis and Design, John Wiley& Sons, Inc,Hoboken, New Jersey, 3rd Edition, 2005

[2] Mircea V. Rusu, Roman Baican, Igor Minin (Ed.) (2010). Microwaveand Millimeter Wave Technologies from Photonic Bandgap Devices toAntenna and Applications, ISBN: 978-953-7619-66-4, InTech 2010

[3] Pavel Hazdra, Milos Mazanek The Miniature Inverted Koch SquareMicrostrip Patch Antenna, International Symposium on Antennas andPropagation (ISAP2005)Seoul, Korea 2005 August 3-5

[4] Elder Eldervitch Carneiro de Oliveira, Antonio Luiz Pereira de SiqueiraCampos, Paulo Henrique da Fonseca Silva Quasi-fractal Koch TriangularAntenna, Microwave and Optoelectronics Conference (IMOC), 2009SBMO/IEEE MTT-S International 3-6 Nov. 2009

2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4−20

−15

−10

−5

0

InputSrefelctionScoefficientSS-SinverseSKochSsquareSfractalSanatenna

FrequencyS[GHz]

Am

plitu

deS[d

B]

SimulatedMeasured

Figure 7. Measured and simulated input reflection

0 50 100 150 200 250 300 350−20

−15

−10

−5

0

5

10

feedHoffsetH−H9mmfeedHoffsetH−H8mmfeedHoffsetH−H7.2mmfeedHoffsetH−H6.2mmfeedHoffsetH−H5.3mm

angleH[deg]

Mag

nitu

deHH[

dBi]

RadiationHpatternHH-planeHH

Figure 8. Distribution of the major beam occurs when the antenna is fedclose to its center

0 50 100 150 200 250 300 350−30

−25

−20

−15

−10

−5

0

5

10feedEoffsetE−E9mmfeedEoffsetE−E8mmfeedEoffsetE−E7.2mmfeedEoffsetE−E6.2mmfeedEoffsetE−E5.3mm

angleE[deg]

Mag

nitu

deEE[

dBi]

RadiationEpatternEE-planeEE

Figure 9. Distribution of the major beam occurs when the antenna is fedclose to its center

[5] S. A. Hamzah, M. S. Zainal, N. Abdullah, Samsul Haimi Dahlan andN. A.Cholan Size Reduction and Multiband Characteristic Using Koch FractalDipole, RF and Microwave Conference, 2006. RFM 2006. International12-14 Sept. 2006

[6] Khatun D., Shahjahan M. Multiband fractal square Koch antenna de-sign for UHF/SHF application Computer and Information Technology(ICCIT), 2012 15th International Conference 22-24 Dec. 2012

Figure 10. Antenna input reflection with changing the feed position

Figure 11. Fabricated fractal antenna array

Figure 12. Monopulse delta channel farfield pattern