Highly directive patch antenna using planar metamaterial.

Gupta, Monish ; Saxena, Jyoti ; Vohra, Anil 等

Introduction

In last few years, there has been a great deal of attention on the study and understanding of metamaterials. Metamaterials are the materials that can have refractive index value that can be negative or positive that is less than one. In our design we will use metamaterial that has refractive index value which is less than one. According to Snells law, a material that has refractive index value less than one can congregate the electromagnetic wave when electromagnetic wave passes through it. Now refractive index less than one can be achieved by keeping the value of permittivity to be less than one or by keeping value of permeability to be less than one as the value of refractive index is square root of permittivity and permeability. Permeability less than one is achieved by using Split Ring Resonator (SRR). SRR structure consists of two concentric annuli of conducting material. There is a gap on each ring and each ring is situated opposite to the gap on the other ring. The schematic of SRR structure is shown in figure 1.

[FIGURE 1 OMITTED]

In our design we are making metamaterial by using two symmetrical layers of SRR. Each layer consists of 3X3 units of SRR. Material to construct SRR is Aluminium Figure 2 shows the top view of split ring resonator metamaterial of our design and the distance(a) between the centers of two SRR is 1.01 mm.

[FIGURE 2 OMITTED]

Figure 3 shows the side view of split ring resonator metamaterial of our design. Here 1 is the distance between the two symmetric layers and is 0.5 mm

[FIGURE 3 OMITTED]

The effective permeability of such structure is

[[mu].sub.eff] = 1 - [[pi]r.sup.2]/[a.sup.2]/1 + 21[sigma]/[??][omega]r [[mu].sub.0] i - [31c.sup.2.sub.0]/ [[pi][??][omega].sup.2] ln 2c/d [r.sup.3]

Literature Review

All known materials have index of refraction which is more than one however in 1968 Veselago [1] found that it is possible to make a material that has index of refraction less than one, even negative. These types of artificial materials are called metamaterials. In 1999 Pendry [2-3] proposed that metamaterial can be generated by incorporating in a periodic manner various types of artificially fabricated, extrinsic, low dimensions in homogeneities. D. R. Smith [4] of Darpa (Defence Advance Research Project Agency) proposed that metamaterials are a new class of ordered composites that exhibit exceptional properties not readily observed in nature. These properties arise from qualitatively new response functions that are: (1) not observed in the constituent materials and (2) result from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities. In electromagnetic any material is described by two factors i.e. electric permittivity ([member of]) and magnetic permeability ([mu]). Electric permittivity describe how material polarize in presence of electric field and magnetic permeability describe how material polarize in presence of magnetic field and Refractive index ([eta]) of material = [+ or -] [square root of (([member of] [mu]))]

Based on electric permittivity and magnetic permeability in 2005 Richard W. Zilkowski [5] proposed one class of metamaterial as zero refractive index metamaterial. In these materials we assume that either electric permittivity or magnetic permeability is almost zero So we have refractive index of material which is positive but nearly equal to zero. Another class of metamaterials is materials with refractive index value which is less zero or negative value of refractive index.

Advantages of Metamaterials in Antenna Design

1) Improvement of directivity of antenna

Directive gain of an antenna in a particular direction is defined as ratio of power density in that direction at a given distance to the power density that would be radiated at the same distance by an isotropic antenna radiating the same total power Maximum Directive gain is defined as directivity of antenna

Consider a monopole antenna placed inside the metamaterial having refractive index [[eta].sub.1]. We assume [[eta].sub.1] equal to zero

[ILLUSTRATION OMITTED]

When electromagnetic wave traverses the interface from a material with refractive index [[eta].sub.1] to another material with refractive index [[eta].sub.2] the change in trajectory can be determined from the ratio of refractive index [[eta].sub.2]/[[eta].sub.1] by using snells law

[[eta].sub.1] sin [[theta].sub.1] = [[eta].sub.2] sin [[theta].sub.2]

sin [[theta].sub.2] = [[eta].sub.1] sin [[theta].sub.1]/[[eta].sub.2]

Here we are assuming c1 to be nearly equal to zero so sin [[theta].sub.2] will come to be nearly equal to zero i.e. [[theta].sub.2] will be nearly equal to zero i.e. by using metamaterial having refractive index nearly equal to zero electromagnetic waves will try to travel in a direction normal to metamaterial surface or we can say the directivity of antenna in a direction normal to material has been improved.

2) Improving bandwidth of antenna

We propose that bandwidth of antenna to achieve particular directivity can be increased by using metamaterial. Directivity of antenna can be increased by using metamaterial having refractive index nearly equal to zero and [eta] = [square root of (([member of] [mu]))]. So at one particular frequency [f.sub.1] we are achieving permittivity [member of] [approximately equal to] = 0, and at frequency [f.sub.2] we are achieving permeability [mu] [approximately equal to] = 0 to attain refractive index nearly equal to zero.

That is to say bandwidth of antenna [f.sub.2] - [f.sub.1] can be improved to any extend by using metamaterial

3) Improving Transmission Efficiency of patch antenna

Transmission efficiency of patch antenna is given by = [2Z.sub.2]/([Z.sub.1] + [Z.sub.2]) Where [Z.sub.1] = impedence of source [Z.sub.2] = Impedance of material which is receiving electromagnetic signals from sourse

Transmission efficiency will be maximum when [Z.sub.1] = [Z.sub.2] i.e maximum power is radiated from source to load when source impedance is equal to load impedance.

For plane wave exiting a material in to free space [[eta].sub.2] = [[eta].sub.0] i.e. [member of] = [member of]o, and [mu] = [[mu].sub.0] So [Z.sub.2] = [square root of (([[mu].sub.0]/[[member of].sub.0]))]

For material we have [member of] = [member of]r [member of]o, and [mu] = [[mu].sub.r] [[mu].sub.0] So [Z.sub.1] = [square root of (([[mu].sub.r] [[mu].sub.0]/[member of]r [member of]o))]

For maximum efficiency we have [Z.sub.1] = [Z.sub.2] i.e. [square root of (([[mu].sub.r]/[member of]r) = 1 or [[mu].sub.r] = [member of]r

As in metamaterial we can change the value of relative permittivity as well as relative permeability at a particular frequency by suitable inclusions so we can achieve maximum radiation intensity by using metamaterial.

Design & Simulation

Simulation of patch antenna with and without metamaterial were computed and it is found that directivity has improved by 38.40%.

Patch antenna in our design consist of a ground of Tin metal whose length in x and y direction are 20 mm and 20 mm. Height in z direction is .25 mm. Substrate is composed of Taconic tly (tm) whose length in x and y direction are 10 mm and 10 mm Height in z direction is .75 mm. Patch is placed on substrate and its length and width are 2 mm and 2 mm. Patch antenna is fed by a micro strip line and a wave port as shown in figure 4.

[FIGURE 4 OMITTED]

Figure 5 shows the radiation pattern obtained by using anasoft hfss for patch antenna.

[FIGURE 5 OMITTED]

Maximum Directivity using far field setup is computed and is found to be .7641 Then this patch antenna is covered by the metamaterial layers as shown in Figure 6.

[FIGURE 6 OMITTED]

Figure 7 shows the radiation pattern obtained by using anasoft hfss for metamaterial covered patch antenna.

[FIGURE 7 OMITTED]

Again Maximum value of directivity using far field set is computed and found to be 1.1486

Conclusion

A new patch antenna with a metamaterial cover has been designed. The directivity achieved for patch antenna was nearly 76.461%. By using metamaterial cover on patch antenna the directivity was increased by 38.40%.

References

[1] Vesalago. V.G. "The Electrodynamics of substances with simultaneously negative values of permittivity and magnetic permeability." Sov. Phys.Usp.,10-4(1968), 509-514.

[2] Pendry. J.B., Etal.: "Extremely low frequency plasmas in metallic microstructures". Phys. Rev. Lett. 76-25(1996), 4773-4776.

[3] Pendry. J.B., Etal.: "Magnetism from conductors and enhanced nonlinear phenomena". IEEE. Trans. Microwave Theory Tech., 47(1999). 2075-2084.

[4] Smith. D.R. and Kroll. N.: "Negative refractive index in left handed materials." Phys. Rev. Lett., 85, 14(2000), 2933-2936.

[5] Richard W. Ziolkowski" Metamaterial properties, design and antenna applications" 2005 IEEE International symposium on Microwave, Antenna, Propagation, and EMC technologies for wireless communications proceedings, 2004.

[6] Fangming Zhu, Qingchun, Lin, Jun Hu "A directive patch antenna with a metamaterial cover", Proceedings of IEEE, Dec 2005.

Monish Gupta

Lecturer, UIET

Kurukshetra University

Kurukshetra

Dr. Jyoti Saxena

Assistant Professor

G.Z.S.C.E.T

Bathinda

Dr. Anil Vohra

Professor, DOE

Kurukshetra University

Kurukshetra