1 Introduction

Metamaterial properties are exotic which it acquires from its structures and not from the constituent material. Various kinds of metamaterial (MTM) structures have been reported in literature. In MTM, the acquired properties of material such as permittivity, permeability and refractive index have effective negative value in designed frequencies when compared with the natural material having positive values for all frequencies [1, 2]. Hence, MTM characteristics include negative values for permeability, permittivity, refractive index, phase velocity which is opposite direction to group velocity, etc. MTM was used as absorber, invisibility cloak, and alter the device normal characteristics. In MTM-inspired antennas, any one of the MTM characteristics was utilized to enhance antenna characteristics. MTM provides increased directivity, gain, obtain multiband in antennas. This is elaborated in the subsequent paragraphs.

More compact antennas were realized using MTM loading [3,4,5,6]. MTM has been analyzed and used in reducing antenna patch size by embedding MTM structure at different locations in substrate between ground and patch [3]. MTM has also been used to replace the substrate and obtained broadband impedance matching for multiband operation of an antenna [7, 8]. These designs were bilayer which lead to increased size and complexity while fabrication. The total size of the design was huge namely 165 × 165 × 4 mm3 [7]. MTM structure etched in ground plane has shown patch size reduction [9]. MTM was used to increase gain and bandwidth [10,11,12]. There were four layers of metamaterial [11] or a layer of additional dielectric and metamaterial [12] placed above the patch which increased the thickness of the antenna and also these were bulky. A method was proposed for directive patch antenna by having MTM located in lattice arrangement above the antenna [13]. MTM has been used as a superstrate to reduce radiation towards biological tissues without compromising far-field radiation characteristics of an antenna [14]. In almost, all of these designs, the concept of patch antenna is changed from 2D antenna to 3D antenna due to additional layers. The overall size of the antennas was huge because of the increase in thickness by the inclusion of additional layers.

MTM structure has been used along with Planar Inverted-F Antenna (PIFA) to achieve dual-band response with improved characteristics in radiation pattern and gain [15]. An array of MTM structures such as square CSRR [16], circular CSRR [17], square SRR [18], I-shaped SRR [19] have been analyzed on patch or ground plane to achieve high gain, reduce size and increase bandwidth. Rhombus-shaped single/multi-ring CSRR(s) have been used in ground plane of patch antenna to achieve directional antenna [20]. In this, the resonant frequency of the antenna was decreasing as the number of MTM on ground plane was increasing with minimal gain trade-off. Tripleband CPW-fed antenna was designed by placing 3-Nos. SRR on back side of the substrate [21]. Complementary spiral resonator transmission line was used in realizing dual-band antenna with good impedance match and better gain value [22]. MTM structures such as single-ring CSRR [23, 24], multiple-ring CSRR [25], square OCSRR(s) [26] and circular OCSRR [27] were engraved in patch for achieving dual/triple-band antenna. Inclusion of CSRR either normal CSRR or OCSRR on patch induces strong resonance at particular frequency. Also, the number of rings in the CSRR provides resonances at different frequencies. By this, multi-band operations were realized. Ultra-wideband antennas were realized using an array of parasitic coupled single-ring square SRR and CRR [28] and MTM-inspired radiating patch [29]. Multi-band antenna was realized and return loss was improved using CRLH MTM-inspired antenna structure [30]. From this, we can conclude that novel properties of MTM are improving the antenna characteristics such as resonance frequencies, bandwidth, gain, radiation pattern, etc.

Having found wide applications of MTM, the inquisitiveness went in analyzing MTM structures as radiating patch. In modern era with many applications in single device, it becomes paramount to have an antenna to operate in more than one band to reduce constraints in space, cost and integration. Different structures of MTM such as polygon-ring SRR [31], rectangular SRR [32], circular SRR [33], hexagonal SRR [34], circular SRR and circular CRR [35, 36], triangular electromagnetic resonator [37] and ELC [38, 39], capacitive ring SRRs on the other side of loop antenna [40] were used in realizing dual/triple band antenna.

In planar form of antenna realization, antenna resonance in more than one band can be obtained by employing either of the following: different dimensions of pole length, MTM, shorting pin, via, slot, etc. This paper investigates square SRR and square CRR for achieving dual-band antenna since significance of this shape is not yet explored.

When compared to circle having diameter ‘x’, the square having side ‘x’ will have larger perimeter. Hence, it can be professed that for the same lateral and vertical dimensions of the patch using circular ring and square ring, square shape will require less space for the given frequency or in other words for same lateral dimension, square will achieve lower-frequency resonance than circle. Even though, there were many shapes of MTM analyzed as radiating elements, the square shape of outer CRR and inner SRR is not attempted so far and also square geometry has larger perimeter than circle. Hence, this research analyzes the square CRR and square SRR as radiating elements.

2 Antenna design and simulated results

The evolution of the proposed antenna configuration is shown in Fig. 1. Initial dimensions of patch, substrate are found by calculating for square patch operating at 5 GHz. Flame Retardant material FR-4 which has relative dielectric constant (εr) of 4.4 + 0.088i is used as substrate. This substrate is readily available and low cost. The height of the substrate is fixed as 1.6 mm. Coplanar waveguide gap and feed width are found for the input impedance value of 50 Ω [41]. Computer program is written for finding these dimensions. This paper analyzes the antenna design using single-ring SCRR and dual-ring SSRR. Hence, the radiating elements are modeled as SSRR and SCRR. As the proposed radiating structure has two resonant elements, this antenna will produce dual-band operation if the dimensions of various sections are correct. It is given that the modification of ground plane will change the resonance characteristics [27, 42]. Hence, it is planned to analyze different structures for ground plane.

Fig. 1
figure 1

Evolution of proposed antenna

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The evolution of this antenna started with rectangular-shaped ground plane which is shown in Fig. 1a. Then, the ground is modified to triangular and to trapezoidal shape. The relations between frequency and dimension of circular CRR and circular SRR are given, respectively, in [43] and [2]. These equations are adjusted according to square geometry and given in Eqs. (1) and (2). Initial dimensions of SCRR and SSRR are found using Eqs. (1) and (2), respectively. The variables used in these equations are mentioned in Fig. 2 and also listed in the following paragraphs. Impedance matching between feed and the radiating elements is explained under parametric studies.

$$f_{{{\text{SCRR}}}} = \frac{c}{{4{ }L_{c} \sqrt {{\text{Re}}(\varepsilon_{r} )} }}$$
(1)
$$f_{{{\text{SSRR}}}} = \frac{c}{{\pi^{2} }} \sqrt {\frac{{3 \left( {l_{1} - l_{2} - 2w } \right) }}{{0.637^{2} {\text{Re}}(\varepsilon_{r} ) l_{2}^{3} }}}$$
(2)

where εr denotes relative permittivity of substrate; c denotes the velocity of light in free space; fSCRR and fSSRR, respectively, denote the resonance frequency of SCRR and SSRR.

Fig. 2
figure 2

Geometry of the proposed antenna

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The rectangular-shaped ground which is shown in Fig. 1a produces band-1 from 2.48 to 2.52 GHz and band-2 from 3.76 to 4.46 GHz. As the ground plane shape is modified to triangular which is shown in Fig. 1b, the resonance changes as band-1 from 2.41 to 2.45 GHz and band-2 from 3.16 to 3.57 GHz. To obtain the bandwidth in intermediate region, it is predicted that trapezoidal shape may give the optimum result. As given in Fig. 1c, the trapezoidal-shaped ground plane gives band-1 from 2.47 to 2.5 GHz and band-2 from 3.58 to 4.29 GHz. As the results of configuration in Fig. 1c tally with the predicted result, it is decided to proceed this research from trapezoidal-shaped ground. The return loss characteristics of all the three antenna configurations given in Fig. 1 are shown in Fig. 3a. The simulations are carried out using Ansys HFSS software.

Fig. 3
figure 3

Return loss characteristics

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To verify the MTM characteristics of SSRR, the MTM property extraction method specified by Smith et al. [44] is used by keeping the MTM inside waveguide arrangement and properly specifying the boundary conditions and excitations. This is also carried out using Ansys HFSS software by making waveguide arrangement and keeping the SSRR inside and following the procedure laid by Smith et al. The result of MTM property extraction is given in Fig. 4. The characteristics such as impedance (z), refractive index (n), permittivity (ε) and permeability (μ) are displayed in this figure. From this, it can be inferred that the refractive index and permeability are having negative values at the frequencies of operation of SSRR MTM.

Fig. 4
figure 4

Properties of SSRR

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The final values of each variable mentioned in Fig. 2 are as follows: Ws = 31.7 mm, Ls = 27 mm, Wt1 = 1 mm, Wt2 = 15 mm, Lg = 10 mm, Wf = 1.3 mm, Lf = 10.2 mm, Gf = 0.2 mm, Lc = 14.5 mm, ring width of SCRR and SSRR w = 0.6 mm, d1 = 2.4 mm, d2 = 0.8 mm, l1 = 8.5 mm, l2 = 5.7 mm, g = 0.5 mm, 11 = 1.17 mm and 12 = 1.053 mm.

3 Parametric studies

Parametric analyses on short base of trapezoidal ground (Wt1), length of feed (Lf), matching section parameter (a) and length of gap (g) are carried out and explained in this section. The necessary parametric studies are done to find the optimum value for the variables given in Fig. 2.

The value of trapezoidal ground plane short base (Wt1) is varied from 1 to 4 mm. As the value is changed from 1 to 4 mm, the band-1 width decreases and starting frequency of band-2 also increases. From this, it is fixed that the value of Wt1 is 1 mm as it covers 2.4–2.5-GHz and 3.37–4.35-GHz bands. This is shown in Fig. 5a.

Fig. 5
figure 5

Parametric analyses

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Length of the feed (Lf) is also one of the main contributors to antenna excitation. Hence, it is varied as 10.2 mm, 10.25 mm and 10.35 mm. From this, the value of Lf is fixed as 10.2 mm as this value gives good coverage of 2.5 GHz band of WLAN and 3.5 GHz band of WiMAX compared to other values of Lf. This is displayed in Fig. 5b.

In all the microwave devices, the impedance matching plays an important role in achieving good performance. To get good return loss in the operating frequencies of the device, there should be proper matching between the different sections of the microwave device or different parts in an antenna. The width of the feed (Wf) and connecting line from outer SCRR to inner ring of SSRR (In) is related as given in Eq. (3).

$$I_{n} = a^{n} \times W_{f} ;n = 1, 2$$
(3)

Hence, the matching section parameter ‘a’ is crucial to obtain two frequency bands exhibiting the required bandwidth. The parametric studies are carried out to find the optimum value of ‘a’. The value of ‘a’ is varied as 0.8, 0.9 and 1. It is evidenced from figure that the value of a = 0.8 does not give any resonance but the value of a = 1 gives two band resonance. Hence, the value of a = 0.9 is analyzed and found that it gives required bandwidth in both bands without affecting minimum value of return loss. From this a = 0.9 is found as the optimum value. The variation of return loss with respect to ‘a’ is shown is Fig. 5c.

The next set of parametric studies is carried out to fix the value of gap length (g) of SSRR. It is varied as 0.4 mm, 0.5 mm and 0.6 mm. The value of g = 0.4 mm gives band-1 from 2.44 to 2.48 GHz, g = 0.6 mm gives band-1 from 2.45 to 2.49 GHz and g = 0.5 mm gives band-1 from 2.40 to 2.50 GHz. The width of band-2 is not affected much with the change in dimension of ‘g’. Hence, the value of g = 0.5 mm is fixed as the optimum value. This is presented in Fig. 5d.

4 Results and discussions

The return loss (S11) characteristics of the three configurations of antenna discussed in design process which are also shown in Fig. 1a–c are given in Fig. 3a. It has been inferred that the trapezoidal ground covers the WLAN frequency band at 2.45 GHz. Then, necessary parametric analyses are carried out and design values are optimized. Fabrication of proposed antenna is very simple as it is fed by CPW and printed on one-sided 35-μm copper clad FR-4 substrate. The proposed antenna shown in Fig. 2 is fabricated and soldered with Sub-Miniature-A (SMA) connector at feed which is shown in Fig. 6. This SMA connector has low VSWR of 1.08 upto 15 GHz. The simulated and measured values of return loss are plotted in Fig. 3b. From this, it can be observed that the simulated and measured values are in good agreement. Comparison between numerical results which are computed using design Eqs. (1) and (2) with actual results of an antenna is presented in Table 1. This demonstrates the close agreement between calculated and measured values as well as validates the proposed design approach. The minor deviation between numerical and actual can be attributed to coupling effect between SCRR and SSRR which is not considered in Eqs. (1) and (2). The comparison of existing antennas with the proposed antenna in terms of size, substrate permittivity, number of bands, bandwidth and the technique used is presented in Table 2. From this, it can be observed that the proposed technique is providing dual band with smaller antenna size.

Fig. 6
figure 6

Photograph of the proposed antenna

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Table 1 Comparison between numerical and actual results
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Table 2 Comparison between existing antennas and proposed antenna
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The measured impedance bandwidth is 100 MHz (2.40–2.50 GHz) and 860 MHz (3.41–4.27 GHz) with resonance frequencies at 2.45 GHz and 3.77 GHz, respectively. The current distribution in an antenna at frequencies namely 2.45 GHz and 3.77 GHz is shown in Fig. 7a, b, respectively. Comparatively, current in outer SCRR is high at 2.45 GHz and current in inner SSRR is high at 3.77 GHz. It can be evidenced from current distribution that the two resonance bands of the antenna clearly attribute to outer SCRR for band-1 and inner SSRR for band-2. From Fig. 4, it is observed that SSRR is resonating at 3.7 GHz. At this frequency, effective permeability provided by SSRR is negative which conforms the MTM characteristics. Hence, SSRR contributes for resonance at 3.7 GHz. The MTM-based antenna provides large bandwidths over which the refractive index remains negative [45]. It can be observed from Fig. 4 that the refractive index is also negative over the particular band of frequencies. The frequency band of operation of antenna at 3.7 GHz is attributable to the effective negative refractive index of the MTM over this frequency range. The antenna far-field radiation patterns are measured by keeping an antenna inside an anechoic chamber as shown in Fig. 8. This is carried out at frequencies namely 2.45 GHz and 3.7 GHz for 360° rotation of receiving antenna at elevation angles of 0° and 90°, respectively, for H-plane and E-plane measurements. These are plotted in figures from Fig. 9a–d. These depict that the far-field pattern are in close agreement with the simulated results and imitate the required dipole antenna pattern. Hence, the proposed antenna can be used for WLAN and WiMAX applications at respective bands.

Fig. 7
figure 7

Current distribution at various frequencies

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Fig. 8
figure 8

Measurement of radiation pattern inside an anechoic chamber

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Fig. 9
figure 9

Far-field radiation pattern

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5 Conclusions

A dual-band antenna is designed by making use of MTM resonator structures as radiating elements. This antenna is designed using SCRR and SSRR. The prototype antenna is fabricated and characteristics are measured. The simulated characteristics such as return loss, gain and radiation pattern are verified with measurements at different frequencies and found to agree with each other. This paper also analyzes the effect of different shapes of ground on return loss characteristics. A technique used to get impedance match between feed and successive elements is neatly presented. Necessary equations related to the design of an antenna are given which emphasis to the operation of an antenna at frequencies specified. Parametric analyses on various geometry of an antenna with its effect on antenna performance are presented. It is proved using simulations as well as equations that the lower-frequency resonance (band-1) is achieved by outer square closed-ring resonator (SCRR) and higher-frequency resonance (band-2) is primarily attributed to inner square split-ring resonator (SSRR). When compared to two separate antennas for each band, the proposed antenna achieves size reduction of 86% which results in compactness and easy fabrication. As this antenna produces dual band from 2.4 to 2.5 GHz and from 3.41 to 4.27 GHz, it can be used for WLAN and WiMAX applications at 2.45-GHz and 3.5-GHz band, respectively.