A Compact Triple Band Antenna Based on Multiple Split-Ring Resonators for Wireless Applications

Abstract

In this paper, a compact multi-split-ring resonator-based antenna is presented for wireless applications. The proposed antenna integrates multiple resonators to achieve multiband operation, where each resonator corresponds to a specific frequency band. A theoretical analysis is conducted to model the equivalent circuit of the proposed antenna, followed by an analytical study to calculate the resonant frequency of each resonator. By integrating these resonators, the proposed antenna achieves a compact size of 23 × 24 × 1.6 mm³ (0.19 × 0.2 × 0.01λ³), resulting in a size reduction of 81.6% compared to a conventional patch antenna, while maintaining gain, improving bandwidth, and providing excellent impedance matching. The proposed antenna covers the 2.4–2.8 GHz (14.55%), 3.25–3.75 GHz (14.28%) and 4.5–7.84 GHz (54.13%) frequency bands, providing acceptable gains of 1.5 dBi, 2 dBi and 3.2 dBi, respectively. The antenna was designed with CST, its performance was verified with HFSS simulations and it was validated with an equivalent circuit in ADS. Finally, the antenna was fabricated to confirm the accuracy and reliability of the simulation results, and it was found that the measurements agreed well with the simulations. This multiband functionality, combined with a compact form factor and simple feed line, makes the antenna cost-effective, easy to manufacture and suitable for various wireless communication applications, including 5G sub-6 GHz mid-band (2.5/3.5/5/5 GHz), RFID (2.45/5.8 GHz), WiMAX (2.4/3.5/5.8 GHz), Wi-Fi 5/6/6E (2.4/5/6 GHz) and WLAN (5.2/5.8 GHz).

1. Introduction

The rapid development of wireless communication systems requires multiband antennas that can serve multiple wireless standards and systems. These antennas are designed to operate in a large number of frequency bands that can support different applications as they transmit and receive in different bands. When small devices integrate multiband antennas, issues such as size limitations or antenna location can arise that affect the overall design or functionality. For these reasons, the use of miniaturized multiband antennas is critical. The characteristics of the factors such as their shape, the feeding techniques used and defective grounds can be modified, leading to a compact multiband antenna design that covers a wide frequency band and makes it easy to integrate into devices such as smartphones, tablets, Internet-of-Things devices and industrial equipment. Since size and performance are key in wireless applications, multiband functionality combined with a compact form factor size increases the potential for integration into various communication systems. In the literature, there are various approaches to realize a compact multiband antenna. One of the methods used includes the slots technique [1,2,3,4]. This technique has attracted much attention recently because slots cut into an antenna act as resonators and enable the antenna to cover multiple frequency bands. In [5], a multiband triangular antenna with dimensions of 57 × 57 × 1.6 mm³ on an FR 4 substrate was proposed to meet the requirements of WLAN and WiMAX. The results showed that the antenna achieved the frequency bands 3.45–3.75 GHz, 4.75–5.5 GHz and 5.95–6.2 GHz by integrating slots in the antenna. However, it is very important to know that this technique comes with its own problems and compromises. The designed antenna can be expensive, as the manufacturing of the additional slots requires high precision. Also, the operating bandwidth of the designed antenna is limited, as the resonant structure resulting from the changes in slot dimensions can cause unwanted resonances. Other approaches to multiband antenna designs include the use of parasitic elements. In [6], a fractal multiband antenna with parasitic elements on an FR4 substrate is proposed to increase the gain. Although the antenna covers the 1.96–2.22 GHz, 3.51–3.91 GHz and 4.78–5.26 GHz frequency bands with dimensions of 37 × 28 × 1.6 mm³ and an acceptable gain of 5 dBi, the parasitic elements increase the size of the antenna because they create a coupling effect that leads to unwanted resonances and makes the design more complex. In addition, these elements cause the antennas to exhibit a narrow operating bandwidth. Another common technique is the use of a reduced ground plane. In [7], a miniaturized antenna is fabricated on both sides of an FR4 substrate. Although this antenna has good impedance matching in the operating band, the reduced ground plane reduces the gain even though the antenna has a size of 46 × 12 × 0.5 mm³. To solve this problem, many researchers have changed the shape of the antenna to obtain more multiband antennas with a compact size that can cover additional applications [8]. In [9], three microstrip antennas with dimensions of 70 × 50 mm², 60 × 50 mm² and 50 × 50 mm² are proposed to cover 1.87–2.66 GHz, 3.33–3.69 GHz and 4.71–5.80 GHz. In [10], a dipole antenna with an overall size of 46 × 10 × 0.8 mm³ is proposed for a wireless local area network. In this technique, the parameters of the antenna are varied to achieve resonance at different frequencies. This can present complex problems and challenges in terms of size, manufacturing complexity and cost. In addition, the use of metamaterials [11] or artificial magnetic conductors in antenna design can extend the frequency band of the antenna. In [12], AMC metasurface antennas are optimized using a surrogate-assisted differential evolution technique, transforming uniform arrays into nonuniform geometries for enhanced wideband performance. The same is true for the technique in [13] that uses the multilayer reflective surface to enhance the broadside directivity of patch antenna. In [14], the design of a multiband monopole antenna with a metamaterial (MTM) loading technique is presented, which has a footprint of 32 × 10 × 1.6 mm³ for vehicular communication. Although this antenna reaches the operating frequencies of 2.4 and 3.8 GHz, it showed a bandwidth of 6% and 9%, with a realized antenna of 3.2 dBi. In [15], a 60 × 60 × 1.6 mm³ antenna with an asymmetric split-ring resonator and a tri-band slot is investigated for three-band applications. The measured impedance bandwidth of the resonant bands is 14.25%, 1.78% and 8.37%, with a peak gain of 3.1 dBi. In [16,17,18], antennas of almost the same size of 35 × 35 × 1.6 mm³ on an FR4 substrate are investigated for operation in the triple [16] and dual [17,18] frequency bands. Although these antennas are smaller, they have several disadvantages, such as a narrow frequency range in each frequency band, as the loaded elements give the antennas a narrow operating bandwidth. To overcome this limitation, the technique in [19] used parasitic strips with slots around a microstrip patch antenna (36 × 37 × 1.6 mm³) to improve gain and bandwidth. Although this design attained broader bandwidths of 160 MHz and 220 MHz, it achieved gains of 3.83 dBi at 3.45 GHz and 0.576 dBi at 5.9 GHz, respectively; a more compact size with a wider frequency band is required.

For each of the aforementioned techniques, existing multiband antenna designs fabricated on FR4 substrates often face challenges such as larger dimensions, limited operating bandwidth and increased design complexity. The high relative dielectric constant (ε_r) of FR4 reduces the bandwidth of the antenna, potentially limiting its application range. Although FR4 is a cost-effective substrate, its performance decreases at higher frequencies. The realized gain of a standard microstrip patch antenna fabricated on an FR4 substrate and operating at 2.45 GHz typically ranges between 1.5 and 3.5 dBi, as discussed in [20]. This value depends on the antenna’s dimensions, which are generally around 0.5λ × 0.4λ. The relatively low gain is primarily attributed to the high dielectric losses of FR4, which result in radiation efficiencies as low as 35–50%. In contrast, antennas fabricated on low-loss substrates such as Rogers RT5880 can achieve higher gains of 5–6 dBi due to their improved efficiency. It is important to note that these values refer to simple patch antennas without additional enhancements such as perfect electric conductor (PEC) backing or superstrate loading. To overcome these challenges, a compact triple-band antenna with multiple split-ring resonators is proposed in this work, which enables significant miniaturization (81.6%) compared to the conventional patch antenna while maintaining acceptable gain and ease of fabrication. The proposed antenna is not only characterized by compact size and wide bandwidth, but also improves multiband capabilities, which makes it suitable for wireless applications especially at 5G Sub-6 GHz Mid-band (2.5/3.5/5), RFID (2.45/5.8), WiMAX (2.4/3.5/5.8 GHz), Wi-Fi 5/6/6E (2.4/5/6 GHz), WLAN (5.2/5.8 GHz).

This paper is structured into five main sections. Following the Introduction, Section 2 presents the design of the split-ring resonator unit cell structure as a metamaterial and its integration into the antenna design. This section also contains the equivalent circuit analysis and the derivation of the input impedance. Section 3 contains simulation results and discussions, including a comparative analysis of multi-SRR loaded antenna configurations, real and imaginary input impedance, VSWR, current distribution, gain performance and parametric study, as well as a comparison between the analytical model, equivalent circuit and numerical simulations. In Section 4, the proposed antenna is fabricated and experimentally measured to validate the design. Finally, in Section 5, the proposed antenna is compared with the state of the art, highlighting its performance and demonstrating its superiority.

2. Construction of the Proposed Multi-SRR-Based Antenna

2.1. Split-Ring Resonator Unit Cell Design

The structure of the split-ring resonator unit cell (SRR) investigated in this paper is shown in Figure 1a,b. It consists of a single octagonal ring with a gap. This SRR was made on a low-cost, lossy FR4 substrate whose unit cell has a thickness of 0.035 mm. The substrate features a dielectric constant of 4.3 and a loss tangent of 0.025. The SRR cell is placed on a substrate area of 23 × 23 mm² and was simulated using CST Microwave Studio. To investigate the properties of the metamaterial, a waveguide simulation is performed by applying electric (E) and magnetic (H) boundary conditions along the Y and Z directions to emulate the walls of a virtual waveguide. A plane wave is aligned parallel to the SRR surface in the X direction. The specific design parameters of the unit cell are Gap = 1.98 mm, R1 = 11.22 mm, R2 = 10.11 mm and Wd = 7.74 mm. The resonant frequency of the SRR can be calculated as follows [16]:

$$f_{SRR}={\displaystyle \frac{c}{2\pi r\sqrt{{\epsilon }_{eff}}}}$$

(1)

where r is the radius of the ring, and ${\epsilon }_{eff}$ is the effective dielectric constant and can be calculated as

$${\epsilon }_{eff}={\displaystyle \frac{{\epsilon }_r+1}{2}}$$

(2)

where ${\epsilon }_r$ represents the relative permittivity of the FR4 substrate. The equivalent circuit of the resonator is shown in Figure 1c. When a time-varying magnetic field H interacts with a split-ring resonator, it induces a circulating current I along the resonator’s structure. This electromagnetic response can be effectively modeled using a series RLC circuit, where the resonant frequency is primarily governed by the following:

-

Inductance (L): Represents the self-inductance of the SRR loop, which is related to the size and shape of the ring.

-

Capacitance (C): Corresponds to the gap of the SRR.

-

Resistance (R): Represents the total ohmic losses in the metallic structure, as well as dielectric losses in the substrate material.

This series RLC circuit models the SRR as a passive resonant scatterer (Figure 2c), responding to incident electromagnetic waves through current-driven excitation. At resonance, the incident magnetic field induces a strong circulating current within the SRR loop, enabling energy storage and scattering. The total impedance is

$$Z_{series}=R+j\left(\omega L-{\displaystyle \frac{1}{\omega .C}}\right)$$

(3)

At resonance:

$${\omega }_0={\displaystyle \frac{1}{\sqrt{\mathrm{LC}}}}$$

(4)

Figure 2a shows the simulated reflection coefficient (S₁₁) and transmission coefficient (S₂₁) of the unit cell. The transmission coefficient (S₂₁) reaches its maximum at 2.7 GHz, which agrees well with the theoretical value of 2.6 GHz calculated from Equation (1). This agreement confirms that the split-ring resonator (SRR) operates effectively at the desired resonant frequency, demonstrating its suitability as a radiating element for antenna applications. Figure 2b shows the effective permeability (μ) of the unit cell, extracted from the real and imaginary components of S₁₁ and S₂₁ using CST Microwave Studio simulations [21].

$${\mu }_{eff}=\pm \sqrt{{\displaystyle \frac{{\left(1+S_{11}\right)}^2-S_{21}^2}{{\left(1-S_{11}\right)}^2-S_{21}^2}}}$$

(5)

Equation (5) [21] was used to calculate the permeability values. It is obvious that the octagonal SRR exhibits negative permeability values in the frequency range of 2.5 GHz to 3 GHz.

2.2. Split-Ring Resonators Loaded Antenna

The design process of the proposed multi-SRR-based antenna is shown in Figure 3. This antenna is based on a structure consisting of four octagonal rings with gaps that are interconnected to achieve multiband functionality. Each ring is sized to resonate at a specific frequency. A reduced ground with an area of 23 mm × 1.6 mm is placed on the bottom of the substrate. The antenna is fed through a transmission line and fabricated on an FR4 substrate with a relative permittivity of 4.4 and a dissipation factor of 0.002. All the design parameters are summarized in

Table 1. Geometrical parameters in mm.

Ws	Wf	R3	R4	Wn	Wt	Wm	R8	R5
23	3	7.94	7.14	1.42	2.43	1.33	3.06	5.67
Ls	Lf	Lm	Lp	Wr	Lt	R7	Ground	R6
24	2.5	5.84	4.17	0.83	2.5	3.4	1.6	5.10

.

2.3. Modeling and Analysis of the Equivalent Circuit for SRR-Based Antenna

Figure 4 illustrates the proposed equivalent circuit of an SRRs-loaded antenna. The antenna is modeled using a series inductor (L₀) and capacitor (C₀), which represent the quasi-static capacitive and inductive behavior of the antenna input. Together, these elements form the foundation of the antenna’s low-frequency equivalent circuit model. Each split-ring resonator is represented by a parallel RLC circuit, leading to a cascade of four parallel RLC branches. When the split-ring resonator functions as a radiating antenna element, its equivalent circuit is altered due to near-field interactions with the feed line. These interactions introduce a parallel resonant (tank) circuit behavior, resulting in maximum impedance and establishing a balanced current distribution across its arms. In the equivalent circuit, the resistance (R) primarily represents the radiation resistance, responsible for radiating power.

In this section, a detailed modeling and analysis of the equivalent circuit for the proposed SRR-based antenna is presented, beginning with the analysis of a parallel RLC circuit. The total admittance $Y$ of a parallel RLC circuit [22,23,24] is the sum of the individual admittances of the resistor, inductor and capacitor, $Y$ = Y_R + Y_L + Y_C, and is expressed as

$$Y={\displaystyle \frac{1}{R}}+j\omega C-{\displaystyle \frac{j}{\omega L}}={\displaystyle \frac{1}{R}}+j\left(\omega C-{\displaystyle \frac{1}{\omega L}}\right)$$

(6)

where $\omega$ is the operating angular frequency defined as $\omega$ = 2πf, and ${\omega }_0$ is the resonant angular frequency, given by Equation (4). At this frequency, the inductive and capacitive effects cancel out, satisfying the condition

$${\omega }_{0}C-{\displaystyle \frac{1}{{\omega }_{0}L}}=0$$

(7)

The quality factor Q for the parallel RLC is given by

$$Q={\omega }_0\mathrm{RC}$$

(8)

At resonance, ${\omega }_0=$ $\omega$, and the circuit exhibits purely resistive behavior. By substituting Equations (7) and (8) into Equation (6), the total admittance at resonance simplifies as follows:

$$Y={\displaystyle \frac{1}{R}}\left[1+jQ\left({\displaystyle \frac{\omega }{{\omega }_0}}-{\displaystyle \frac{{\omega }_0}{\omega }}\right)\right]$$

(9)

According to Equation (9), the impedance Z of a parallel RLC circuit can be expressed as [22,23,24]

$$Z_{RLC}\left(\omega \right)={\displaystyle \frac{1}{Y}}={\displaystyle \frac{R}{1+jQ\left(\frac{\omega }{{\omega }_0}-\frac{{\omega }_0}{\omega }\right)}}$$

(10)

Since Figure 4 contains four cascaded parallel RLC circuits, the total impedance of the equivalent circuit can be expressed as the sum of the individual resonant circuits. The impedance $Z_{RLC}\left(\omega \right)$ is given by [22,23,24]

$$Z_{RLC}\left(\omega \right)={\sum }_{n=1}^4{\displaystyle \frac{R_n}{1+j{Q}_n\left(\frac{\omega }{{\omega }_n}-\frac{{\omega }_n}{\omega }\right)}}$$

(11)

where n represents the number of resonant modes needed to accurately synthesize the antenna’s input impedance. R_n, L_n, Q_n and C_n represent the resistance, inductance, quality factor and capacitance, respectively, describing each resonant mode. ω_n is the resonant angular frequency of the nth resonant mode, given by ${\omega }_n={\displaystyle \frac{1}{\sqrt{L_n{C}_n}}}$. The quality factor is defined as $Q_n={\omega }_n{R}_n{C}_n$. These four cascaded parallel RLC circuits are connected in series with the antenna input impedance $Z_{feed}\left(\omega \right)$, which accounts for the effects of $L_0$ and $C_0$. In this model, $L_0$ represents the antenna input inductance, while $C_0$ corresponds to the total low-frequency (quasi-static) capacitance seen at the antenna input. Together, these elements influence both the impedance matching and the overall resonant behavior of the proposed antenna. $Z_{feed}\left(\omega \right)$ is expressed as

$$Z_{feed}\left(\omega \right)=j\omega L_0+{\displaystyle \frac{1}{j\omega .C_0}}$$

(12)

Equation (12) can be simplified as follows [22,23,24]:

$$Z_{feed}\left(\omega \right)=j\left(\omega L_0-{\displaystyle \frac{1}{\omega .C_0}}\right)=j{\displaystyle \frac{{\omega }^2{L}_0{C}_0-1}{\omega .C_0}}$$

(13)

The final input impedance $Z_{antenna}\left(\omega \right)$ of the proposed antenna is the sum of the antenna input impedance, given in Equation (13), and the equivalent impedance of the RLC network, given in Equation (11), $Z_{antenna}\left(\omega \right)=Z_{feed}\left(\omega \right)+Z_{RLC}\left(\omega \right)$. It is expressed as

$$Z_{antenna}\left(\omega \right)=j{\displaystyle \frac{({\omega }^2{L}_0{C}_0-1)}{\omega C_0}}+{\sum }_{n=1}^4{\displaystyle \frac{R_n}{1+j{Q}_n\left(\frac{\omega }{{\omega }_n}-\frac{{\omega }_n}{\omega }\right)}}$$

(14)

The quasi-static input capacitance C₀ can be determined as follows [22,23,24]:

$$C_0=\underset{\omega \to 0^{+}}{\mathit{lim}}{\displaystyle \frac{\mathit{Im}\left\{Y_{\mathit{in}}\left(\omega \right)\right\}}{\omega }}=\underset{\omega \to 0^{+}}{\mathit{lim}}{\displaystyle \frac{\partial \mathit{Im}\left\{Y_{\mathit{in}}\left(\omega \right)\right\}}{\partial \omega }}\cong \underset{\omega \to 0^{+}}{lim}{\displaystyle \frac{Im\left\{Y_{in}\left(∆\omega \right)\right\}}{∆\omega }}$$

(15)

where $∆\omega$ is the harmonic frequency step, defined as $∆\omega =2\pi {∆}_f$. Based on the value of $C_0$, the inductance $L_0^{\left(0\right)}$ can be estimated by identifying the lowest frequency at which the imaginary part of the input impedance crosses zero. The inductance $L_0^{\left(0\right)}$ models feed-in effects and higher-order electromagnetic phenomena and can be expressed as [22,23,24]

$$L_0^{\left(0\right)}={\displaystyle \frac{1}{{\left({\omega }_0^{\left(0\right)}\right)}^2{C}_0}}$$

(16)

where ${\omega }_0^{\left(0\right)}$ is the lowest frequency for which $Im=\left\{Z_{in}\left({\omega }_0^{\left(0\right)}\right)\right\}=0$.

At each estimated resonant frequency ${\omega }_0^{\left(0\right)}$, we take the real part of the impedance [22,23,24]:

$$R_n^{\left(0\right)}=Re\left\{Z_{in}\left({\omega }_n^{\left(0\right)}\right)\right\}$$

(17)

Since the imaginary part is nearly zero, the input impedance is primarily resistive. We can estimate the quality factor $Q_n^{\left(0\right)}$ as follows [22,23,24]:

$$Q_n^{\left(0\right)}={\omega }_n^{\left(0\right)}{\displaystyle \frac{Im\left\{Z_{in}\left({\omega }_n^{\left(0\right)}-∆\omega \right)\right\}-Im\left\{Z_{in}\left({\omega }_n^{\left(0\right)}+∆\omega \right)\right\}}{4R_n^{\left(0\right)}∆\omega }}$$

(18)

Each parallel RLC branch consists of R_i (resistance), L_i (inductance) and C_i (capacitance). Each stage (for i = 1, 2, 3, 4) corresponds to one of the resonance peaks in the input impedance curve of the antenna. The inductance for each resonance branch is given by [22,23,24]:

$$L_i={\displaystyle \frac{R_i}{2\pi f_{ri}{Q}_i}}$$

(19)

where $f_{ri}$ is the resonant frequency of the i-th mode. Based on Equation (19), we can calculate $C_i$ as follows [24]:

$$C_i={\displaystyle \frac{1}{{\left(2\pi f_{ri}\right)}^2{L}_i}}$$

(20)

At each resonance, the Q_i value provides an estimate of how narrow or wide the bandwidth is relative to the center frequency, and it is given by the following expression [24]:

$$Q_i={\displaystyle \frac{f_{ri}}{f_u-f_l}}$$

(21)

where $f_u\mathrm{a}\mathrm{n}\mathrm{d}{f}_l$ are the upper and lower frequency of the bandwidth around f_ri. As a result, the fractional bandwidth (FBW) is also determined by [24]:

$$FBW={\displaystyle \frac{1}{Q}}={\displaystyle \frac{f_u-f_l}{f_{ri}}}$$

(22)

The frequency bandwidth around each resonance can be estimated using $R_i$ and $C_i$, as follows [24]:

$$BW={\displaystyle \frac{1}{R_i{C}_i}}$$

(23)

Based on Equations (19) and (20), the angular resonant frequency can be calculated using this equation:

$${\omega }_0={\displaystyle \frac{1}{\sqrt{L_i{C}_i}}}$$

(24)

3. Results and Discussion

The S11 parameter results for antenna 1 to antenna 4 (proposed antenna) are shown in Figure 5a, while the step-by-step scalable equivalent circuit model is illustrated in Figure 5c. As can be seen in Figure 5a, antenna 1 with a single octagonal ring achieves a single resonant frequency band from 2.35 GHz to 3 GHz, with a maximum return loss of −30 dB at 2.69 GHz and a bandwidth of 24.34%. When SRR 2 is added in antenna 2, a second resonant frequency occurs and forms bands at 2.4–2.8 GHz and 3.25–4.25 GHz, with maximum return losses of −29 dB and −34 dB at 2.68 GHz and 3.55 GHz, respectively. The introduction of this second band demonstrates good multiband operation without compromising the original 2.5 GHz band. Following the simulation results, antenna 3 with three rings has three separate resonant frequency bands: 2.4–2.77 GHz, 3.25–3.77 GHz and a wide band from 4.5 GHz to 6.47 GHz. This wider third band, which has peak return losses of −43 dB at 4.9 GHz and −37 dB at 5.8 GHz, has better broadband characteristics. The additional bandwidth of the third band (35.94%) emphasizes the better ability to cover the higher frequencies. The final design, antenna 4, adds a fourth ring and achieves three optimized bands of 2.4–2.8 GHz, 3.25–3.75 GHz and a significantly extended broadband range of 4.5 GHz to 7.84 GHz. The peak return losses of −31 dB, −37 dB and −35/−25 dB within these bands indicate good impedance matching, with the widest bandwidth of 54.13% being achieved in the highest band.

Figure 5b compares the simulated return losses (S11) of the proposed antenna design, which were determined using ADS and CST. Both results show multiple resonant frequencies, indicating multiband operation. The strong agreement in the resonant positions and bandwidths confirms the effectiveness of the equivalent circuit model in predicting the antenna behavior.

Figure 6a shows the design and electromagnetic response of the proposed metamaterial structure based on multiple split-ring resonators. The real part of the permeability, as shown in Figure 6b, shows that the MTM exhibits negative permeability at certain resonant frequencies. These frequencies coincide with the resonant frequencies observed in the S11 parameter plot of the proposed multi-SRR-based antenna (Figure 5a). This strong correlation confirms that the negative permeability introduced by the MTM plays an important role in achieving multiband resonance and miniaturization of the antenna.

Figure 7a shows the real and imaginary curves of the input impedance of the antenna over the entire frequency range. In the 2.4–2.8 GHz, 3.25–3.75 GHz and 4.5–7.84 GHz bands, the real part of the impedance is about 50 Ω, while the imaginary part is close to 0 Ω, indicating excellent impedance matching. Figure 7b shows the corresponding VSWR curve falling below 2 in these frequency bands, further confirming the good impedance matching at the resonant frequencies. These results are consistent with the reflection coefficient observed in Figure 5a and confirm that the antenna operates efficiently in the targeted frequency bands.

Table 2. Comparison of resonant frequencies obtained from analytical study (two methods), equivalent circuit analysis and numerical simulation for the proposed multi-SRR-based antenna.

SRR	Radius (mm)	Length (mm)	Equivalent Circuit Parameters	fr (GHz) Analytical (Method 1)	fr (GHz) Analytical (Method 2)	fr (GHz) ADS Circuit	fr (GHz) CST Simulation
1	11.22	35.45	C0 = 0.21 pF, L0 = 4.2 nH, C1 = 3.06 pF, L1 = 1.17 nH, R1 = 790 Ω	2.55 GHz	2.58 GHz	2.65	2.65
2	7.94	26.13	C2 = 3.74 pF, L2 = 0.52 nH, R2 = 500 Ω	3.53 GHz	3.50 GHz	3.60	3.50
3	5.67	19.70	C3 = 0.70 pF, L3 = 1.25 nH, R3 = 1 Ω	4.90 GHz	4.80 GHz	4.84	4.83
4	3.40	12.90	C4 = 0.70 pF, L4 = 0.995 nH, R4 = 84 Ω	7.40 GHz	7.06 GHz	6.03	6.80

shows the resonant frequencies of the proposed multi-SRR-based antenna, which were determined by equivalent circuit analysis, numerical simulations and analytical calculations. The resonant frequencies from the analytical approach were estimated using two distinct methods:

-

Method 1 models the split-ring resonator as a resonant ring, where the effective electrical length is proportional to the physical circumference. The resonance frequency is calculated using the following expression:

$$f_{SRR}={\displaystyle \frac{c}{(2.\pi .r_{SRRn}+L_f)\sqrt{{ϵ}_{re}}}}$$

(25)

-

Method 2 treats the arms of the SRR as equivalent dipole antennas with an effective length L_SRRn, leading to the resonance frequency

$$f_{SRR}={\displaystyle \frac{c}{2.L_{SRRn}.\sqrt{{ϵ}_{re}}}}$$

(26)

where

$$L_{SRRn}=Wn+Lf+{\sum }_{i=1}^{i=4}{L}_{ni}$$

(27)

As an illustrative example, for SRR₁, the total effective length is given by

L_SRR1 = W_n+ L_f+ L₁₁ + L₁₂ + L₁₃ + L₁₄ = 35.45 mm

Both methods provide results that closely match those obtained from numerical simulations, validating the proposed modeling approach. The results show strong agreement between the analytical study and the numerical simulations and the equivalent circuit model, especially for the first three resonances of SRR 1, SRR 2 and SRR 3. This confirms the validity of the circuit-based model in accurately representing the behavior of the SRR. Minor deviations observed at higher frequencies (SRR 4) are due to the small size of this ring and parasitic effects. Overall, the agreement between the different methods confirms the robustness of the design and the reliability of using analytical and circuit-based techniques to predict the electromagnetic response of the proposed metamaterial structure.

Figure 8 presents the surface current distribution the proposed multi-SRR-Based antenna at operating frequencies of 2.5 GHz, 3.5 GHz and 6.8 GHz, respectively. At 2.5 GHz, the current is predominantly concentrated around the largest ring (SRR 1). This confirms that this ring plays the dominant role for the resonance at the lower frequency. Its dimensions result in an electrical length that matches the wavelength associated with 2.5 GHz. As the frequency rises to 3.5 GHz, the current begins to concentrate more on the second, smaller split-ring resonator (SRR 2). This redistribution of current means that the second ring takes the responsibility for resonance, since its shorter electrical length matches better with the shorter wavelength at 3.5 GHz. At 4.8 GHz and 6.8 GHz, the current is concentrated in the third and fourth rings, which consist of the smallest elements in the design. Their small size and close coupling enable effective resonance and wide frequency bands.

Figure 9 shows the effectiveness of design development in improving gain. The gain characteristics of the antenna stages show a clear and progressive improvement as the number of integrated SRRs increases. Starting with antenna 1, which contains a single SRR, the gain is relatively low, peaking at about 1.1 dB and covering a single frequency band. With each additional SRR from antenna 2 to antenna 4, not only does the peak value increase, but the gain also becomes more stable over a wider frequency band. It is noteworthy that antenna 4 with four SRRs achieves the highest gain of about 3.2 dB, indicating that the successive integration of SRRs significantly improves the antenna gain.

Table 3. Frequency characteristics comparison of various SRR-loaded antenna designs.

Antennas	No. of Band	Frequency Band (GHz)	fr (GHz)	Bandwidth in %	Peak Gain (dBi)	Directivity (dBi)	Efficiency %
Reference patch antenna	Band 1	2.47–2.53	2.5	2.41	1.88	6.35	35.7
Antenna 1	Band 1	2.35–3	2.69	24.34	1.1	3.12	62.8
Antenna 2	Band 1	2.4–2.8	2.68	15.38	1.1	3.14	62.5
	Band 2	3.25–4.25	3.55	26.66	1.1	3.08	63.5
Antenna 3	Band 1	2.4–2.77	3.66	14.34	1.1	3.12	62.8
	Band 2	3.25–3.77	3.49	15.56	1.2	3.26	62.2
	Band 3	4.5–6.47	4.9/5.8	35.94	2.02	3.56	70.3
Antenna 4 (Proposed antenna)	Band 1	2.4–2.80	2.65	14.55	1.5	3.11	69.1
	Band 2	3.25–3.75	3.47	14.28	2	3.2	75.9
	Band 3	4.5–7.84	4.8/6.6	54.13	3.1	4.52	72.1

summarizes the frequency characteristics of the different SRR-loaded antenna designs (from reference patch antenna to antenna 4). As shown in Figure 3 and interpreted in Figure 5a, the smaller ring (SRR 4) resonates at higher frequencies, while the larger ring (SRR 1) resonates at lower frequencies, as the resonant frequency of each ring is determined by its effective electrical length. In addition, the mutual coupling between the rings increases the antenna’s ability to cover a wide frequency band, especially in the higher bands. As observed in Table 3, the radiation efficiency of the proposed antenna is improved despite the use of FR4. This improvement can be attributed to two primary design strategies. First, the use of multi-resonant elements enhances surface current distribution (as illustrated in Figure 8) and effectively suppresses surface wave propagation, thereby reducing radiation losses. Second, the integration of split-ring resonators, known for their strong electromagnetic coupling and field localization capabilities, contributes to miniaturization while enhancing efficiency. SRRs help mitigate substrate-induced losses by concentrating the electromagnetic fields and reducing dielectric absorption. In contrast, the reference antenna exhibits low efficiency (35.7%), which is primarily due to higher substrate losses from the FR4 material and the lack of structural optimization.

Figure 10 illustrates the radiation patterns of the proposed multi SRR-Based antenna at frequencies of 2.6 GHz, 3.5 GHz and 6.2 GHz. As can be seen, the radiation patterns are omnidirectional in the E and H planes, with the antenna achieving a maximum gain of 3.2 dB at 6.2 GHz. The radiation patterns of the proposed antenna with multi SRRs were simulated with CST Studio Suite 2019 software and validated with HFSS 15.0 software. A strong correlation was observed, highlighting the design’s reliability.

Figure 11 and Figure 12 and the corresponding

Table 4. Effect of W2 on proposed antenna frequency band, return loss, resonant frequency and bandwidth.

Parameter (mm)	Frequency Band (GHz)	Max Return Loss (dB)	Fr (GHz)	Bandwidth in %
W2 = 0.6	3.25–3.75	−37	3.48	14.28
W2 = 0.8	3.17–3.85	−30	3.46	19.37
W2 = 1	3.1–3.95	−26	3.45	24.11

and

Table 5. Effect of W4 on proposed antenna frequency band, return loss, resonant frequencies and bandwidth.

Parameter (mm)	Frequency Band (GHz)	Max Return Loss (dB)	Fr (GHz)	Bandwidth in %
W4 = 0.14	4.75–6.5	−45	5.3	26.43
W4 = 0.24	4.5–6.75	−37/−36	4.78/6.1	40.03
W2 = 0.34	4.5–7.84	−34/25	4.8 /6.8	54.13

show the effects of the variation of the geometrical parameters W2 and W4 on parameter S11 of the proposed antenna. The parametric analysis clearly shows that increasing the values of W2 and W4, which correspond to the physical width of the SRR 2 and SRR4 structures, respectively, increases the bandwidth. This observation is consistent with the principle BW = 1/RC (Equation (23)). As W2 and W4 increase, the effective resistance R of the metallic path decreases due to the larger current-carrying cross-section, which increases the bandwidth. This result implies that thicker or wider SRR structures reduce the effective resistance and thus enable wider operating bandwidths.

Table 6. Comparative analysis showing trade−offs between a conventional patch antenna and the proposed miniaturized multiband antenna.

Parameter	Conventional Patch Antenna	Proposed Antenna	Trade-Off Analysis
Antenna dimension (mm³)	60 × 50 × 1.6	23 × 24 × 1.6	Significant size reduction
Electrical size (λ3)	0.5 × 0.4 × 0.01	0.19 × 0.2 × 0.01
Miniaturization in (%)	-	81.6	Achieved via proposed Multi SRR technique
Operating Frequency (GHz)	2.5	2.5, 3.5, 4.5−7.84	Multiband functionality
Bandwidth in (%)	2.41	14.55, 14.28, 54.13	Improved bandwidth in all bands
Peak Gain in (dBi)	1.87	1.5/2/3.1	Slightly reduced gain
Directivity (dBi)	6.35	3.11, 3.2, 4.52	Significant reduced directivity
Radiation efficiency in (%)	37.7	69.1, 75.9, 72.1	Higher radiation efficiency despite FR4 losses

presents a comparative analysis between a conventional rectangular patch antenna (Figure 3a) and the proposed compact multiband antenna (Figure 3e), evaluating size, operating frequency, bandwidth, gain and efficiency. A key advantage of the proposed design is its significant miniaturization—from 60 × 50 × 1.6 mm³ in the conventional antenna to just 23 × 24 × 1.6 mm³, achieving an 81.6% size reduction. Despite its compact form, the proposed antenna supports multiband operation at 2.5 GHz, 3.5 GHz and 4.5–7.84 GHz, making it suitable for a range of wireless communication standards, whereas the conventional design is limited to a single band centered at 2.5 GHz. In terms of bandwidth, the proposed antenna demonstrates substantial improvements, achieving 14.55% at 2.5 GHz, 14.28% at 3.5 GHz and 54.13% across the 4.5–7.84 GHz range. This contrasts sharply with the conventional antenna’s narrow 2.41% bandwidth, which restricts its applicability in wideband or dynamic environments. The proposed multi-SRR-based antenna also achieves acceptable gain levels of 1.5 dBi, 2 dBi and 3.1 dBi across its resonant bands. Although there is a slight reduction in peak gain and a more noticeable drop in directivity due to the smaller radiating aperture, these limitations are offset by a substantial increase in radiation efficiency—from 35.7% in the conventional design to over 70% across all bands in the proposed antenna. This performance enhancement is largely attributed to the integration of split-ring resonator (SRR) structures, which effectively increase the current path without enlarging the antenna’s footprint. Additionally, SRRs help suppress substrate losses—a common issue with FR4 as a material—thereby enabling high efficiency and robust performance in compact, multiband configurations.

4. Fabrication and Measurement

The proposed Multi-SRR-based antenna was fabricated, as can be seen in Figure 13. The measured S11 was evaluated by comparing the simulated S11 results of HFSS and CST, as shown in Figure 14. These simulations showed a strong correlation, underlining the accuracy of the design, which confirmed good agreement with the measurement result. Table 3 presents a comparison of the simulated and measured values for return loss and bandwidth of the proposed multi-SRR antenna. The results show good agreement in band positioning, with some variation in bandwidth. In Band 1, the measured bandwidth (23.5%) slightly exceeds the simulated bandwidth (14.55%), covering important standards such as Wi-Fi 6, WLAN, RFID and 5G. Band 2 also shows a larger measured bandwidth (18.9%) compared to the simulated result (14.28%), successfully covering the 5G and WiMAX mid-bands. For Band 3, the simulated bandwidth is wider (54.13%), but the measured range (20.47%) still covers important applications such as Wi-Fi 5/6/6E, WLAN and RFID.

As can be seen in Figure 14, a distinct increase in frequency was also observed in the third band. This frequency shift is attributed to manufacturing tolerances, especially due to the compact dimensions of SRR 3 and SRR 4, as we mentioned in the previous section (current distribution). These components are very sensitive to even small manufacturing deviations, which can have a significant impact on the resonant frequency. In addition, the limitations of the VNA at 7 GHz in our laboratory also contribute to the lower accuracy of measurements in higher frequency bands. The slight frequency deviation has minimal impact and does not compromise the overall performance of the antenna. Overall, the measured results match well with the simulations, confirming the antenna’s suitability for multi-standard wireless applications. This is further illustrated in

Table 7. Comparison of the simulated and measured S11 bandwidths and the corresponding wireless standards.

Band No.	Bandwidth (Simulation)	Bandwidth (Measurement)	Covered Bands
1	2.4–2.80 GHz (14.55%)	2.25–2.85 GHz (23.5%)	WLAN, RFID, Wi-Fi 6 (802.11ax) (2.4–2.48 GHz), 5G Sub-6 GHz Mid-band (2.5–2.6 GHz), WiMAX (2.3–2.5 GHz), Wi-Fi 7
2	3.25–3.75 GHz (14.28%)	3.35–4.05 GHz (18.9%)	5G Sub-6 GHz Mid-band (3.3–3.8 GHz), WiMAX (3.3–3.8 GHz)
3	4.5–7.84 GHz (54.13%)	5.7–7 GHz (20.47%)	RFID (5.725–5.875 GHz), Wi-Fi 5/6/7 (5.15–5.875 GHz), Wi-Fi 6E/7 (5.92–7.12 GHz), WLAN (5.15–5.35 GHz/5.725–5.825 GHz), WiMAX (5.725–5.850 GHz), 5G Sub-6 GHz Mid-band (4.5–5 GHz)

.

The proposed design allows selective activation of resonant elements, enabling application-specific optimization.

Table 8. Application-specific configuration of the proposed multiband antenna.

Device Type	Active SRRs	Optimized For	Application
Basic IoT Device	SRR1	2.4 GHz	Wi-Fi 4/Bluetooth/Zigbee/IoT
Wi-Fi 7 Router	SRR1 + SRR3 + SRR4	2.4/5/6 GHz	Wi-Fi 4/5/6/6E/7
Enhanced Wi-Fi Device	SRR1 + SRR3	2.4/5.8	Wi-Fi 4/5
5G NR Device	SRR2 + SRR3	3.5/5.8	5G NR mid-band (n77/n78), Wi-Fi 5 (5.8 GHz)

shows how the proposed multiband antenna can be optimized for different applications by selectively activating specific SRRs. Each device type uses a unique combination of SRRs to target required frequency bands. This flexibility supports various wireless standards like Wi-Fi, Bluetooth, Zigbee and 5G NR

5. Comparative Study

Table 9. Performance comparison between the proposed multi-SRR-Based antenna and reported compact multiband antennas.

Ref.	Year of Pub	Antenna Size mm3	Substrate Material	Frequency (GHz)	Gain (dBi)	Efficiency (%)	BW (%)	Techniques
[2]	2021	87.5 × 61 × 1.6	FR4	1.8–2.9/3.4–4.6/5–5.6	2.98/2.5/3.34	75/95	42.5/30/11.3	Slot
[3]	2021	50 × 50 × 0.8 0.39 λ × 0.39 λ	FR4	2.24–2.59/3.91–4.52	3/3.8	74/81	14/14.52	Slot
[9]	2022	50 × 50 0.31 λ × 0.31 λ	FR4	1.87–2.66/3.33–3.69/4.71–5.80	Max 4	70	35.4/5.5/20.7	Antenna shape
[13]	2024	60 × 60 × 1.6 0.43 λ × 0.43 λ	FR4	2.24/2.97/3.66	3.1/2.18/3.29	-	14.25/1.78/8.37	SRR
[17]	2023	36 × 37 × 1.6	FR4	3.59–3.69/6–6.21	3.83/0.537	97/99	2.75/3.44	Parasitic strips
This work	-	23 × 24 × 1.6 0.19 λ × 0.2 λ × 0.01 λ	FR4	2.4–2.80/3.25–3.75/4.5–7.84	1.5/2/3.1	69/76/72	14.55/14.28/54.13	Multi SRR

compares the proposed multi-SRR-based antenna with reported compact multiband antennas on FR4 substrate. As can be seen in this table, although the proposed antenna achieves gains of 1.5, 2 and 3.1 dBi over the respective frequency bands, which are comparable to the gains reported in previous studies, it is important to note that this performance is achieved despite a significant size reduction of 87.77%. In addition, the proposed antenna has a relatively wide operating bandwidth in three different frequency bands and outperforms most of its competitors in this respect. Thus, this study achieves an efficient balance between the dimensions, bandwidth and gain, which makes it very suitable for modern communication systems.

Our proposed design prioritizes a compact footprint, low cost and multiband operation, which inherently limits the achievable gain. Nevertheless, we fully recognize the importance of gain optimization, especially for emerging high-frequency wireless applications such as 5G. To this end, we are actively exploring several strategies to enhance gain in future work, including the development of compact MIMO configurations. Transitioning from a single-element to a MIMO architecture not only improves gain and diversity performance but also enhances robustness for 5G and IoT scenarios. This direction is particularly promising for achieving both wideband operation and higher gain within a compact form factor.

6. Conclusions

In this paper, a miniaturized multiband antenna (0.19 λ × 0.2 λ × 0.01λ) based on multiple split-ring resonators was proposed for modern wireless applications. The integration of SRRs enabled a significant miniaturization of 81.6% compared to a conventional antenna, while achieving satisfactory gains of 1.5 dBi, 2 dBi and 3.2 dBi across the operating bands 2.4–2.8 GHz, 3.25–3.75 GHz and 4.5–7.84 GHz, respectively. The antenna also exhibited excellent bandwidths of 14.55%, 14.28% and 54.13%, respectively. An analytical study was conducted and validated by an equivalent circuit model and numerical simulations, showing strong agreement between the results. A detailed analysis has revealed that the multiband capability and broadband performance of the antenna is primarily due to the ability of the metamaterial to exhibit negative permeability at certain resonant frequencies. This confirms the critical role of the integrated SRR structure in enhancing the overall performance and functionality of the proposed antenna. The proposed multi-SRR-based antenna offers a miniaturized size and efficient solution for multiband wireless communication systems, making it well-suited for potential applications in 5G sub-6 GHz mid-band (2.5/3.5/5 GHz), RFID (2.45/5.8 GHz), WiMAX, WiFi 5/6/6E and WLAN technologies.