# Compact Wideband Dual-Frequency Antenna Based on a Simplified Composite Right/Left-Handed Transmission Line with Hilbert Curve Loading

Authors: Tianpeng Li; Jian Zhang; Baowei Cheng; Xue Lei; Zhijian Xu; Jun Gao
Journal: International Journal of Antennas and Propagation
 (2019)

---

## Abstract

This paper addresses the issues of low bandwidth, gain, and efficiency of miniaturized microwave antennas by proposing a novel wideband dual-frequency coplanar waveguide antenna design based on a simplified composite right/left-handed (SCRLH) transmission line structure with Hilbert curve loading. The multifrequency characteristics of the SCRLH transmission line structure are evaluated theoretically, and the antenna parameters promoting bandwidth broadening under zeroth-order resonance (ZOR) and first-order resonance (FOR) mode operation are evaluated. The bandwidth broadening in the ZOR and FOR modes is accordingly revealed to be independent of the antenna length, and the structure therefore facilitates wideband operation under miniaturization. Finally, the dual-frequency ZOR and FOR mode antenna design with center frequencies off0 = 1.865 GHz and f1 = 2.835 GHz is validated via simulation, and the performance of a compact prototype antenna is evaluated experimentally. The −10 dB return loss bandwidths at f0 and f1 are 187 MHz (from 1.773 GHz to 1.96 GHz) and 368 MHz (from 3.002 GHz to 3.37 GHz), and the corresponding relative bandwidths are 10.1% and 11.5%, respectively. The experimentally measured peak gains and radiation efficiencies at f0 are 1.54 dB and 81.3%, respectively, and those at f1 are 1.71 dB and 74.2%, respectively.


---

## Body

## 1. Introduction

Wireless communication systems have been increasingly subjected to the parallel development trends of miniaturization and integration in both military and civilian applications [1]. However, this is particularly problematic when integrating antennas with miniaturized wireless communication devices because they invariably degrade the performance of the antenna, such as by narrowing the bandwidth and deteriorating the directivity pattern. In addition, an increasing state of technological development creates increasingly scarce spectrum resources while increasing the demand for higher communication quality. These conditions collectively require communication systems to work efficiently in different frequency bands. Therefore, the development of compact wideband dual-frequency antenna designs that support or even improve antenna performance is essential to meet the increasingly stringent requirements of wireless communication systems [2–4].Excellent multifrequency antenna performance has been achieved by antennas based on composite right/left-handed (CRLH) transmission lines owing to their unique dispersion controllability and the capability of controlling their negative-, zeroth-, and positive-order resonance frequencies. For example, Narieda et al. [5] proposed a coplanar waveguide (CPW) dual-frequency antenna design based on a one-dimensional CRLH transmission line structure using the zeroth-order resonance (ZOR) mode and the positive first-order resonance (FOR) mode. Gummalla et al. [6] proposed a three-frequency antenna based on a two-dimensional CRLH transmission line using the ZOR, positive FOR, and positive second-order resonance modes. However, while these past studies have both achieved multifrequency antenna performance, the antenna designs suffered from unacceptably narrow bandwidths.As a means of addressing the issue of bandwidth narrowing, continuing CRLH transmission line research has increasingly focused on new forms, such as negative dielectric constant (i.e.,ε-negative (ENG)) transmission lines and negative magnetic permeability (i.e., μ-negative (MNG)) transmission lines. Because both ENG and MNG transmission lines can be regarded as the result of removing the series capacitance or the shunt inductance of a CRLH transmission line, some researchers have denoted these designs as simplified CRLH (SCRLH) transmission lines [7, 8]. However, current efforts in this area suffer from deficiencies, such as low peak gain, degraded directivity, and low radiation efficiency.This paper addresses these issues by proposing a new wideband dual-frequency CPW antenna design based on an SCRLH transmission line structure with Hilbert curve loading. The multifrequency characteristics of the SCRLH transmission line structure are evaluated theoretically, and the antenna parameters promoting bandwidth broadening under ZOR and FOR mode operation are evaluated. The analysis reveals that the bandwidth broadening of the ZOR and FOR modes is independent of the antenna length, and the SCRLH transmission line structure therefore facilitates wideband operation under miniaturization. Finally, the dual-frequency ZOR and FOR mode antenna design is validated via simulation, and the performance of a compact prototype antenna is evaluated experimentally. The experimental results are found to be in excellent agreement with the simulation results and thereby validate the proposed antenna design.


## 2. Bandwidth Broadening Based on an SCRLH Transmission Line

Figure1 shows an equivalent circuit of a single SCRLH transmission line unit structure of length d consisting of a series-connected right-handed inductor LR, a shunt left-handed inductor LL, and a shunt right-handed capacitor CR.Figure 1
Equivalent circuit of a single SCRLH transmission line unit of lengthd.As discussed, the equivalent circuit in Figure1 differs from that of a standard CRLH transmission line only in that it has omitted a series left-handed capacitor. Applying the Bloch–Floquet theorem to a single SCRLH transmission line unit yields the following dispersion equation [9]:(1)βω=1dcos−11−ω22ωR2+ωE22ωR2,where ωE=1/LLCR is the resonance frequency of the shunt branch of the equivalent circuit and ωR=1/LRCR is the resonance frequency of the right-handed part of the equivalent circuit. For a multiunit SCRLH transmission line of length l and a signal wavelength λ, the resonance order n, phase constant βn, number of units N, and unit length d satisfy the following relationship:(2)θ=βnl=βnNd=2πλnλ2=nπ.Solving equations (1) and (2) simultaneously yields the following expression for the resonance frequencies of an SCRLH transmission line:(3)ωn=1CR1LL+2LR−2LRcosnπN.In equations (2) and (3), n = 0, 1, 2, …, N − 1, indicating that the SCRLH transmission line has one ZOR mode and N − 1 positive resonance modes, for a total of N resonance modes. This differs from conventional right-handed transmission lines and pure left-handed transmission lines and is the very reason that a CRLH transmission line is capable of multifrequency operation. Figure 2 shows the dispersion curve of an SCRLH transmission line and a selection of its resonance modes corresponding to ωn.Figure 2
Dispersion curve and corresponding resonance modes of anN-unit SCRLH transmission line of length l = Nd.


### 2.1. ZOR Mode Bandwidth Broadening

Forn = 0, equation (3) yields the following:(4)ωZORopen=ω0=1LLCR=ωE,where the superscript open indicates that both ends of the SCRLH transmission line are open circuits. Equation (4) indicates that the ZOR frequency of the SCRLH transmission line is equal to the resonance frequency of the shunt branch of the equivalent circuit. As a result, ω0 is related only to the values of LL and CR and is unrelated to the physical dimension of the SCRLH transmission line. The no-load quality factor Q for an SCRLH transmission line operating in the ZOR mode can also be obtained under the open circuit condition as(5)QZORopen=1/NGωZORopenLL/N=1GCRLL,where G is the transmission loss of the shunt branch of the equivalent circuit. Finally, the relationship between the bandwidth BW and the Q factor can be employed to obtain the bandwidth of an SCRLH transmission line operating in the ZOR mode under the open circuit condition as(6)BWopen=1QZORopen=GLLCR.An inspection of equations (4) and (6) indicates that increasing the bandwidth of an SCRLH transmission line operating in the ZOR mode under the open circuit condition without changing the resonance frequency requires that LL be increased and CR decreased simultaneously while keeping their product constant.It is also of interest to determine the input impedance of the SCRLH transmission line operating in the ZOR mode under an open circuit condition. Here, one end of the transmission line appears as the input impedance of the other end under the open circuit condition. Therefore, the input impedance of the SCRLH transmission line can be given according toZ and the shunt impedance of the equivalent circuit Y−1 as(7)Zinopen=−jZ0cot−1βlβ⟶0≈−jZ01βl=1NY.Here, we have substitutedZ0=Z/Y and γ=jβ=ZY. This indicates that the input impedance of the entire transmission line is 1/N times the shunt impedance of the equivalent circuit.


### 2.2. FOR Mode Bandwidth Broadening

Forn = 1 and N = 3, equation (3) yields the following:(8)ω1=1CR1LL+2LR−2LRcosπN=1CR1LL+1LR.We note here that equations (4) and (8) are of an equivalent form if we substitute the relation(9)1Ls=1LL+1LR,into equation (8). In other words, the value of ω1 for a 3-unit SCRLH transmission line is related only to the values of Ls and CR and is unrelated to the physical dimension of the SCRLH transmission line. Because FOR occurs when the electrical energy and magnetic energy stored in the resonance cavity are equal, the value of the no-load factor Q under an open circuit condition is given as follows:(10)QFORopen=ωFOR2WePloss=ωFORCRG=1GCRLR+LLLRLL,and the bandwidth of the FOR mode is given by(11)BWopen=1QFORopen=GLsCR.An inspection of equations (9) and (11) indicates that increasing the bandwidth of a 3-unit SCRLH transmission line operating in the FOR mode under the open circuit condition without changing the resonance frequency requires that Ls be increased and CR decreased simultaneously while keeping their product constant.The above analysis demonstrates that the resonance frequency of an antenna based on a 3-unit SCRLH transmission line operating in the FOR mode depends only on the parameters of the equivalent circuit, not on its physical dimensions, and therefore differs markedly from conventional half-wavelength microstrip antennas operating in the FOR mode. For this reason, an antenna based on an SCRLH transmission line operating in the FOR mode offers excellent potential for miniaturization.


## 2.1. ZOR Mode Bandwidth Broadening

Forn = 0, equation (3) yields the following:(4)ωZORopen=ω0=1LLCR=ωE,where the superscript open indicates that both ends of the SCRLH transmission line are open circuits. Equation (4) indicates that the ZOR frequency of the SCRLH transmission line is equal to the resonance frequency of the shunt branch of the equivalent circuit. As a result, ω0 is related only to the values of LL and CR and is unrelated to the physical dimension of the SCRLH transmission line. The no-load quality factor Q for an SCRLH transmission line operating in the ZOR mode can also be obtained under the open circuit condition as(5)QZORopen=1/NGωZORopenLL/N=1GCRLL,where G is the transmission loss of the shunt branch of the equivalent circuit. Finally, the relationship between the bandwidth BW and the Q factor can be employed to obtain the bandwidth of an SCRLH transmission line operating in the ZOR mode under the open circuit condition as(6)BWopen=1QZORopen=GLLCR.An inspection of equations (4) and (6) indicates that increasing the bandwidth of an SCRLH transmission line operating in the ZOR mode under the open circuit condition without changing the resonance frequency requires that LL be increased and CR decreased simultaneously while keeping their product constant.It is also of interest to determine the input impedance of the SCRLH transmission line operating in the ZOR mode under an open circuit condition. Here, one end of the transmission line appears as the input impedance of the other end under the open circuit condition. Therefore, the input impedance of the SCRLH transmission line can be given according toZ and the shunt impedance of the equivalent circuit Y−1 as(7)Zinopen=−jZ0cot−1βlβ⟶0≈−jZ01βl=1NY.Here, we have substitutedZ0=Z/Y and γ=jβ=ZY. This indicates that the input impedance of the entire transmission line is 1/N times the shunt impedance of the equivalent circuit.


## 2.2. FOR Mode Bandwidth Broadening

Forn = 1 and N = 3, equation (3) yields the following:(8)ω1=1CR1LL+2LR−2LRcosπN=1CR1LL+1LR.We note here that equations (4) and (8) are of an equivalent form if we substitute the relation(9)1Ls=1LL+1LR,into equation (8). In other words, the value of ω1 for a 3-unit SCRLH transmission line is related only to the values of Ls and CR and is unrelated to the physical dimension of the SCRLH transmission line. Because FOR occurs when the electrical energy and magnetic energy stored in the resonance cavity are equal, the value of the no-load factor Q under an open circuit condition is given as follows:(10)QFORopen=ωFOR2WePloss=ωFORCRG=1GCRLR+LLLRLL,and the bandwidth of the FOR mode is given by(11)BWopen=1QFORopen=GLsCR.An inspection of equations (9) and (11) indicates that increasing the bandwidth of a 3-unit SCRLH transmission line operating in the FOR mode under the open circuit condition without changing the resonance frequency requires that Ls be increased and CR decreased simultaneously while keeping their product constant.The above analysis demonstrates that the resonance frequency of an antenna based on a 3-unit SCRLH transmission line operating in the FOR mode depends only on the parameters of the equivalent circuit, not on its physical dimensions, and therefore differs markedly from conventional half-wavelength microstrip antennas operating in the FOR mode. For this reason, an antenna based on an SCRLH transmission line operating in the FOR mode offers excellent potential for miniaturization.


## 3. Compact Dual-Frequency Wideband Antenna Based on an SCRLH Transmission Line Operating in ZOR and FOR Modes

### 3.1. Structural Characteristics and Analysis

To realize the ZOR mode bandwidth broadening principle described above and to match the special case of FOR mode operation with three units, we designed a new CPW structure based on an SCRLH transmission line with Hilbert curve loading. As shown in Figure3, the CPW is a cascaded structure composed of three SCRLH transmission line units with the same size parameters. The left and right sides are grounded metal plates, and the middle is a radiating metal plate connected to the grounded plate on the right side with metal wires arranged in the shape of a second-order Hilbert curve, which forms the left-handed shunt inductances LL of the 3-unit SCRLH transmission line. The width of the wires and the distances between the wires are denoted by w6 and w7, respectively. In addition, when current is flowing on the middle plate, it inevitably introduces a right-handed inductance LR. Furthermore, the gap of width w1 between the grounded plate on the left side and the middle plate results in a distributed right-handed capacitance CR whose magnitude is inversely proportional to the value of w1. The other physical dimensions are clearly denoted in the figure.Figure 3
Dual-frequency wideband CPW antenna design based on a 3-unit SCRLH transmission line with Hilbert curve loading.The Hilbert curve proposed by Hilbert in 1891 is a continuous fractal space-filling curve that fills a two-dimensional plane with one-dimensional line segments. According to its fractal nature, it is characterized by simplicity, self-similarity, and self-avoidance. The formation process is illustrated in Figure4. The zeroth-order Hilbert curve (n = 0) is a line bent into a U-shape, and higher-order curves maintain the same exterior dimensions as the zeroth-order curve. Therefore, the first-order curve (n = 1) consists of four U-shaped curves of equivalent exterior dimensions, and their connecting lines are shown as dashed lines in the figure. The second-order curve (n = 2) consists of four first-order curves, and their connecting lines are again shown as dashed lines in the figure. This procedure can be repeated indefinitely.Figure 4
Hilbert curve formation process.
(a)
(b)
(c)The use of Hilbert curves has been widely reported in microwave antenna applications [10]. Because the magnitude of the inductance of a metal wire is directly proportional to its length and inversely proportional to its width, the use of Hilbert curves effectively extends the wire length over a small area and hence greatly increases the value of LL. According to the above discussion, suitably increasing the value of LL can broaden the bandwidth of the antenna under ZOR and FOR mode operation while achieving miniaturization. In addition, we note that the currents in adjacent parallel wires of the Hilbert curve are opposite in direction and may interfere with each other when insufficiently separated. Therefore, taking the effects of manufacturing precision into consideration, we adopted a second-order Hilbert curve with a wire width of w6 = 0.3 mm and an adjacent wire separation of w7 = 0.4 mm. We also note that according to the above discussion, suitably decreasing the value of CR can broaden the bandwidth of the antenna under ZOR and FOR mode operation while achieving miniaturization, and the value of CR of the CPW structure is inversely proportional to w1. Therefore, taking the effects of manufacturing precision into consideration, we adopted a value w1 = 3.0 mm. Compared with a CRLH transmission line structure realized by a conventional microstrip structure, the advantage of using a CPW structure is that it avoids the large plate capacitance between the upper microstrip and the lower metallic grounded plate, although the plate capacitance introduced here cannot be effectively reduced due to the large area of the metallic plate.


### 3.2. Simulation and Fabrication of the Antenna Design

A structural model of the proposed antenna design was built and simulated using Ansoft HFSS simulation software to validate the proposed structure and its theoretical analysis and to further investigate its structural characteristics. The parameters were set asw1 = 3.0 mm, w2 = 4.6 mm, w3 = 39 mm, w4 = 17.5 mm, w5 = 0.45 mm, w6 = 0.3 mm, w7 = 0.4 mm, w8 = 0.36 mm, w9 = 0.36 mm, and l = 24.5 mm. After initially employing the parameter-scanning function of the simulation software to optimize the design, the value of w1, related to CR, was adjusted to 5.7 mm, and w6 and w7, related to LL, were adjusted to 0.3 mm and 0.4 mm, respectively. This process is relatively simple, so it is not described here for the sake of brevity. Finally, in light of engineering requirements, the operating frequency of the antenna was made to cover the WiMax standard (3.5 GHz), and the values of w2 and l were adjusted to achieve impedance matching.A prototype antenna was fabricated based on the optimized antenna design parameters to further validate the proposed design. The dielectric board used for the CPW was a polytetrafluoroethylene glass scrim board (F4B-2) with a relative dielectric constant of 2.65 and a thickness of 1 mm. Figure5 presents an image of the prototype antenna. The overall dimensions of the antenna for the ZOR mode are 0.24λ0 × 0.15λ0 × 0.006λ0. The electrical dimensions of the SCRLH transmission line unit structure are even smaller, indicating a high degree of miniaturization.Figure 5
Prototype ZOR mode and FOR mode dual-frequency wideband antenna based on a 3-unit SCRLH transmission line with Hilbert curve loading.Figure6 presents the simulation and experimental results of the return loss for the proposed ZOR and FOR mode dual-frequency wideband antenna. The figure shows that the proposed antenna provided center frequencies of f0 = 1.865 GHz and f1 = 2.835 GHz, and that the −10 dB return loss bandwidths for the ZOR and FOR modes were, respectively, 187 MHz (from 1.773 GHz to 1.96 GHz) and 368 MHz (from 3.002 GHz to 3.37 GHz). The corresponding relative bandwidths were, respectively, 10.1% and 11.5%. In addition, we note that the experimental results were in excellent agreement with the simulation results. The designed antenna can therefore be applied to multiple wireless communication systems simultaneously.Figure 6
Simulation and experimental results of the return loss for the proposed ZOR and FOR dual-frequency wideband antenna.Figure7 presents the simulation and experimental results of the directivity patterns of the antenna gain for f0 (ZOR mode) and f1 (FOR mode) center frequencies under copolarization (Co-pol) and cross-polarization (X-pol) conditions in the yoz and xoy planes. As shown in Figures 7(a) and 7(c), the radiation directivity pattern of the antenna in the yoz plane is relatively uniform under Co-pol conditions, and omnidirectional radiation is realized over the entire operating frequency band. Furthermore, as shown in Figures 7(b) and 7(d), the directivity patterns under Co-pol conditions in the xoy plane present standard figure, eight shapes with a horizontal deviation less than 15° over the entire operating frequency band, which are similar to the radiation directivity pattern of a dipole antenna. We also note that the cross-polarization of the antenna is also small. The experimental and simulated peak gains in the yoz and xoy planes are essentially equivalent at both f0 and f1. The experimental peak gains at f0 and f1 are 1.54 dB and 1.71 dB, respectively, which are very close to the corresponding simulated peak gains of 1.86 dB and 1.97 dB. The radiation efficiency of the antenna is also very good, and the efficiencies for the ZOR and FOR modes are 79.3% and 74.2%, respectively. In contrast, with a conventional half-wave resonant microstrip patch antenna, where the phase lag can cause excessive current concentration and high conductor loss, the conductor loss of the proposed antenna operating in the ZOR mode due to the metal patch is small because the antenna has a uniform amplitude and in-phase electric field distribution. The antenna therefore increases the radiation efficiency in the ZOR mode and alleviates to some extent the gain and radiation efficiency reduction due to miniaturization.Figure 7
Simulated and measured directivity patterns of the ZOR mode (center frequencyf0 = 1.865 GHz) and FOR mode (center frequency f1 = 2.835 GHz) dual-frequency wideband antenna. In the yoz plane (H-plane): (a) f0; (c) f1. In the xoy plane (E-plane): (b) f0; (d) f1.
(a)
(b)
(c)
(d)The performance parameters of the wideband dual-frequency antenna designed in this paper are summarized in Table1, which includes the operating frequency, bandwidth, peak gain, and radiation efficiency. F.O.M. is the ESA figure-of-merit (=G_ant/(VSWR × L)). L = D/lambda and D is the maximum dimension of the antenna, and lambda is the wavelength for the lowest frequency, and VSWR is the 10 dB bandwidth. To further illustrate the performance advantages of the proposed antenna, Table 1 includes the reported performance parameters of previously proposed antenna designs based on the CRLH transmission line structure. The results indicate that the antenna designed in this paper offers considerable advantages in terms of expanded bandwidth and higher gain and efficiency.Table 1
Comparison of the performance parameters of the antenna designed in this paper with those of other antenna designs presented in the literature.
Comparison category
This work
Narbudowicz et al. [4]
Jang et al. [11]
Lai et al. [12]
Electronic size
0.24λ0 × 0.15λ0 × 0.006λ0
0.28λ0 × 0.28λ0 × 0.006λ0
0.145λ0 × 0.172λ0 × 0.011λ0
0.33λ0 × 0.33λ0 × 0.018λ0
Transmission line
APW SCRLH
CRLH
CRLH
CRLH
With/without through holes
Without
With
Without
With
Mode of operation
ZOR
FOR
ZOR
FOR
ZOR
ZOR
Operating frequency (GHz)
1.867
2.835
1.329
2.756
2.03
3.38
Relative bandwidth (%)
10.1
11.5
1.35
2.02
6.8
0.1
Peak gain (dB)
1.86
1.97
−0.7
−0.2
1.35
0.87
F.O.M.
0.0409
0.0129
−0.16
−0.007
0.058
1.524
Radiation efficiency (%)
81.3
74.2
Not given
62
70


## 3.1. Structural Characteristics and Analysis

To realize the ZOR mode bandwidth broadening principle described above and to match the special case of FOR mode operation with three units, we designed a new CPW structure based on an SCRLH transmission line with Hilbert curve loading. As shown in Figure3, the CPW is a cascaded structure composed of three SCRLH transmission line units with the same size parameters. The left and right sides are grounded metal plates, and the middle is a radiating metal plate connected to the grounded plate on the right side with metal wires arranged in the shape of a second-order Hilbert curve, which forms the left-handed shunt inductances LL of the 3-unit SCRLH transmission line. The width of the wires and the distances between the wires are denoted by w6 and w7, respectively. In addition, when current is flowing on the middle plate, it inevitably introduces a right-handed inductance LR. Furthermore, the gap of width w1 between the grounded plate on the left side and the middle plate results in a distributed right-handed capacitance CR whose magnitude is inversely proportional to the value of w1. The other physical dimensions are clearly denoted in the figure.Figure 3
Dual-frequency wideband CPW antenna design based on a 3-unit SCRLH transmission line with Hilbert curve loading.The Hilbert curve proposed by Hilbert in 1891 is a continuous fractal space-filling curve that fills a two-dimensional plane with one-dimensional line segments. According to its fractal nature, it is characterized by simplicity, self-similarity, and self-avoidance. The formation process is illustrated in Figure4. The zeroth-order Hilbert curve (n = 0) is a line bent into a U-shape, and higher-order curves maintain the same exterior dimensions as the zeroth-order curve. Therefore, the first-order curve (n = 1) consists of four U-shaped curves of equivalent exterior dimensions, and their connecting lines are shown as dashed lines in the figure. The second-order curve (n = 2) consists of four first-order curves, and their connecting lines are again shown as dashed lines in the figure. This procedure can be repeated indefinitely.Figure 4
Hilbert curve formation process.
(a)
(b)
(c)The use of Hilbert curves has been widely reported in microwave antenna applications [10]. Because the magnitude of the inductance of a metal wire is directly proportional to its length and inversely proportional to its width, the use of Hilbert curves effectively extends the wire length over a small area and hence greatly increases the value of LL. According to the above discussion, suitably increasing the value of LL can broaden the bandwidth of the antenna under ZOR and FOR mode operation while achieving miniaturization. In addition, we note that the currents in adjacent parallel wires of the Hilbert curve are opposite in direction and may interfere with each other when insufficiently separated. Therefore, taking the effects of manufacturing precision into consideration, we adopted a second-order Hilbert curve with a wire width of w6 = 0.3 mm and an adjacent wire separation of w7 = 0.4 mm. We also note that according to the above discussion, suitably decreasing the value of CR can broaden the bandwidth of the antenna under ZOR and FOR mode operation while achieving miniaturization, and the value of CR of the CPW structure is inversely proportional to w1. Therefore, taking the effects of manufacturing precision into consideration, we adopted a value w1 = 3.0 mm. Compared with a CRLH transmission line structure realized by a conventional microstrip structure, the advantage of using a CPW structure is that it avoids the large plate capacitance between the upper microstrip and the lower metallic grounded plate, although the plate capacitance introduced here cannot be effectively reduced due to the large area of the metallic plate.


## 3.2. Simulation and Fabrication of the Antenna Design

A structural model of the proposed antenna design was built and simulated using Ansoft HFSS simulation software to validate the proposed structure and its theoretical analysis and to further investigate its structural characteristics. The parameters were set asw1 = 3.0 mm, w2 = 4.6 mm, w3 = 39 mm, w4 = 17.5 mm, w5 = 0.45 mm, w6 = 0.3 mm, w7 = 0.4 mm, w8 = 0.36 mm, w9 = 0.36 mm, and l = 24.5 mm. After initially employing the parameter-scanning function of the simulation software to optimize the design, the value of w1, related to CR, was adjusted to 5.7 mm, and w6 and w7, related to LL, were adjusted to 0.3 mm and 0.4 mm, respectively. This process is relatively simple, so it is not described here for the sake of brevity. Finally, in light of engineering requirements, the operating frequency of the antenna was made to cover the WiMax standard (3.5 GHz), and the values of w2 and l were adjusted to achieve impedance matching.A prototype antenna was fabricated based on the optimized antenna design parameters to further validate the proposed design. The dielectric board used for the CPW was a polytetrafluoroethylene glass scrim board (F4B-2) with a relative dielectric constant of 2.65 and a thickness of 1 mm. Figure5 presents an image of the prototype antenna. The overall dimensions of the antenna for the ZOR mode are 0.24λ0 × 0.15λ0 × 0.006λ0. The electrical dimensions of the SCRLH transmission line unit structure are even smaller, indicating a high degree of miniaturization.Figure 5
Prototype ZOR mode and FOR mode dual-frequency wideband antenna based on a 3-unit SCRLH transmission line with Hilbert curve loading.Figure6 presents the simulation and experimental results of the return loss for the proposed ZOR and FOR mode dual-frequency wideband antenna. The figure shows that the proposed antenna provided center frequencies of f0 = 1.865 GHz and f1 = 2.835 GHz, and that the −10 dB return loss bandwidths for the ZOR and FOR modes were, respectively, 187 MHz (from 1.773 GHz to 1.96 GHz) and 368 MHz (from 3.002 GHz to 3.37 GHz). The corresponding relative bandwidths were, respectively, 10.1% and 11.5%. In addition, we note that the experimental results were in excellent agreement with the simulation results. The designed antenna can therefore be applied to multiple wireless communication systems simultaneously.Figure 6
Simulation and experimental results of the return loss for the proposed ZOR and FOR dual-frequency wideband antenna.Figure7 presents the simulation and experimental results of the directivity patterns of the antenna gain for f0 (ZOR mode) and f1 (FOR mode) center frequencies under copolarization (Co-pol) and cross-polarization (X-pol) conditions in the yoz and xoy planes. As shown in Figures 7(a) and 7(c), the radiation directivity pattern of the antenna in the yoz plane is relatively uniform under Co-pol conditions, and omnidirectional radiation is realized over the entire operating frequency band. Furthermore, as shown in Figures 7(b) and 7(d), the directivity patterns under Co-pol conditions in the xoy plane present standard figure, eight shapes with a horizontal deviation less than 15° over the entire operating frequency band, which are similar to the radiation directivity pattern of a dipole antenna. We also note that the cross-polarization of the antenna is also small. The experimental and simulated peak gains in the yoz and xoy planes are essentially equivalent at both f0 and f1. The experimental peak gains at f0 and f1 are 1.54 dB and 1.71 dB, respectively, which are very close to the corresponding simulated peak gains of 1.86 dB and 1.97 dB. The radiation efficiency of the antenna is also very good, and the efficiencies for the ZOR and FOR modes are 79.3% and 74.2%, respectively. In contrast, with a conventional half-wave resonant microstrip patch antenna, where the phase lag can cause excessive current concentration and high conductor loss, the conductor loss of the proposed antenna operating in the ZOR mode due to the metal patch is small because the antenna has a uniform amplitude and in-phase electric field distribution. The antenna therefore increases the radiation efficiency in the ZOR mode and alleviates to some extent the gain and radiation efficiency reduction due to miniaturization.Figure 7
Simulated and measured directivity patterns of the ZOR mode (center frequencyf0 = 1.865 GHz) and FOR mode (center frequency f1 = 2.835 GHz) dual-frequency wideband antenna. In the yoz plane (H-plane): (a) f0; (c) f1. In the xoy plane (E-plane): (b) f0; (d) f1.
(a)
(b)
(c)
(d)The performance parameters of the wideband dual-frequency antenna designed in this paper are summarized in Table1, which includes the operating frequency, bandwidth, peak gain, and radiation efficiency. F.O.M. is the ESA figure-of-merit (=G_ant/(VSWR × L)). L = D/lambda and D is the maximum dimension of the antenna, and lambda is the wavelength for the lowest frequency, and VSWR is the 10 dB bandwidth. To further illustrate the performance advantages of the proposed antenna, Table 1 includes the reported performance parameters of previously proposed antenna designs based on the CRLH transmission line structure. The results indicate that the antenna designed in this paper offers considerable advantages in terms of expanded bandwidth and higher gain and efficiency.Table 1
Comparison of the performance parameters of the antenna designed in this paper with those of other antenna designs presented in the literature.
Comparison category
This work
Narbudowicz et al. [4]
Jang et al. [11]
Lai et al. [12]
Electronic size
0.24λ0 × 0.15λ0 × 0.006λ0
0.28λ0 × 0.28λ0 × 0.006λ0
0.145λ0 × 0.172λ0 × 0.011λ0
0.33λ0 × 0.33λ0 × 0.018λ0
Transmission line
APW SCRLH
CRLH
CRLH
CRLH
With/without through holes
Without
With
Without
With
Mode of operation
ZOR
FOR
ZOR
FOR
ZOR
ZOR
Operating frequency (GHz)
1.867
2.835
1.329
2.756
2.03
3.38
Relative bandwidth (%)
10.1
11.5
1.35
2.02
6.8
0.1
Peak gain (dB)
1.86
1.97
−0.7
−0.2
1.35
0.87
F.O.M.
0.0409
0.0129
−0.16
−0.007
0.058
1.524
Radiation efficiency (%)
81.3
74.2
Not given
62
70


## 4. Conclusions

This paper proposed a new wideband dual-frequency CPW antenna design based on an SCRLH transmission line structure with Hilbert curve loading. The multifrequency characteristics of the SCRLH transmission line structure were evaluated theoretically, and the antenna parameters promoting bandwidth broadening under ZOR and FOR mode operation were evaluated. The analysis revealed that the bandwidth broadening of the ZOR and FOR modes is independent of the antenna length, and the SCRLH transmission line structure therefore facilitates wideband operation under miniaturization. Finally, the proposed dual-frequency ZOR and FOR mode antenna design was validated by the excellent agreement between the simulation results and experimental results for a highly compact prototype antenna. The bandwidth, gain, and efficiency of the antenna were demonstrated to be superior to those obtained by antennas based on the CRLH transmission line structure.



---

*Source: 7380621-2019-12-27.xml*