Metamaterial Based Circular Disc Patch Antenna Miniaturization

A novel metamaterial structure has been proposed for its operation at 2.4 GHz. A circular disc patch antenna resonating at dual band frequency with 2.4 GHz and 3.36 GHz has been designed using full field solver CST MWS tool and the loading effect of the metamaterial has been shown. The loading of metamaterial shows a radial size reduction of 56.71% in the circular disc patch (dimensional space reduction by 81.26%) while the effect of loading the metamaterial array and loading the metamaterial with defected ground plane show that without reducing the disc patch radius, the patch antenna can resonate at 1.00 and 1.942 GHz respectively, these yield a lower frequency shift of 58.33% and 19.79%. The designed metamaterial consists of two copper conductive concentric circular rings over a polyimide substrate. Various antenna parameters such as S11, VSWR, Bandwidth, Gain, Directivity and Radiation efficiency have been obtained for the circular disc patch antenna, circular disc patch antenna loaded with the metamaterial, circular disc patch antenna loaded with an array of metamaterial and are compared. A spice circuit has been derived for the reflection coefficient of the circular disc patch without loading the metamaterial, circular disc patch loaded with metamaterial using Keysight based ADS tool for its inclusion in a traditional electrical circuit solver tool.


Introduction
An influx of portable electronic devices has brought new challenges in the electronics component miniaturization. The antenna being the communication media across various components needs to be miniaturized to save the real estate. The PCB based microstrip antennas although are small and low profile in size, at lower frequency for its applications such as Bluetooth, WLAN, WiFi and RFID the antenna dimension is still large. Past studies have shown many miniaturization techniques such as high permittivity substrate [1][2][3], dielectric loading [4,5], shorting pins [6][7][8] and slots [9] towards antenna patch miniaturization but the side effect arising out of the miniaturization brings in some reduction in its efficiency, gain and a decrease in bandwidth [10,11] apart from the impedance mismatch. An artificial metamaterial with its negative permittivity and permeability being loaded over the ground plane for the patch antenna allows it to resonate in the desired frequency range at smaller dimension without a loss in its antenna parameters. This is achieved due to the metamaterial structure itself providing resonance at the subwavelength. Previous works with the application of metamaterial by many authors [12][13][14][15][16][17][18][19] have brought new research with the metamaterial being used for its gain enhancement and bandwidth improvement for a radiating patch. Although there can be variety of metamaterial shapes, a simple metamaterial structure using two concentric metal rings has been used here. The work presented here provides a design of Circular Ring Resonator (CRR) based Double Negative (DNG) metamaterial over the frequency range 1.5 -4 GHz. The loading of this CRR metamaterial allows a radial size reduction from 39.32 mm to 17.02 mm (reduction of 56.71%) in the patch element for its resonance at 2.4 GHz while providing a similar bandwidth, gain and efficiency. In addition to the miniaturization of the radiating patch element with the metamaterial, the loading of metamaterial array over a fixed size patch element has shown a lowering in resonance frequency from 2.4 GHz to 1.00 GHz (reduction by 58.33%) while the loading of metamaterial array with defected ground plane provides a lowered resonance frequency shift from 2.4 GHz to 1.942 GHz (reduction by 19.79%). Since the reflection coefficient for the patch element has been obtained using full field solver tool CST MWS, an equivalent transfer function for its spice circuit has been obtained using Keysight based ADS tool (2012.08) and compared for its verification. The paper has been divided into the following Sections with Sec. 1 for the Introduction, Sec. 2 presents components of antenna with Sec. 2.1 for CRR metamaterial design, Sec. 2.2 for patch design with and without loading metamaterial while Sec. 3 talks about the planar patch and its resonance frequency shift with the loading of DNG metamaterial structure and its patch size equivalence without loading CRR metamaterial. The result has been described in Sec. 4. The Spice circuit provides a convenient mechanism to integrate electrical element into any circuit solver tool, its extraction has been also shown in Sub-sec. 2

CRR metamaterial
The metamaterial is a type of material which does not exist or does not fall within a class of conventional materials however is created using natural materials. A metamaterial gains its properties ('ε', 'µ') from its structure rather than the material itself thus any material in a defined shape can form a metamaterial. First appearance and application of metamaterial was described by Pendry et al. [4,5], [20], Smith et al. [21,22] in the early 2000 where it was shown that metamaterial can provide a negative permittivity 'ε' and permeability 'µ'. It led towards the development of experimental verification of the LHM metamaterial. However within the last few years, the application of metamaterials has become widespread with many researchers across various disciplines [14][15][16][17][18][19]. A DNG material is known for its provision of negative refractive index and supports forward and backward energy flow at the same time with a 180° phase shift in phase (vp) and group velocity (vg) [6]. Fig. 1 shows two concentric rings made of copper conductor with its thickness of 0.01 mm and outer radius 'R' of 7.1 mm, width 'w' 0.8 mm and spacing 'g' of 0.5 mm has been designed over a polyimide substrate (dielectric constant of 3.5 and tangent loss of 0.0027) with a dimension of 14.6 mm x 14.6 mm x 1.6 mm. CST microwave studio has been used to design the model and get its simulation results. The analytical function (1)(2)(3)(4)(5) can be used to plot the permittivity and permeability function over the frequency range and is shown in Fig. 2.
(1)   The CRR structure is completely embedded within a TEM waveguide to derive the simulation result and is excited with an electric field along its x-direction while PEC and PMC conditions are applied along its orthogonal directions. Fig. 3 shows the plot of the return, transmission and absorption magnitude [23,24] of the CRR structure.

Planar patch
Times Fig. 4 shows a design of circular disc patch antenna without loading CRR metamaterial with its resonance at 2.4 and 3.36 GHz while Fig. 5 shows the bottom side of the circular disc patch with loading CRR. Similarly Fig. 6 shows the bottom side of the circular disc patch antenna when the ground is defected with loading of CRR metamaterial and resonates at 2.4 GHz.   The patch antenna has a circular disc element with its 39.32 mm radius and 0.01 mm copper conductive thickness and the patch is connected with a copper conductive feed of dimension 40.32 mm x 3.6 mm x 0.01 mm. The patch element has been designed over 1.6 mm thick polyimide substrate (with its relative permittivity 3.5 and tangent loss of 0.0027) with its dimension of 126.64 mm x 142.96 mm x 0.01 mm while the substrate has been laid over a copper conductive patch for its ground layer and has a dimension of 126.64 mm x 142.96 mm x 0.01 mm. The circular disc patch antenna loaded with CRR metamaterial has been designed using copper conductive element with 17.02 mm for outer radius and thickness 0.01 mm while its feed has a dimension of 19.72 mm x 3.6 mm x 0.01 mm. Similar to the patch antenna without CRR metamaterial, the patch element has been designed over 1.6 mm thick polyimide substrate (with its relative permittivity 3.5 and tangent loss of 0.0027) with its dimension of 50.6 mm x 54.5 mm x 0.01 mm while the substrate has been laid over a copper conductive patch for its ground layer and has a dimension of 50.6 mm x 54.5 mm x 0.01 mm. The CRR metamaterial has been loaded at its ground layer at (-4.7 mm, 7 mm) from the center of the circular patch.  A comparison of the reflection coefficient for the patch antenna without loading CRR metamaterial and with loading CRR metamaterial has been plotted and is shown in Fig. 6. As shown in Fig. 7, the patch element loaded with CRR metamaterial resonates at 2.4 and 3.36 GHz while providing a radial size reduction of 56.71% with the radius from 39.32 mm to 17.02 mm, thus saving a dimensional space by 81.26%. The S11 parameter for the patch without the metamaterial has been similar to the S11 parameter for the patch element loaded with metamaterial with the magnitude below -10 dB and they provide comparable antenna parametric results. The antenna radiation for the planar patch without metamaterial while resonating at 2.4 and 3.36 GHz is shown in Figs. 8 and 9.

Spice circuit for patch without CRR
As the spice circuit of the antenna can provide electrical inclusion in the traditional circuit solver tools, an equivalent spice circuit has been derived here using ADS. Figure 12: S11 original and fitted magnitude for patch without CRR.   Figures 12 and 13 show the original and fitted response of the magnitude and phase for the S11 parameter. Figure 14 shows the obtained equivalent spice circuit while Table 1 provides the individual RLC parametric value. These plots show that the fitted parameters provide a similar response of a full field solver tool response.

Spice circuit for patch loaded with CRR
As defined in Sec. 2.2.1, the spice circuit equivalence of the S11 parameter for the planar patch antenna loaded with CRR metamaterial has been obtained and their S11 magnitude and phase plots have been shown in Figs. 15 and 16. Table 2 provides the obtained RLC parameters while Fig. 17 shows the spice circuit. Figure 15: S11 original and fitted magnitude for patch with CRR. Figure 16: S11 original and fitted phase for patch with CRR. Figure 17: Spice circuit for patch antenna with CRR.

Spice circuit for patch loaded with CRR defected ground
An equivalent spice circuit has been derived here using ADS. Figure 18: S11 original and fitted magnitude with CRR defected ground. Figure 19: S11 original and fitted magnitude with CRR defected ground.     Figures 18 and 19 show the original and fitted response of the magnitude and phase for the S11 parameter. Figure 20 shows the obtained equivalent spice circuit while Table 3 provides the individual RLC parametric value. These plots show that the fitted parameters provide a similar response of a full field solver tool response. The dimensional size of the patch configuration as defined in previous Sec. 2.2 has been used for the design here and is shown in Fig. 20 while the patch element loaded with an array of CRR metamaterial is shown in Fig. 21. The circular disc patch in this Section (when not loaded with CRR metamaterial and loaded with CRR metamaterial) has 39.32 mm radius and 0.01 mm copper conductive thickness, the patch is connected to copper conductive feed of dimension 40.32 mm x 3.6 mm x 0.01 mm. The patch element has been designed over 1.6 mm thick polyimide substrate (with its relative permittivity 3.5 and tangent loss of 0.0) with its dimension of 126.64 mm x 142.96 mm x 0.01 mm while the substrate has been laid over a PEC conductive patch for its ground layer and has a dimension of 126.64 mm x 142.96 mm x 0.01 mm.      Figure 24. With the application of loading an array of CRR metamaterial and CRR metamaterial with defected ground with x-and ydirectional spacing of 14.6 mm, the same size patch element provides a downward resonance shift while resonating at 1.00 GHz and 1.942 GHz respectively. Here the disc patch, feed, substrate and ground dimensions are kept the same throughout these designs.

Simulation results
Various antenna parameters such as resonance frequency, S11 parameter, bandwidth, gain, directivity and radiation efficiency when patch is not loaded with CRR metamaterial and when patch is loaded with CRR metamaterial are shown in

Conclusions
This paper presents an effective miniaturization technique for a standard sized patch antenna with the loading of CRR metamaterial structure in its individual element and array form. The patch element designed over the CRR metamaterial shows that the loading of the metamaterial reduces the patch radial size by 56.71% (or its dimensional space by 81.26%) and provides an increase in radial efficiency. Similarly the loading of CRR metamaterial array while maintaining the patch size as of the patch element (without loading it with CRR metamaterial) provides a downward resonance frequency shift with resonance at 1.00 GHz for CRR array loaded patch and 1.942 GHz for CRR array defected ground plane. A mechanism to derive the spice circuit for the patch antenna with and without CRR metamaterial loading has also been obtained for its inclusion in electrical circuit.