1 Introduction

The design of dual-band antenna with broad bandwidth is very much desirable to cover all the specified frequencies. This technique can be used to replace many antennas by single antenna. Numerous techniques have been investigated to achieve dual-band antenna design. Rectangular notch [1], loop structure [2], embedding slot [3], and parasitic element [4] in the radiating patch are few among them to realize dual-band antenna. Recently electromagnetic (EM) metamaterial has got great attention in antenna design for enhancing the antenna performances.

Metamaterial offers negative values of permeability (µ) and permittivity (ε) from its basic elements such as split-ring resonator (SRR) and its dual element (CSRR). These unique properties are not found in natural materials. Metamaterial-inspired split ring, SRR and CSRR, structures have been used as radiating elements for improving antenna radiation characteristics [5,6,7,8,9,10,11]. Inscription of metamaterial-inspired split-ring structure has been investigated in attaining multiband antenna due to band notch characteristics [12] and reconfigurability [13]. Negative refractive index-transmission line (NRI-TL) [14, 15] satisfies the metamaterial properties due to its series capacitance and shunt inductance for designing broad-bandwidth antenna. Large number of researchers have concentrated on split-ring structure for achieving bandwidth improvement.

In this paper, a miniaturized dual-band antenna based on the metamaterial-inspired split ring and HCSRR is proposed for ISM/WiMAX/WLAN (2.4/3.5/5.5 GHz) applications. HCSRR is capable of creating new resonance frequency of 2.4 GHz. The split in the ring element induces a time-varying magnetic field and in turn used to create a broad bandwidth. The metamaterial characteristics of HCSRR are verified for achieving a lower resonance frequency to realize antenna miniaturization. A good mechanism is used to cover dual band and bandwidth enhancement without altering the size of the antenna.

2 Antenna design and principle of operation

The design steps of the prototype antenna are described in Fig. 1. Configuration A shows a hexagonal ring radiating element. The resonance frequency of ring radiating element is calculated by [5]

Fig. 1
figure 1

Evolution stages of prototype antenna

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$$f_{{\text{r}}} = \frac{1.8412 \times c}{{2\pi S\sqrt {\varepsilon_{{\text{r}}} } }} = \frac{{1.8412 \times 3 \times 10^{8} }}{{2 \times \pi \times 12 \times 10^{ - 3} \times \sqrt {4.4} }} = 3.5\,\,{\text{GHz}}$$
(1)

here, S is the side length of the hexagonal ring radiating element and \(\varepsilon_{{\text{r}}}\) is the dielectric constant of the FR-4 substrate. Therefore, the antenna resonates at 3.5 GHz for a side length of 12 mm. In configuration B, a small hexagonal patch is introduced. The metallic stub is used to connect hexagonal ring radiating element and hexagonal patch. The stub is used to couple the electromagnetic energy from the hexagonal ring to hexagonal patch. After that, HCSRR is embedded at the distance (\(d_{1}\)) of 11.05 mm (\(\lambda_{{\text{g}}} /5.71)\) from the bottom of the feed position. It changes the current path of patch antenna and in turn creates dual-band characteristics. In the next step, to achieve wider bandwidth, a split is created in the horizontal arm of the outer hexagonal ring as shown in configuration C.

The layout of the proposed antenna along its side view is shown in Fig. 2, and dimensions are listed in Table 1. The snapshot of the fabricated antenna is shown in Fig. 3.

Fig. 2
figure 2

Geometry of the proposed antenna. a Top view and b side view

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Table 1 Parameters of the prototype antenna
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Fig. 3
figure 3

Photograph of the fabricated proposed antenna (top view and bottom view)

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The simulations are carried out using finite element method (FEM)-based Ansoft high-frequency structure simulator (HFSS) V.15.0 software. The comparison of the reflection coefficient of the antenna with three different configurations is shown in Fig. 4. It depicts that, configuration A has a single-band resonance around 3.5 GHz with a wider impedance bandwidth of 3190 MHz (2.82–6.01 GHz). When the HCSRR is introduced (configuration B), dual-band characteristics have been observed. The first band has a resonance frequency of 2.4 GHz with an impedance bandwidth of 180 MHz (2.32–2.50 GHz) and the second band has dual resonance of 4.07 GHz and 4.8 GHz with an impedance bandwidth of 2230 MHz (3.13–5.36 GHz). In configuration C (proposed antenna), a split is embedded in the horizontal arm of the outer hexagonal ring. Now, the impedance bandwidth of second band has been improved without affecting the first band. Also, it is found that there is a shift in resonant frequency of 4.8–5.25 GHz due to its capacitance effect of the split ring.

Fig. 4
figure 4

Reflection coefficient of the antenna with three different configurations

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The proposed antenna exhibits dual-band characteristics. The first band has a resonance frequency of 2.4 GHz with an impedance bandwidth of 180 MHz (2.32–2.50 GHz) and the second band has dual resonance of 4.07 GHz and 5.25 GHz with an impedance bandwidth of 2610 MHz (3.13–5.74 GHz).

3 Parametric study

Parametric investigation is done on the reflection coefficient of the proposed antenna for various ground plane lengths (\(L_{{\text{g}}}\)), the width of the hexagonal ring (\(W_{1}\)), and width of the feed line (\(W_{{\text{f}}}\)) to achieve the optimum dimensions of the antenna. The ground plane length (\(L_{{\text{g}}}\)) is varied from 4.5 to 6 mm and width of the hexagonal ring (\(W_{1}\)) is varied from 3 to 1.5 mm with incremental step of 0.5 mm, which are shown in Figs. 5 and 6, respectively. It is found that wider bandwidth is observed for \(L_{{\text{g}}}\) = 6 mm and \(W_{1}\) = 1.5 mm.

Fig. 5
figure 5

Reflection coefficient of the antenna for variation of \(L_{{\text{g}}}\)

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Fig. 6
figure 6

Reflection coefficient of the various width \((W_{1}\)) of the hexagonal ring

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Similarly, reflection coefficient of the microstrip feed width (\(W_{{\text{f}}}\)) is shown in Fig. 7. The width (\(W_{{\text{f}}}\)) creates an essential role for determining impedance matching (50 \(\Omega\)) of the antenna, which is varied from 0.9 to 1.7 mm in steps of 0.2 mm. It is inferred that, as the width of the microstrip feed (\(W_{{\text{f}}}\)) increases, the impedance matching of second band is affected more compared with first band. However, the optimum performance of the antenna is obtained for \(W_{{\text{f}}}\) = 1.5 mm. Hence, based on the parametric study, dimensions are chosen for fabrication.

Fig. 7
figure 7

Reflection coefficient of the antenna with variation of \(W_{{\text{f}}}\)

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The evaluation of prototype antenna with other metamaterial antennas is listed in Table 2. From Table 2, it is perceived that the prototype antenna covers dual band for ISM, WiMAX, and WLAN applications with compact size. This paper highlights the equivalent circuit analysis of HCSRR and the evidence of metamaterial property (negative permittivity) for generating a new resonance frequency. The antennas listed in reference failed to study metamaterial property.

Table 2 Comparison of other metamaterial antennas
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4 Equivalent circuit analysis of HCSRR

HCSRR creates a new resonance frequency of 2.4 GHz, which is examined by LC equivalent circuit model [16], as illustrated in Fig. 8. The metal slit between the HCSRR slot is essential for constructing passband characteristics. HCSRR slot produces the capacitance effect \(\left( {C_{{{\text{HCSRR}}}} } \right)\) and metal slit between the HCSRR slot produces an inductance effect \(\left( {L_{{{\text{HCSRR}}}} } \right)\). Therefore, the resonance frequency of HCSRR \(\left( {f_{{{\text{HCSRR}}}} } \right)\) is evaluated by [17]

Fig. 8
figure 8

HCSRR and its equivalent circuit model

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$$f_{{{\text{CSRR}}}} = \frac{1}{{2\pi \sqrt {L_{{{\text{CSRR}}}} C_{{{\text{CSRR}}}} } }},$$
(2)
$$C_{{{\text{CSRR}}}} = \frac{N - 1}{2}\left[ {2L - \left( {2N - 1} \right) \, \left( {W + S} \right)} \right]C_{0} ,$$
$${ }C_{0} = \varepsilon_{0} \frac{{K\left( {\sqrt {1 - K^{2} } } \right)}}{K\left( k \right)}\,\, {\text{and}}\,\,k = \frac{{{\raise0.7ex\hbox{$S$} \!\mathord{\left/ {\vphantom {S 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}}{{W + {\raise0.7ex\hbox{$S$} \!\mathord{\left/ {\vphantom {S 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}},$$
$$L_{{{\text{CSRR}}}} = { 4\mu_{0}}\left[ {L - \left( {N - 1} \right)\; \left( {S + W} \right)} \right] \left[ {{\ln}\left( {\frac{0.98}{\rho }} \right) + {1.84}{\varvec{\rho}}} \right]$$
$${\varvec{\rho}} = \frac{{\left( {{\text{N}} - 1} \right)\left( {{\text{W}} + {\text{S}}} \right)}}{{1 - \left( {{\text{N}} - 1} \right)\left( {{\text{W}} + {\text{S}}} \right)}}.$$

Here, L is the HCSRR side length, slot width (W) = 0.5 mm, slit width (S) = 0.5 mm, number of HCSRR (N) and \(K\) is the elliptic integral \(K \left( k \right)\). These empirical equations are evaluated by MATLAB program to compute the HCSRR resonance frequency due to capacitance (\(C_{{{\text{HCSRR}}}}\)) and inductance (\(L_{{{\text{HCSRR}}}}\)) values.

For side length of HCSRR (L) = 7.5 mm.

Thus, \(C_{{{\text{HCSRR}}}}\) = 7.5476 \(\times 10^{ - 14}\) (Farad) and \(L_{{{\text{HCSRR}}}}\) = 5.8537 \(\times 10^{ - 08}\) (Henry). Therefore, the proposed HCSRR resonance frequency is \(f_{{{\text{HCSRR}}}}\) = \(\frac{1}{{2\pi \sqrt {C_{{{\text{HCSRR}}}} L_{{{\text{HCSRR}}}} } }}\) = 2.4 GHz.

From this LC equivalent circuit investigation, it is observed that the proposed HCSRR generates the resonance frequency of 2.4 GHz. It matches with a simulated resonance frequency of the proposed HCSRR.

5 HCSRR analysis

The band characteristics of HCSRR are analyzed using the waveguide setup [18]. The reflection coefficient \(\left( {S_{11} } \right)\) creates a passband behavior for generating a new resonance frequency and transmission coefficient \(\left( {S_{21} } \right)\) creates a stopband for notch characteristics [19]. The S-parameters \(S_{11}\) and \(S_{21}\) of HCSRR are extracted and compared as shown in Fig. 9. It depicts the two passband \(\left( {S_{11} } \right)\) characteristics at 2.4 GHz and 4.8 GHz. Here, 2.4 GHz verifies to the equivalent circuit design equation of \(f_{{{\text{HCSRR}}}}\) = \(\frac{1}{{2\pi \sqrt {C_{{{\text{HCSRR}}}} L_{{{\text{HCSRR}}}} } }}\). Thus, it allocates the lower order mode, explained to be \(f_{0}\). Also, the higher order mode is obtained at 2\(f_{0}\), as defined in [1]. The lower order mode is a unique consideration, because it confirms with the HCSRR resonance frequency of 2.4 GHz.

Fig. 9
figure 9

Simulated S-parameters \(\left( {S_{11} {\text{and}} S_{21} } \right)\) of HCSRR

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The extracted negative permittivity \(\left( \varepsilon \right)\) of the HCSRR is depicted in Fig. 10. It illustrates that the permittivity \(\left( \varepsilon \right)\) value at 2.4 GHz is negative due to lower order \(\left( {f_{0} } \right)\) mode of HCSRR. From this S-parameter extraction, it is agreed that negative permittivity offers a new resonance frequency. Thus, the proposed HCSRR with optimized parameters has contributed a new resonance frequency of 2.4 GHz for achieving dual band antenna.

Fig. 10
figure 10

Negative permittivity characteristics of HCSRR

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6 Results and discussion

Figure 11 shows the simulated and measured \(S_{11} \left( {{\text{dB}}} \right)\) of the proposed antenna. Both results coincide with each other. The measured data show dual-band characteristics. The first band has a resonance frequency of 2.56 GHz, and the second band has a dual resonance of 3.93 GHz and 5.44 GHz. The measured result covers -10 dB impedance bandwidth of 180 MHz (2.43–2.61 GHz) and 2400 MHz (3.43–5.83 GHz) which is useful for ISM and WLAN frequency bands. The performance evaluations of measured and simulated values are listed in Table 3.

Fig. 11
figure 11

Simulated and measured \(S_{11} \left( {{\text{dB}}} \right)\) of the proposed antenna

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Table 3 Comparison of measured and simulated results
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The measured E-plane \(\left( {\phi = 90^{^\circ } } \right)\) and H-plane \(\left( {\phi = 0^{^\circ } } \right)\) radiation patterns of the proposed antenna compared with simulated radiation pattern is exposed in Fig. 12. It illustrates that the prototype antenna covers the desired directions at the resonance frequencies of 2.53 GHz, 3.93 GHz, and 5.44 GHz. The measured peak gains of the prototype antenna are shown in Fig. 13. The peak gains 0.66 dBi, 1.64 dBi, and 1.72 are inferred at 2.53 GHz, 3.93 GHz, and 5.44 GHz, respectively.

Fig. 12
figure 12

Radiation pattern of proposed antenna. a 2.54 GHz, b 3.93 GHz, and c 5.44 GHz

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Fig. 13
figure 13

Gain of the prototype antenna

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7 Conclusion

The metamaterial-based monopole antenna is developed and validated on a 30 × 30 × 0.8 mm3 FR-4 substrate. In the proposed design, a HCSRR is nested with inner monopole and split is introduced on the outer horizontal arm for the radiation. The negative permittivity characteristics of HCSRR at 2.4 GHz have been examined with passband behavior. The proposed antenna has tiny size, homogeneous radiation pattern, and wider bandwidth, which is applicable for ISM and WLAN wireless applications. The simulated results are endorsed with the measured results.