Electrical Size Reduction of Microstrip Antennas by Using Defected Ground Structures Composed of Complementary Split Ring Resonator

In this study the effects of using defected ground structures (DGS) composed of a complementary split ring resonator (CSRR) and CSRR with dumbbell (CSRR-D) for rectangular microstrip antennas are investigated. On this aim, two different antennas, which are Antenna B having CSRR etched DGS and Antenna C having CSRR-D etched DGS are designed and fabricated in comparison with the ordinary rectangular patch antenna, which is Antenna A. In both Antenna B and C, CSRR structures are etched in the same position of the ground planes. On the other hand, another ordinary microstrip antenna, called Antenna D, is designed at resonance frequency of Antenna C. For the characterization, resonance frequencies, voltage standing wave ratios, percentage bandwidths, gains, ka values and gain radiation patterns are investigated both in simulations and experiments. The numerical analyses show that 29.39 % and 44.49 % electrical size reduction (ESR) ratios are obtained for Antenna B and Antenna C, respectively in comparison to Antenna A. The experimental results verify the ESR ratios with 29.15 % and 44.94 %. Supporting, Antenna C promises 68.12 % physical size reduction (PSR) as it is compared with Antenna D. These results reveal that Antenna C is a good alternative for DGS based microstrip electrically small antennas. INDEX TERMS Complementary split ring resonator, defected ground structure, electrical size reduction, microstrip patch antenna, miniature antenna.

In this study, ESR of microstrip antennas are studied by using CSRR based DGSs. On this aim, four different microstrip antennas are designed, fabricated, and characterized. The first antenna, which is Antenna A, is an ordinary rectangular patch antenna with 2.45 GHz resonance frequency in simulation. The second one, which is Antenna B, is the rectangular patch antenna having the DGS which is composed of a rectangular shaped CSRR. Following the third one, which is Antenna C, is the rectangular patch antenna having the DGS composed of a modified CSRR i.e., CSRR-D, and finally the fourth one is, which is Antenna D, an ordinary rectangular patch antenna whose resonance frequency is the same with Antenna C in simulation. Antenna A and Antenna D have entire copper sheets as the ground plane. On the other hand, in both Antenna B and C, CSRR structures are etched in the same position of the ground planes. It is important to note that a very similar topology to Antenna B has been studied by Rajeshkumar and Raghavan (2013) to provide a dual band of operation and electrical size reduction. In the topology, different than Antenna B, the gap of the CSRR is directed upwards [27]. Although there is a similar topology in the literature, the presentation of Antenna B in this study is important, since it forms the starting point of the proposed Antenna C and make it possible to reveal the improvements come from Antenna C in a fair comparison.
For the characterization of the antennas, resonance frequencies (f0), voltage standing wave ratios (VSWR), percentage bandwidths (% BW), ka values (i.e., a figure of merit for the electrical size of an antenna), % ESR rations, gain values (G) and gain radiation patterns are investigated both in simulations and experiments. Besides radiation efficiencies (ecd) and directivities (D) are investigated numerically.

II. DESIGN
The schematic views of the antenna structures and their design parameters are illustrated in Fig. 1. In more detail, Fig. 1(a) represents the top views of all antennas. On the other hand, Fig. 1(b) represents the bottom views (i.e., ground planes) of the antennas A and D, Fig. 1(c) represents the ground plane for Antenna B and finally Fig. 1(d) shows the ground plane for Antenna C. All the antennas are designed by using Ws × Ls sized Arlon AD300A laminates, which have 1.524 mm-thick-dielectric layers (i.e., h = 1.524 mm) with dielectric constant ε ! = 3 and dielectric loss tangent tanδ = 0.002 at 10 GHz sandwiched by 0.035 mmthick-copper layers (i.e., t = 0.035 mm, "# = 5.8 × 10 $ S/m). A W × L sized metallic patch is placed at the center of the top layer as shown in Fig. 1(a). The distance of the upper edge of the patch from the upper edge of the substrate is defined by parameter b. The patch is fed by 50 Ω microstrip line having line width Wf. An inset cavity is applied at the feeding point for impedance matching between the antenna and the transmission line [27]. The width and length of the inset cavity are represented by x0 and y0, respectively. It is important to note here that depending on the positions of CSRR-D and CSRR on the ground plane, i.e., depending on the parameter d in Fig. 1(d), the input impedance of the antenna changes and hence, this results with a change in y0 in each design. For Antenna B and C, the DGS consists of a Wr × Lr sized CSRR structures having groove width s and gap width g. Herein, the projection lines of the upper edges of the patches are separated with the resonators by the distance d. For Antenna C a few additional parameters are also needed to be defined, which are dumbbell width u, dumbbell inner length m and dumbbell outer length n as shown in in Fig. 1(c) and (d). The values of the design parameters were decided in house based on a series of detailed parametric analyses in simulations. During the simulations, the dimensions of the CSRR based resonators were limited in the projection area of the rectangular patch to avoid an increase in the overall structures' electrical size due to the additional CSRR. Moreover, the values of the design parameters were determined to achieve a higher gain and in the meanwhile a better ESR. On this purpose u, m, and n parameters, which came together with the proposal of Antenna C, provided an important flexibility and improvement. As the output, some pioneering numerical studies were presented in a national conference [19]. In this study, the design given in reference [19] is examined in more detail considering further numerical analyses, fabrication, and experimental studies. This examination is performed in a comparative manner firstly with the Antennas A, B and D and secondly with the related literature. All the final design parameters and their values are tabulated in Table I including their explanations.  For the experimental purposes, the designed antennas are fabricated, and the photographs of Antenna A, B and C are shown in Fig. 2 including their top and bottom views. Besides, the top view of the fabricated Antenna D is presented in Fig. 3 in comparison to that of Antenna C to reveal the PSR. For all antennas, SMA type connectors with 50 Ω characteristic impedances are mounted at the transmission line ends.

IV. RESULTS
| %% | versus frequency plots obtained by simulations and experiments are shown in Fig. 5 Herein, although the lower order resonance frequencies for Antenna B and C are observed around 1.1 and 0.92 GHz, respectively and these resonance frequencies promise much smaller electrical size reductions, they are out of concern since their | %% | values cannot reach −10 dB despite the detailed impedance matching studies. Moreover, the higher order resonance observed for Antenna D, which is around 2.31 GHz, is also out of interest, since Antenna D is mainly designed to operate at 1.36 GHz, which is the f0 of Antenna C to compare their physical sizes.  antennas under test, Antenna C is the electrically smallest one whose ka value is less than 1. For electrical size reduction studies, ka is an important and commonly used figure of merit [7,37], where k is the wavenumber which is defined as k = 2π/λ, where λ is the free space wavelength at f0 of the antenna and a is defined as the radius of the smallest sphere which is able to surround the antenna. ka is required to be less than 1 for being electrically small, however for the antenna structures having completely ground plane, ka is required be less than 0.5 [7].
Supporting the ESR, Fig. 3 reveals the PSR due to this electrical small design, where the larger physically sized antenna is Antenna D and the smaller one is Antenna C. Herein, Antenna D is the ordinary microstrip antenna, which is designed at ( of Antenna C. 2a value is measured to be 55.54 mm for Antenna C and 97.95 mm for Antenna D. In this study, the % PSR is defined as the percentage reduction in the metallic patch area. In more detail, for Antenna C the patch area is calculated to be 1506.49 mm 2 . On the other hand, for Antenna D the patch area is 4725 mm 2 . Therefore, a 68.12 % PSR has been achieved which is consistent with the ESR values of Antenna C. To demonstrate the effects of the DGS on the antenna radiation mechanism, the surface current plots of Antenna B at 1.73 GHz and 2.45 GHz and of Antenna C at 1.36 GHz and 2.45 GHz are presented in Fig. 6(a) and 6(b), all in 0° phase angles. The rainbow scale bar provides surface current intensities in A/m whose maximum value is clamped at 600 A/m for better demonstration of the difference in the surface currents. The selected frequencies are important, since 1.73 GHz is the ( of Antenna B, 1.36 GHz is the ( of Antenna C and 2.45 GHz is the ( of Antenna A. The figure shows that at 1.73 GHz, the surface current densities on CSRR structure is much stronger than that of 2.45 GHz revealing that CSRR has an active role in the radiation mechanism at 1.73 GHz. Similarly, at 1.36 GHz, the surface current densities on CSRR-D structure are much stronger than that of 2.45 GHz revealing that CSRR-D has an active role in the radiation mechanism at 1.36 GHz.   7 shows the simulated and the measured E-and Hplane radiation patterns in terms of antenna gains in dBi with respect to the elevation angle θ. In general, the results are compatible with each other. Although at first sight there seem to exist some discrepancies especially in the crosspolarization (i.e., crosspol) results, in fact they are close to each other in linear scale. On the other hand, the discrepancies observed in the co-polarization (i.e., copol) results may be due to imperfect fabrications, imperfect soldering process of the connectors, and measurement errors. The radiation patterns of Antenna B and C present increased backward radiations due to the CSRR and CSRR-D slots patterned in the ground planes in comparison to the reference antenna. This may explain the reduced directivity of the designs with the defected ground structures.  The remaining characterization results obtained by the simulations and experiments are % BW and VSWR where % BW is calculated at -10 dB. As an observation, the % BW of Antenna C increases slightly as compared to Antenna B and decreases slightly as compared to Antenna A, however the changes are not found to be significant. On the other hand, VSWR values do not exceed 1.27 in general which is the proof of good impedance matchings. All the results are tabulated in Table II for better visualization. The simulation and experimental gain values in Table II represent the maximum gains obtained by considering both E and Hplanes for each antenna. For the antenna performance comparisons, the specific antenna parameters (i.e., ( , and G) together with the % ESR and % PSR values are listed in Table III, if exists, regarding the proposed Antenna C together with the other single microstrip antennas reported in literature whose DGS are composed of CSRRs. Herein multiple input multiple output (MIMO) antenna designs [22,44,53] are not included in the comparison table since the usage of multiple antennas in the design may affect the individual antenna performances and this may cause an unfair comparison. In addition, the CSRR based DGS structures reported in reference [48] are also not included in the comparison table since the study mainly focuses on the sensor application rather than designing a small antenna thus the fundamental antenna parameters such as gain, efficiency and radiation pattern are not provided.
It is important to note that the % ESR values presented in Table III are calculated by using Equation (1), which is based on the resonance frequency, and % PSR values are calculated considering the reduction in the patch areas reported in each study. Since all the studies do not include both simulation and experimental analyses, Table III includes only simulation or experimental results for some references.
The studies that are used in the comparison can be classified in four groups: The first group consists of the studies which promise higher gain values, however lower % ESR than our study [12,25,32]. In contrary, the second group consists of the studies which promise lower gain values, however higher % ESR [27,30,32]. The third group consists of the studies which promise both lower gain and lower % ESR [18,45]. It is important to note that references [32] and [45] applied some major geometrical modifications on the metallic patch in addition to DGS structure. Especially, the modifications made by reference [32] in their final design increased the area of the radiating element which may be a handicap in the concern of ESR and PSR. Finally, for the fourth group, references [29], [46], and [47] propose lower % PSR values, however higher gain values than that of this study. Among the references discussed in Table III, especially references [12], [25], [32], [45], [46], and [47] offers more complex DGS patterns as compared to this study. As the result, the proposed Antenna C promises an advantage at least on one parameter under interest as compared with the closely related literature. [32] 6.3 6.3 6.3 6.3 6.3 n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a 5.0 @ 5.20 GHz 6.3 @ 3. n/a n/a n/a n/a n/a n/a