1 Introduction

Recently, substrate integrated waveguide (SIW) cavity backed antennas have been developing as an eminent candidate in modern wireless technology due to better isolation (Kumar et al. 2018), unidirectional pattern (Chaturvedi et al. 2019), high gain (Mukherjee and Biswas 2018), combining planar and non- planar configurations (Nigam et al. 2020), circular polarization (Priya et al. 2020), Phase correction (Gong et al. 2017) and reduce the side lobe level (Gong et al. 2016). These characteristics can be realized using metallic waveguide structure. The rows of metallic vias in SIW are formed to create waveguide side walls for preventing spurious radiation. SIW techniques have been utilized in designing MIC components such as filters (Shi et al. 2018), microwave sensor (Yun and Lim 2014), power divider (Gatti and Rossi 2018) and body area network devices (Chaturvedi 2020). Bow-tie slot (Mukherjee and Biswas 2016) and dumbbell shaped slot (Mukherjee and Biswas 2017) are used to attain hybrid modes in the SIW cavity for achieving multiband frequency response.

Metamaterial is a non-natural electrodynamics substances with negative values of permeability (µ) and permittivity (\(\upvarepsilon\)). These specified features can be governed ZOR (Zeroth Order Resonance) for reducing the size of the antenna (Samson Daniel 2020). Complementary split ring resonatorbased metamaterial configurations have been revealed for multiband along with the compact size of the antenna (Samson Daniel et al. 2018b). The series and shunt element of complementary split ring resonator influences electric current to construct a lower mode resonance with better return loss characteristics (Samson Daniel et al. 2018c). The EM radiation is controlled by EM absorber, which includes the permeability and permittivity of the material. Due to the high electrical conductivity, the electromagnetic shielding materials block the transmission radiation to prevent the harmful radiation (Zhang et al. 2021). The amalgamation of green electromagnetic interference with “non-crosstalk” multiple perceptions are beneficial to construct next-generation devices, such as medical treatment, remote sensing and aerospace engineering (Cao et al. 2020). EM response mechanism and their properties of low-dimensional material are used to design nano-micro devices in the microwave frequency range (Cao et al. 2019).

In this article, a low-profile substrate integrated waveguide (SIW) antenna loaded with complementary split ring resonator (CSRR) metamaterial is designed for dual-band operations. To realize lower hybrid modes for antenna miniaturization, CSRR metamaterial is loaded on the ground plane. The desired operating bands are achieved by tuning series capacitance and shunt inductance parameters of CSRR. An electrical size of the proposed antenna is 0.25 λ0 × 0.25 λ0 × 0.0133 λ0,where \({\uplambda }_{0}\) is the free space wavelength at f0 = 2.5 GHz. Due to band characteristics of CSRR and its negative permittivity attributes, the proposed fashion is useful to ascertain applications for nanoelectronics and telecommunication devices.

2 Antenna description and simulated results

The designed antenna has been fashioned from a dual-band rectangular SIW cavity backed antenna as described in the prototype (A) of Fig. 1. To attain lower hybrid modes from this rectangular SIW cavity resonator, the complementary split ring resonator (CSRR) metamaterial is loaded on the ground plane as described in the prototype (B) of Fig. 1. CSRR is reasonable to generate electric resonance for achieving dual-band at 2.5 GHz and 5.4 GHz due to the CSRR structural configuration. The slit (\({\mathbf{S}}_{1}\)) and width (\({\mathbf{S}}_{2}\)) of the CSRR are preserved as a constant value of 1 mm for homogeneity. The schematic representation of the proposed antenna is depicted in Fig. 2 and its parameters have been listed in Table.1.

Fig. 1
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Prototype geometry

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Fig. 2
figure 2

Schematic representation of the proposed antenna

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Table 1 Antenna dimensions
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The proposed antenna is designed by using Ansys HFSS V.14.0 EM tool. The simulated \({\mathbf{S}}_{11}\)(dB) of Prototype (A) and Prototype (B) are depicted in Fig. 3. The SIW cavity (\({\mathbf{L}}_{\mathbf{c}} \times {\mathbf{W}}_{\mathbf{c}}\)) is realized by using copper claddings with metallic via-array, which constructs the sidewalls of the SIW. The diameter (d) and pitch distance (p) of the metallic vias have been attuned to ensure \(\mathbf{d}/{{\varvec{\uplambda}}}_{0}\) ≤ 0.1 and \(\mathrm{d}/\mathrm{p}\) ≥ 0.5 for avoiding spurious radiation (Mukherjee and Biswas 2017). The rectangular SIW cavity length (\({\mathbf{L}}_{\mathbf{c}})\) and width (\({\mathbf{W}}_{\mathbf{c}}\)) are computed from the precise design equation (Chaturvedi 2020).

$${\text{f}}_{{\text{r}}} \left( {{\text{TE}}_{{{\text{mnp}}\prime }} } \right) = \frac{{\text{c}}}{{2\sqrt {\varepsilon_{{\text{r}}} } }}\sqrt {\left( {\frac{{\text{m}}}{{\text{L}}}} \right)^{2} + \left( {\frac{{\text{n}}}{{\text{W}}}} \right)^{2} + \left( {\frac{{{\text{p}}\prime }}{{\text{h}}}} \right)^{2} }$$
(1)
$${\text{where}},L\,\,{\text{or}}\,W = {\varvec{L}}_{{\varvec{c}}} \,{\text{or}}\,{\varvec{W}}_{{\varvec{c}}} - 1.08\frac{{\varvec{d}}}{{\varvec{p}}}^{{\varvec{2}}}$$
Fig. 3
figure 3

\({\mathrm{S}}_{11}\)(dB) for prototype A and prototype B

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Here, \({\varepsilon }_{r}\) is the relative permittivity of the FR-4 dielectric substrate, length of the SIW cavity \({\mathrm{L}}_{\mathrm{c}}\)=17 mm, width of the SIW cavity \({\mathrm{W}}_{\mathrm{c}}\)=21 mm, \({f}_{r}\) is the resonance frequency and m, n, \({p}^{^{\prime}}\) are mode integers. Thus, it supports \({\mathrm{TE}}_{110}\) mode at 3.53 GHz and \({\mathrm{TE}}_{120}\) mode at 5.83 GHz. CSRR is a resonant behavior as its perimeter is double the resonant wavelength equivalent to cavity mode. Due to CSRR coupling, the fundamental cavity modes (\({\mathrm{TE}}_{110}\) and \({\mathrm{TE}}_{120}\)) become attuned and provides the reconstructed modes \({\mathrm{TE}}_{110}\) and \({\mathrm{TE}}_{120}\) towards the lower resonance frequencies of 2.5 GHz and 5.4 GHz, respectively.

The comparative analysis of the proposed antenna with earlier published work is detailed in Table 2. It has been recognized that the proposed antenna offers dual band operating frequencies with small size equated with previously described works. This paper accentuates CSRR band nature as well as \(\upvarepsilon\)-negative for constructing lower hybrid modes.

Table 2 Examination of the designed antenna with previouslyreported work
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3 Operating mechanism

The real part input impedance of the rectangular SIW cavity resonator (Prototype A) and rectangular SIW cavity resonator loaded with complementary split ring resonator (CSRR) (Prototype B) are shown in Fig. 4. It is inferred that loading of the CSRR, significantly impacts cavity modes (\({\mathrm{TE}}_{110}\) and \({\mathrm{TE}}_{120}\)) and yields two hybrid modes at 2.5 GHz and 5.4 GHz. Similarly, Fig. 5 explains the same. The electric field distribution of rectangular SIW cavity according to cavity modes \({\mathrm{TE}}_{110}\) (at 3.53 GHz) and \({\mathrm{TE}}_{120}\) (at 5.83 GHz) are illustrated in Fig. 5a, which affects each other after loading the CSRR and produce lower hybrid modes at 2.5 GHz and 5.4 GHz as illustrated in Fig. 5b. Thus, the hybrid modes \({\mathrm{TE}}_{110}\) and \({\mathrm{TE}}_{120}\) are governed predominantly by the CSRR and maximum electric field is induced in the outer aperture of the SIW cavity due to changes in phaseand magnitude of the electric field intensity at the different side of the CSRR slot.

Fig. 4
figure 4

Real part input impedance of the SIW cavity

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Fig. 5
figure 5

Electric field distribution at the top view of substrate a without CSRR and b with CSRR

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4 Study of CSRR metamaterial

To confirm the resonance behavior, the complementary split ring resonator (CSRR) band nature is explained in this segment. The waveguide theory is utilized to perceive the scattering parameters for computing transmission \(\left({\mathrm{S}}_{21}\right)\) and reflection \(\left({\mathrm{S}}_{11}\right)\) coefficients of CSRR (Samson Daniel et al. 2018a). The \({\mathrm{S}}_{11}\)(dB) influences pass band nature owing to band pass filter for creating resonance characteristics and \({\mathrm{S}}_{21}\)(dB) influences stop band nature owing to band stop filter. Figure 6a describes the stop band \(\left({\mathrm{S}}_{21}\right)\) and pass band \(\left({\mathrm{S}}_{11}\right)\) nature of the CSRR metamaterial unit cell. It is understood that CSRR has two pass bands \(\left({\mathrm{S}}_{11}\right)\) at 2.5 GHz and 5.4 GHz. Here, 2.5 GHz supports the lower hybrid mode \({\mathrm{TE}}_{110}\). Thus, it designates to be first order pass band \({f}_{0}\). Also, the hybrid mode \({\mathrm{TE}}_{120}\) (at 5.4 GHz) is attained at second order pass band \(\approx\) 2 \({f}_{0}\), as detailed in Murugeshwari et al. 2019. These pass bands are beneficial for constructing dual operating bands in the proposed antenna design.

Fig. 6
figure 6

a Scattering parameters of CSRR, b Permittivity of CSRR

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An effective permittivity (\(\upvarepsilon\)) of the CSRR is represented in Fig. 6b. It shows that the permittivity (\(\upvarepsilon\)) becomes negative at 2.5 GHz owing to first order pass band \({f}_{0}\) and at 5.4 GHz owing to second order pass band \(\approx\) 2 \({f}_{0}\). Thus, the CSRR with optimized values have induced operating frequencies of 2.5 GHz and 5.4 GHz for designing dual band antenna.

5 Equivalent circuit investigation of CSRR

The resonance frequencies of complementary split ring resonator (CSRR) have been verified by an equivalent circuit (Mukherjee and Biswas 2017), as depicted in Fig. 7. The capacitance of the CSRR \(\left({\mathrm{C}}_{\mathrm{CSRR}}\right)\) is influenced by slit surrounded by a slot and the inductance of the CSRR \(\left({\mathrm{L}}_{\mathrm{CSRR}}\right)\) is influenced by slot surrounded by a slit. After introducing CSRR metamaterial, the reconstructed modes \({\mathrm{TE}}_{110}\) (at 2.5 GHz) and \({\mathrm{TE}}_{120}\) (at 5.4 GHz) are produced with better return loss characteristics. These resonance frequencies have been evaluated by Samson Daniel 2020

Fig. 7
figure 7

Equivalent circuit topology

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$${\mathrm{f}}_{\mathrm{CSRR}}=\frac{1}{2\uppi \sqrt{{\mathrm{L}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{L}}}}$$
(2)

where

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

Here, L is the average length of the CSRR ring, N = 2 number of rings, S = 1 mm spacing between two rings, W = 1 mm width of the ring and \(\mathrm{K}(k)\) first order elliptical integral. These formulas are estimated by MATLAB program to determine CSRR resonance owing to inductance and capacitance values.

For outer ring CSRR, Average Length (L) = \(\frac{{l}_{1}+{W}_{1}}{2}\)  = 12.5 mm.

Hence, \({\mathrm{C}}_{\mathrm{CSRR}}= 7.5476 \times {10}^{-14}\) (Farad) and \({\mathrm{L}}_{\mathrm{CSRR}}\)= 5.3128 \(\times {10}^{-08}\) (Henry). So, the outer ring CSRR resonance frequencyis \({f}_{CSRR}=\frac{1}{2\uppi \sqrt{{\mathrm{L}}_{\mathrm{CSRR}}{\mathrm{C}}_{\mathrm{CSRR}}}}= 2.51\mathrm{ GHz}\)

For inner ring CSRR, Average Length (L) = \(\frac{{l}_{2}+{W}_{2}}{2}\)  = 8.5 mm.

Hence, \({\mathrm{C}}_{\mathrm{CSRR}}\) = 3.2803 \(\times {10}^{-14}\) (Farad) and \({\mathrm{L}}_{\mathrm{CSRR}}\)= 2.6173 × 10–08 (Henry). So, the inner ring CSRR resonance frequencyis \({f}_{\mathrm{CSRR}}=\frac{1}{2\uppi \sqrt{{\mathrm{L}}_{\mathrm{CSRR}}{\mathrm{C}}_{\mathrm{CSRR}}}}= 5.43\quad\mathrm{GHz}\).

From this equivalent circuit topology, it predicts that CSRR yields resonance at 2.51 GHz and 5.43 GHz, which is recognized with simulated resonance at 2.5 GHz and 5.4 GHz.

6 Parametric study

The structural parameters of the antenna are minimized by evaluating \({\mathrm{S}}_{11}\)(dB) behavior of the CSRR slit (\({\mathrm{S}}_{1}\)), the width of the CSRR (\({\mathrm{S}}_{2}\)), length of the CSRR (\({l}_{1}\)) and feed width \(\left({\mathrm{W}}_{\mathrm{f}}\right)\). Figures 8 and 9 represents the variation of \({\mathrm{S}}_{11}\)(dB) on various dimensions of \({\mathrm{S}}_{1}\) and \({\mathrm{S}}_{2}\), respectively. Basically \({\mathrm{S}}_{1}\)(metal strip between the slots) governs the shunt inductance and \({\mathrm{S}}_{2}\)(slot between the metal strip) governs the series capacitance in the CSRR metamaterial. It can be revealed that both \({\mathrm{S}}_{1}\) and \({\mathrm{S}}_{2}\) contributes power to be distributed into the load for the first and second band because of the connection between the CSRR on the ground plane and SIW cavity resonator.

Fig. 8
figure 8

Effect of CSRR slit (\({\mathrm{S}}_{1}\)) on \({\mathrm{S}}_{11}\)(dB)

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Fig. 9
figure 9

Effect of CSRR width (\({\mathrm{S}}_{2}\)) on \({\mathrm{S}}_{11}\)(dB)

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Figure 10 describes the \({\mathrm{S}}_{11}\)(dB) by changing the length of the CSRR (\({l}_{1}\)). It is inferred that this parameter plays an eminent impact for impedance matching of the second band. The higher order mode can be adjusted by series parameters instead of shunt parameters. However, this shunt parameter is capable of tuning lower resonance frequency. The width (\({\mathrm{W}}_{\mathrm{f}}\)) of the microstrip feed line performs prominent role to drive the radiating modes and impedance characteristics. The feed width is increased from 1.6 mm to 2 mm and the conforming \({\mathrm{S}}_{11}\)(dB) characteristics are shown in Fig. 11. It is understood that by increasing the width of the microstrip feed, the dual band radiation with better impedance matching is obtained. Hence, the maximum possible value \({\mathrm{W}}_{\mathrm{f}}\) = 2 mm is designated to resonance at 2.5 GHz and 5.4 GHz.

Fig. 10
figure 10

Effect of CSRR length (\({l}_{1}\)) on \({\mathrm{S}}_{11}\)(dB)

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Fig. 11
figure 11

Effect of feed width (\({\mathrm{W}}_{\mathrm{f}}\)) on \({\mathrm{S}}_{11}\)(dB)

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7 Measurement results

The proposed antenna is fabricated with the help of MITS PCB prototyping machine, which involves the process of creating photo film, printing layers, aligning the layers, drilling the holes, applying solder mask and silkscreen, final cutting. The major dimension of the fabricated prototype has high quality, reliability and extraordinary precision compared with designed antenna by using the Ansys HFSS electromagnetic tool. The picture of the fabricated antenna is shown in Fig. 12. Anritsu Vector Network Analyzer MS46122B has been used to measure the \({\mathrm{S}}_{11}\) (dB) of the fabricated antenna. An experimental and simulated \({\mathrm{S}}_{11}\)(dB) response of the designed antenna is explained in Fig. 13. Experimental data exhibits an –10 dB impedance bandwidth of 100 MHz (2.45–2.55 GHz) and 130 MHz (5.33–5.46 GHz) with 4% (\({f}_{c}\) = 2.5 GHz) and 2.4% (\({f}_{c}\) = 5.4 GHz) fractional bandwidths respectively. Figure 14 shows the normalized field pattern over the dual band radiation. The unidirectional and broadside radiation is obtained in E-plane (YZ plane) and H-plane (XZ plane) due to the SIW structural configuration. Experimental cross-polarization components are –23 dB and –15 dB in the E-plane and –24 dB and 19 dB in the H-plane at 2.5 GHz and 5.4 GHz, respectively.

Fig. 12
figure 12

Picture of the fabricated antenna a Top view b Bottom view

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Fig. 13
figure 13

\({\mathrm{S}}_{11}\)(dB) response of the proposed antenna

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Fig. 14
figure 14

E-plane and H-plane radiation patterns a 2.5 GHz b 5.4 GHz

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The peak gain values of the antenna have been computed using gain transfer procedure (Samson Daniel et al. 2018b) and plotted in Fig. 15. In this method, the experimental peak gains are obtained by measuring the ratio of peak power of the fabricated antenna under test with the standard gain horn antenna. It provides an experimental peak gain of 3.43 dBi at 2.5 GHz and 5.31 dBi at 5.4 GHz. Basically metamaterial elements induce a negative or low gain value in the lower resonance frequency (Samson Daniel 2020) due to antenna compactness. Thus, the high level of antenna miniaturization affects radiation characteristics which leads to reduce the gain.

Fig. 15
figure 15

Proposed antenna gain plot

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8 Conclusion

A low-profile complementary split ring resonator loaded SIW cavity backed antenna is designed using mode theory mechanism for dual band radiation. It exposes that CSRR is essential in addition to the rectangular SIW cavity resonator, to obtain lower hybrid modes \({\mathrm{TE}}_{110}\) and \({\mathrm{TE}}_{120}\) for reducing the size of the antenna. The performance of the proposed configuration has been elucidated by parametric examination. An electrical size of the designed antenna is 0.25 λ0 × 0.25 λ0 × 0.0133 λ0. The fabricated antenna has low-profile geometry and its radiation characteristics are tested. The measured radiation pattern exhibits unidirectional and lower cross polarization power levels for 2.5 GHz WiMAX and 5.4 GHz WLAN applications.