# Design and Analysis of a Metamaterial-Inspired Miniaturized Quadband Antenna

Authors: Si Li; Shitao Sun; Yunlong Mao
Journal: International Journal of Antennas and Propagation
 (2022)

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## Abstract

A metamaterial-inspired miniaturized quadband antenna is designed and discussed with a transmission line model to study the theory of miniaturization and multiband in this paper. A conventional printed monopole antenna is assumed as a primary antenna and then surrounded by an array of 4 × 2 interdigital LHMs. The proposed antenna has a compact size of36mm×24mm×1mm, and operates at 2.40–2.55 GHz, 3.02–3.38 GHz, 5.04–5.52 GHz, and 7.08–7.38 GHz. Good gain and omnidirectional radiation patterns are observed in simulations and measurements. A simplified transmission line modal was established to study the reasons for miniaturization and multiband that were brought about by the LHM array. Related results verified the theoretical analysis and indicated that the proposed antenna is a good candidate for wireless communication applications.


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## Body

## 1. Introduction

In modern wireless systems, a common trend for antennas is to be miniaturized while maintaining good radiation properties to fulfill multiband requirements, especially for ongoing wireless communication systems.Various types of miniaturized multiband antennas were reported. In some of these designs, multiband property is archived with different shaped strips, such as the C- and L-shapes [1], the Y-shape [2], and the rhombus shape [3]. In some other designs, multiband property is archived by etching different slots, such as the U-shape [4, 5], the F-shape [6], and the T-shape [7] slots. Recently, metamaterials have been investigated for antenna miniaturization and enabling multiband operation [8]. Different kinds of split-ring resonators (SRRs) are used in antenna designs [9–15]. Among these designs, SRRs were used as radiating elements [10–12] to surround the radiating elements [13], or were printed on the ground plane side of the radiating elements [9, 14, 15]. Especially, in [11, 13, 14], the special personality of the metamaterials is designed to generate required passing bands of the proposed antennas, while in [12], it is responsible for the notched bands. In some other designs, metamaterials are used as near-field resonant parasitic (NFRP) elements [16–19], for the purpose to increase effective inductance and capacitance, hence achieving miniaturization and multiband. However, it would be better if a transmission model could be established to analyze the mechanism for miniaturization and multiband properties in detail.In this work, a metamaterial-inspired miniaturized quadband antenna is presented. The proposed antenna has a compact size of36mm×24mm×1mm (0.27λ×0.18λ×0.008λ) and is printed on an FR4 substrate with a tangent loss of 0.02. A conventional printed monopole is assumed as the primary antenna. Later, a 4 × 2 array of interdigital LHM is applied to surround the monopole. This LHM is verified with negative permeability and permittivity from 2.75 GHz to 3.75 GHz. The proposed antenna works at 2.40–2.55 GHz, 3.02–3.38 GHz, 5.04–5.52 GHz, and 7.08–7.38 GHz. Compared to the conventional monopole, the employment of LHMs not only reduced antenna size, but also added two more frequency bands. A simplified transmission line model for the proposed antenna has been established, and the mechanism of LHMs as NFRP elements is analyzed. The proposed antenna is fabricated and measured, and the results match well with simulations. Finally, a conclusion is drawn, pointing out that the proposed antenna is a good candidate for wireless communication applications.


## 2. Antenna Design Procedure

### 2.1. Left-Handed Metamaterial Design

For the purpose of multiresonances and miniaturization, an interdigital LHM is designed as shown in Figure1. This structure is printed on an FR4 substrate with relative permeability equals to 4.4 and its thickness is 1 mm. The parameters are listed in Table 1.Figure 1
Structure of the designed LHM unit.Table 1
Parameters for an interdigital LHM unit.
l (mm)wabcd10.54.5 mm1.2 mm0.5 mm0.5 mm0.2 mmThis LHM unit is composed of a few coupled strips, providing magnetic resonance; the currents are forced to flow in a vertical direction, providing electric resonance. Therefore, this LHM should be capable of exhibiting double negative properties.Simulations were operated and the results are displayed in Figure2. It is observed that there are two resonances, and the passing band is from 2.0 GHz to 3.27 GHz. Therefore, this LHM is capable of generating resonances at frequencies of around 2.4 GHz.Figure 2
Simulated S parameters of the proposed LHM unit.To investigate its electromagnetic properties, we apply ‘S parameter Retrieval’ method [20]. Retrieved effective permeability, permittivity, impedance, and refractive index are displayed in Figure 3.Figure 3
Retrieved effective parameters using ‘S Parameters Retrieval Method:’ (a) effective permittivity, (b) effective permeability, (c) normalized impedance, and (d) refractive index.
(a)(b)(c)(d)Figure3(a) displayed the retrieved effective permittivity, as observed, was negative at the frequency from 2.75 GHz to 4 GHz. Figure 3(b) displayed the retrieved effective permeability, which is negative at the frequency range from 2.75 GHz to 3.45 GHz. Therefore, the proposed LHM exhibits double negative property and negative refractive index (Figure 3(d)) at the frequency range from 2.75 GHz to 3.45 GHz.


### 2.2. Design of the LHM-Inspired Antenna

The design procedure of this antenna is shown in Figure4.Figure 4
Design procedure of the proposed antenna.First, a conventional monopole antenna (Ant 1) is designed. A rectangular slot is etched on the ground for the purpose of impedance matching. This monopole works at two different frequency ranges, which correspond to the first and third resonances, respectively. Later, 4 LHM elements are applied to surround the monopole. For further miniaturization and better impedance matching, another four LHM elements are added. The parameters for this antenna are listed in Table2.Table 2
Parameters for the proposed antenna.
ls (mm)ws1dwd1gwg3624 mm30 mm3 mm10 mm0.5 mmSimulations were operated for all 3 antennas. The proposed antenna (Ant 3) is also fabricated and measured, as displayed in Figure5. Simulated and measured S parameters are displayed in Figure 6, and their corresponding working bands are listed in Table 3.Figure 5
Prototype of the proposed antenna and the measurement environment: (a) prototype of the proposed antenna and (b) measurement environment.
(a)(b)Figure 6
Simulated and measured S parameters.Table 3
Working frequency ranges of different antennas.
AntennaFrequency ranges (GHz) (S11 < −10 dB)Ant 12.7–3.076.17–7.04Ant 22.57–2.723.06–3.435.10–5.386.89–7.27Ant 32.40–2.553.02–3.385.04–5.527.08–7.38Ant 3 measured2.30–2.463.28–3.595.18–5.566.98–7.44Compared to the primary monopole antenna, the introduction of LHMs has brought significant miniaturization as the first working frequency has been shifted from 2.7 GHz (Ant 1) to 2.4 GHz (Ant 3). Additionally, two more working frequencies are observed, achieving multiband property.The radiating pattern of the proposed antenna is also simulated and measured at 4 different resonances, as displayed in Figure7. Good agreements are also obtained. Gain and radiation efficiency are also obtained through simulation, as displayed in Figure 8. The efficiency is greater than 46% and as high as 93%. Even at a few frequencies, the gain is smaller than 0 dBi. However, at higher frequencies, the peak gain can be as large as 3.8 dBi. Therefore, the proposed antenna exhibits good gain and efficiency.Figure 7
Radiation pattern of the proposed antenna at different resonances: (a) 2.49 GHz, (b) 3.22 GHz, (c) 5.23 GHz, and (d) 7.15 GHz.
(a)(b)(c)(d)Figure 8
Gain and efficiency of the proposed antenna.


## 2.1. Left-Handed Metamaterial Design

For the purpose of multiresonances and miniaturization, an interdigital LHM is designed as shown in Figure1. This structure is printed on an FR4 substrate with relative permeability equals to 4.4 and its thickness is 1 mm. The parameters are listed in Table 1.Figure 1
Structure of the designed LHM unit.Table 1
Parameters for an interdigital LHM unit.
l (mm)wabcd10.54.5 mm1.2 mm0.5 mm0.5 mm0.2 mmThis LHM unit is composed of a few coupled strips, providing magnetic resonance; the currents are forced to flow in a vertical direction, providing electric resonance. Therefore, this LHM should be capable of exhibiting double negative properties.Simulations were operated and the results are displayed in Figure2. It is observed that there are two resonances, and the passing band is from 2.0 GHz to 3.27 GHz. Therefore, this LHM is capable of generating resonances at frequencies of around 2.4 GHz.Figure 2
Simulated S parameters of the proposed LHM unit.To investigate its electromagnetic properties, we apply ‘S parameter Retrieval’ method [20]. Retrieved effective permeability, permittivity, impedance, and refractive index are displayed in Figure 3.Figure 3
Retrieved effective parameters using ‘S Parameters Retrieval Method:’ (a) effective permittivity, (b) effective permeability, (c) normalized impedance, and (d) refractive index.
(a)(b)(c)(d)Figure3(a) displayed the retrieved effective permittivity, as observed, was negative at the frequency from 2.75 GHz to 4 GHz. Figure 3(b) displayed the retrieved effective permeability, which is negative at the frequency range from 2.75 GHz to 3.45 GHz. Therefore, the proposed LHM exhibits double negative property and negative refractive index (Figure 3(d)) at the frequency range from 2.75 GHz to 3.45 GHz.


## 2.2. Design of the LHM-Inspired Antenna

The design procedure of this antenna is shown in Figure4.Figure 4
Design procedure of the proposed antenna.First, a conventional monopole antenna (Ant 1) is designed. A rectangular slot is etched on the ground for the purpose of impedance matching. This monopole works at two different frequency ranges, which correspond to the first and third resonances, respectively. Later, 4 LHM elements are applied to surround the monopole. For further miniaturization and better impedance matching, another four LHM elements are added. The parameters for this antenna are listed in Table2.Table 2
Parameters for the proposed antenna.
ls (mm)ws1dwd1gwg3624 mm30 mm3 mm10 mm0.5 mmSimulations were operated for all 3 antennas. The proposed antenna (Ant 3) is also fabricated and measured, as displayed in Figure5. Simulated and measured S parameters are displayed in Figure 6, and their corresponding working bands are listed in Table 3.Figure 5
Prototype of the proposed antenna and the measurement environment: (a) prototype of the proposed antenna and (b) measurement environment.
(a)(b)Figure 6
Simulated and measured S parameters.Table 3
Working frequency ranges of different antennas.
AntennaFrequency ranges (GHz) (S11 < −10 dB)Ant 12.7–3.076.17–7.04Ant 22.57–2.723.06–3.435.10–5.386.89–7.27Ant 32.40–2.553.02–3.385.04–5.527.08–7.38Ant 3 measured2.30–2.463.28–3.595.18–5.566.98–7.44Compared to the primary monopole antenna, the introduction of LHMs has brought significant miniaturization as the first working frequency has been shifted from 2.7 GHz (Ant 1) to 2.4 GHz (Ant 3). Additionally, two more working frequencies are observed, achieving multiband property.The radiating pattern of the proposed antenna is also simulated and measured at 4 different resonances, as displayed in Figure7. Good agreements are also obtained. Gain and radiation efficiency are also obtained through simulation, as displayed in Figure 8. The efficiency is greater than 46% and as high as 93%. Even at a few frequencies, the gain is smaller than 0 dBi. However, at higher frequencies, the peak gain can be as large as 3.8 dBi. Therefore, the proposed antenna exhibits good gain and efficiency.Figure 7
Radiation pattern of the proposed antenna at different resonances: (a) 2.49 GHz, (b) 3.22 GHz, (c) 5.23 GHz, and (d) 7.15 GHz.
(a)(b)(c)(d)Figure 8
Gain and efficiency of the proposed antenna.


## 3. Analysis and Discussions of the proposed antenna

### 3.1. Transmission Line Model Analysis

To analyze its working principle, we start with the transmission line model. A conventional monopole antenna can be regarded as a transmission line, as illustrated in Figure9, where L0 and C0 are the equivalent inductance and capacitance. Employment of LHMs is like adding an inductor and a capacitor to the transmission line model, as illustrated in Figure 10.Figure 9
Equivalent circuit of conventional monopole antenna.Figure 10
Equivalent circuit of conventional monopole with LHM.Strong near-field resonant coupling occurs between the monopole antenna and the LHMs. The simplified equivalent circuit is displayed in Figure10, where C1 and L1 are mainly decided by LHMs. For a microsection in z direction Δz , one can obtain(1)−∂U∂z=R0+jωL0I=Z0I,−∂I∂z=G0+jωC21−ω2L1C2+jωC1U=Y0U,where R0 and G0 are the corresponding impedance and conductance, Δt is a time sampling period.Therefore, the character impedance is calculated as(2)Zc=Z0Y0=R0+jωL0G0+jωC2/1−ω2L1C2+jωC1≈L0C1+C2/1−ω2L1C2.And the input impedance can be expressed as(3)Zinl=ZcZL+jZctanβlZc+jZLtanβl.At resonances, the imaginary part of the input impedance should be zero. Hence, we rewrite (3) as(4)Zinl=Zc1+tan2βlZc2+ZL2tan2βl+jZcZc2−ZL2tanβlZc2+ZL2tan2βl.That is to make(5)Zc2−ZL2tanβl=0,where ZL=1/jωC0.From equation (5), if tanβl=0, since it is a period function, there will be higher harmonics that may bring more than one working band. On the other hand, if Zc2−ZL2=0, we substitute (2) into equation (5), after a series of transformations, one can obtain that(6)ω=L0C0−L1C1C2±L1C1C2+L0C02+4L1L0C0C222L1L0C0C2.That is to say, strong coupling between the monopole antenna and the LHMs will add working frequency ranges.Similarly, without LHM, the phase constantβ is(7)β=12ω2L0C0−R0G0+R02+ω02L02G02+ω02C02.However, the employment of LHMs will increase the conductance. We substituteG0=G0+jωC2/1−ω2L1C2 into (7), we figure out that larger G0 will bring larger β, hence shorter l can make tanβl=0, thus achieving miniaturization.


### 3.2. Surface Current Distribution Analysis

Current distributions at 4 different resonances of the proposed antenna are also displayed in Figure11. At these frequencies, strong coupled currents are observed flowing on the LHMs. However, since the LHM unit is symmetrical, the radiating far-field of these currents will cancel each other out, so they do not contribute to the far-field radiation. Thus, together with the transmission line model analysis, it is obvious that the LHMs only help to achieve miniaturization and multiband but will not affect far-field radiation.Figure 11
Current distribution at different frequencies of the proposed antenna: (a) 2.48 GHz, (b) 3.17 GHz, (c) 5.27 GHz, and (d) 7.22 GHz.
(a)(b)(c)(d)


## 3.1. Transmission Line Model Analysis

To analyze its working principle, we start with the transmission line model. A conventional monopole antenna can be regarded as a transmission line, as illustrated in Figure9, where L0 and C0 are the equivalent inductance and capacitance. Employment of LHMs is like adding an inductor and a capacitor to the transmission line model, as illustrated in Figure 10.Figure 9
Equivalent circuit of conventional monopole antenna.Figure 10
Equivalent circuit of conventional monopole with LHM.Strong near-field resonant coupling occurs between the monopole antenna and the LHMs. The simplified equivalent circuit is displayed in Figure10, where C1 and L1 are mainly decided by LHMs. For a microsection in z direction Δz , one can obtain(1)−∂U∂z=R0+jωL0I=Z0I,−∂I∂z=G0+jωC21−ω2L1C2+jωC1U=Y0U,where R0 and G0 are the corresponding impedance and conductance, Δt is a time sampling period.Therefore, the character impedance is calculated as(2)Zc=Z0Y0=R0+jωL0G0+jωC2/1−ω2L1C2+jωC1≈L0C1+C2/1−ω2L1C2.And the input impedance can be expressed as(3)Zinl=ZcZL+jZctanβlZc+jZLtanβl.At resonances, the imaginary part of the input impedance should be zero. Hence, we rewrite (3) as(4)Zinl=Zc1+tan2βlZc2+ZL2tan2βl+jZcZc2−ZL2tanβlZc2+ZL2tan2βl.That is to make(5)Zc2−ZL2tanβl=0,where ZL=1/jωC0.From equation (5), if tanβl=0, since it is a period function, there will be higher harmonics that may bring more than one working band. On the other hand, if Zc2−ZL2=0, we substitute (2) into equation (5), after a series of transformations, one can obtain that(6)ω=L0C0−L1C1C2±L1C1C2+L0C02+4L1L0C0C222L1L0C0C2.That is to say, strong coupling between the monopole antenna and the LHMs will add working frequency ranges.Similarly, without LHM, the phase constantβ is(7)β=12ω2L0C0−R0G0+R02+ω02L02G02+ω02C02.However, the employment of LHMs will increase the conductance. We substituteG0=G0+jωC2/1−ω2L1C2 into (7), we figure out that larger G0 will bring larger β, hence shorter l can make tanβl=0, thus achieving miniaturization.


## 3.2. Surface Current Distribution Analysis

Current distributions at 4 different resonances of the proposed antenna are also displayed in Figure11. At these frequencies, strong coupled currents are observed flowing on the LHMs. However, since the LHM unit is symmetrical, the radiating far-field of these currents will cancel each other out, so they do not contribute to the far-field radiation. Thus, together with the transmission line model analysis, it is obvious that the LHMs only help to achieve miniaturization and multiband but will not affect far-field radiation.Figure 11
Current distribution at different frequencies of the proposed antenna: (a) 2.48 GHz, (b) 3.17 GHz, (c) 5.27 GHz, and (d) 7.22 GHz.
(a)(b)(c)(d)


## 4. Conclusions

An LHM-inspired miniaturized quadband antenna is designed and analyzed in this paper. We first designed a novel LHM and then verified its double negative property through simulations and retrieved effective parameters. Then, this LHM is applied to surround a conventional monopole antenna. The proposed antenna is fabricated and discussed with simulations and measurements. A transmission line model for the proposed antenna is established to analyze the mechanism of miniaturization and multiband property. All the results indicate that near-field resonant coupling between LHMs and the monopole brought miniaturization and multiband properties, and the proposed antenna is a good candidate for wireless communications.



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*Source: 3447055-2022-03-27.xml*