A Flexible Multi-Band Antenna with a Spider Web-like Structure for 4G/5G/GPS/WIMAX/WLAN Applications

Abstract

In this paper, based on bionics, a flexible multi-band antenna is designed to mimic the structure of a spider’s web, which supports various communication standards such as 4G, 5G, and GPS. The antenna lays out multiple loop branches in a limited space to achieve wideband operations from 1.31 GHz to 2 GHz (42.4%), from 3.4 GHz to 4 GHz (16.2%), and from 5.1 GHz to 5.78 GHz (12.5%). The antenna selects 40 × 50 × 0.1 mm³ polyimide as the dielectric substrate and trapezoidal coplanar waveguide feed. A simulation and experimental analyses demonstrate that the antenna exhibits consistent performance when subjected to different bending scenarios. The design scheme utilizing a flexible dielectric substrate streamlines the integration process, offering a promising avenue for deployment in smart wireless devices. The results of the consistent tests and simulations demonstrate that the device meets the requisite standards for wireless communication.

1. Introduction

With the rapid advances in mobile communications technology, the demand for miniaturized, flexible, and multi-band antennas is becoming more and more urgent. A flexible antenna, as a new type of antenna structure that is bendable, stretchable, light, and thin, has a broad application prospect in wireless communication systems [1].

Flexible antennas have been developing rapidly in recent years due to their lightweight and comfortable properties, which can be well conformed to devices. PDMS antennas can be applied by some researchers and scholars for the design of flexible antennas due to their soft and transparent properties. Researchers proposed a circularly polarized antenna based on flexible materials such as PDMS and silver nanowires [2], and the results show that the antenna has very small frequency deviation under bending. In addition, PI materials are promising for flexible antenna design. A study proposed a broadband flower antenna based on coplanar waveguide feed (CPW) [3] in which the radiating unit of the antenna is supported by a PI substrate. The literature [4] compared the antenna with others and verified that the antenna still maintains good radiation performance at different bending angles.

Bionic design is an innovative approach that draws on the form and function of natural organisms, and the term ’bionic antenna’ is used to describe the practice of applying the principles of bionics in the field of antenna design [5]. Researchers have also proposed some bionic antennas [6]. A coplanar waveguide (CPW) antenna using the shape of a daisy as a radiator has been designed and presented in the literature [7]. In addition, there are antennas that mimic the morphology of ginkgo biloba to achieve broadband characteristics [8], and multi-band antennas have been designed to mimic the structure of banana leaf [9].

Multi-band [10] antennas are widely used in radio communication [11], measurement and control, electronic countermeasures, and other fields. Researchers have found that a monopole plus resonant branch [12] or a monopole with a slotted radiator [13] can realize multi-band transmission. A miniaturized coplanar waveguide-fed slotted monopole antenna was proposed in [14], and it can operate in the 3.4 GHz, 5.5 GHz, and 8.2 GHz bands. By adding a semicircular arc branch to a circular monopole, the antenna can be made to expand from a single band to a dual band [15]. The coplanar waveguide feeding method effectively achieves bandwidth expansion [16].

In this paper, a three-band spider web antenna designed on the basis of bionics is proposed and discussed. The antenna is fed by a coplanar waveguide, achieving the characteristics of having multiple bands and miniaturization. After a simulation analysis and experimental verification, the antenna exhibits three efficient operating frequency bands covering the frequency ranges of 1.31–2 GHz (42.4%), 3.4–4 GHz (16.2%), and 5.1–5.78 GHz (12.5%), which are suitable for a wide range of communication applications such as GPS, 4G, 5G, WIMAX, and WLAN.

2. Antenna Structure and Process

The design of the antenna comes from the polygonal structure of a spider’s web, which uses a polygonal structure to make the best use of space. For the antenna, the hexagonal rings and hexagonal patches on both sides can evenly distribute the electric field energy, improve space utilization, increase the electrical length, and realize miniaturization, and its symmetry converges the phase difference between the radiating units, which produces a more concentrated radiation direction, helping to increase the signal strength in the desired direction and the combination of multiple hexagonal rings to realize multi-banding. We use ANSYS Electronics Desktop (HFSS) (Version 2021 R1) software for the original design of the antenna model based on the theory of coplanar waveguide antenna. Figure 1 shows the design iteration process, and the S11 simulation curves of the iterative antenna are shown in Figure 2. S11 refers to the reflection coefficient (Reflection Coefficient), also known as the scattering parameter (Scattering Parameter S11) of the input port. The proposed antenna with a trapezoidal grounding patch is printed on the polyimide substrate and fed by a 50 Ω microstrip feed line.

Figure 1a depicts a monopole antenna comprising a hexagonal radiator patch fed by a rectangular coplanar waveguide. This antenna is notable for its lack of fractals or slots. As can be seen the S11 simulation in Figure 2, the antenna has only one band. In order to reduce the frequency point to a level that meets the requisite specifications for the frequency band, the radiator is modified to a ring structure, as illustrated in Figure 1b. The ring structure extends the circuit path, the operating frequency will be reduced, and the simulation results show that the frequency band moves to the left. To realize multi-frequency bands, the second branch and resonant patch are added, and the transformation of the rectangular coplanar waveguide structure into a trapezoidal coplanar waveguide structure is illustrated in Figure 1c,d, which demonstrate the resulting changes to the antenna’s structure. The S11 simulation shown in Figure 2 indicates that the final model generates three frequency bands.

The research objective is to optimize the model parameters, such as the position of each ring and the size of the resonant patch, and analyze the results using HFSS software to produce the other desired resonant frequencies for the desired multi-band design.

The length of L3 ranges from a 25.6 mm scan to 26.4 mm in S11, as shown in Figure 3. In the first band section, the bandwidths corresponding to different L3 lengths do not differ much, but the S11 value at 26 mm is the smallest and corresponds to the desired band; as the size increases, the frequency points of the second and third frequency bands are not affected very much, and the third band is slightly shifted to the right. All things considered, L3 is 26 mm.

The reflection coefficients for the length range of L4, spanning from 33.1 mm to 33.9 mm, are illustrated in Figure 4. It is evident that as the length of L4 increases, the frequency point of L4 in the first band is situated at 1.61 GHz when it reaches 33.5 mm. Conversely, the resonant frequency points of the second and third frequency bands demonstrate a tendency to shift to the left, yet they still fluctuate approximately around 3.5 GHz and 5.5 GHz, respectively. In light of the aforementioned considerations, the diameter of L4 is 33.5 mm.

As illustrated in Figure 5, the S11 variation in the L2 length ranges from 21.6 mm to 22.4 mm. Upon examination of this figure, it becomes evident that the increase in length is accompanied by a rightward shift in the center frequency point of the first band. The frequency points below −10 dB are 1.4 GHz, 1.5 GHz, 1.6 GHz, and 1.7 GHz, respectively. The center frequency points of the second and third bands shift slightly to the left as the length of L2 increases, with the center frequencies of both being around 3.5 GHz and 5.5 GHz. Overall, an L2 of 22 mm is chosen as an appropriate location for the small hexagonal ring branch.

The layout of the antenna is shown in Figure 6, and

Table 1. Antenna model parameter dimensions.

Dimensions Parameters	Unit (mm)	Dimensions Parameters	Unit (mm)
W	40	S1	0.5
L	50	S2	0.4
L1	23	S3	0.6
L2	7	a	7.3
L3	9	b	14.3
L4	18.5	h	10

details its dimensions. A polyimide dielectric substrate with a thickness of 0.1 mm was selected for the antenna, with a dielectric constant of 3.5 and a loss tangent of 0.008. As for the radiator, it consists of nested hexagonal loops and resonant patches. The nesting hexagonal loop is inspired by the common spider web pattern in nature and is optimized by the introduction of a loop branching structure to achieve the tri-band of the antenna.

3. Results and Discussion

The ANSYS Electronics Desktop (HFSS) (Version 2021 R1) software package was used for the simulation. HFSS software adopts the adaptive mesh dissection technique to automatically generate accurate and effective meshes according to the error criterion set by the user to complete the discretization of the analyzed object; we used the delta S of 0.02 as a judgment criterion for the convergence error.

3.1. Simulation Results

Figure 7 illustrates the simulated reflection coefficient curves of the antenna with resonant frequencies of 1.45 GHz, 3.52 GHz, and 5.54 GHz; S11 values of −30.16 dB, −33.24 dB, and −19.92 dB; and a bandwidth of 1. The bandwidths are in the ranges of 1.29–1.70 GHz, 3.34–3.66 GHz, and 5.05–5.92 GHz, with relative bandwidths of 27%, 9%, and 16%, respectively. The frequency bands covered by the antenna are presented in

Table 2. Spider web-like tri-band flexible antenna coverage of application bands.

No.	Bandwidth (Simulation)	Application Bands Covered
1	1.29–1.70 GHz (27%)	4G LTE (1.447–1.467 GHz) GPS L1 (1.574–1.576 GHz) BeiDou BD2 B1(1.559–1.563 GHz)
2	3.34–3.66 GHz (9%)	TDD (3.4–3.6 GHz) WIMAX (3.3–3.8 GHz) 5G n77 (3.3–4.1 GHz) 5G n88 (3.3–3.8 GHz)
3	5.05–5.92 GHz (16%)	WLAN (802.11 a/n: 5.15–5.35 GHz, 5.725–5.825 GHz)

.

The antenna was modeled in HFSS software to conform to the cylinder along both axes, the angle, $\theta$, of the co-form; the cylindrical radius, $R$; and the arc length, $l$, and they are related as follows:

$$l={\displaystyle \frac{\theta \times R\times \pi }{180°}}$$

(1)

The arc length $l$ is 40 mm when bent along the X-axis and 50 mm when bent along the Y-axis. Taking the Y-axial bending of $\theta$ = 45° as an example, the arc length is $l$ = 50 mm, which can be substituted to obtain $R$ ≈ 64 mm.

The resulting bending morphology when this arc length corresponds to angles of 45°, 60°, and 90° is presented in Figure 8 and Figure 9. The S11 values under bending conditions along different angles are shown in Figure 10 and Figure 11, where the antenna maintains three bands after bending. The initial frequency band of an antenna bent along the X-axis is subject to a variable degree of shift in accordance with the extent of the bending, the frequency point of the second band is diverted to the left by about 0.1 GHz, and the frequency band is changed from 3.34–3.66 GHz to 3.24–3.66 GHz. The antenna is obviously shifted in the third frequency band, and the center frequency point is transferred to the left from 5.54 GHz to 5.2 GHz.

After bending along the short side, as shown in S11 in Figure 11, the first and third frequency bands of the antenna are shifted from 5.54 GHz to 5.2 GHz; in comparison with the theoretical plane S11, the first and second bands of the antenna are shifted to the right with an increasing bandwidth, which may be due to a change in the actual length and effective electrical length when the antenna is bent, but the bending of S11 still covers the effective frequency point, and there is no drastic change in the performance caused by bending. A comprehensive analysis shows that the reflection coefficient of the antenna will not lose its original frequency point due to the bending of the antenna, indicating that flexible antennas can adapt to different directions of bending conformal to a certain extent.

Figure 12 presents the surface current dispersion of the antenna at 1.45 GHz, 3.52 GHz, and 5.54 GHz frequencies, and its radiation vectors are characterized. When observing this figure, operating at 1.45 GHz, it can be seen that its main current distribution is more uniform and concentrated in the first-order loop region. At 3.52 GHz, the current not only has a significant distribution in the first-order loop, but also extends to the second-order loop, and the current strength in the minor loop is enhanced. As for 5.54 GHz, the distribution pattern of the antenna current changes and shows a uniform distribution in both the outer loop and the minor loop.

The calculation can be performed to determine the relationship between effective electrical length and frequency. The electrical length is denoted as $L$, and the central frequency of its operation is labeled as $f$. In addition, the free-space speed of light c (3 × 10⁸ m/s) is introduced, as well as the dielectric constant ${\epsilon }_r$ of the dielectric substrate.

$$f={\displaystyle \frac{c}{2\left(L+2∆\mathrm{L}\right)\sqrt{{\epsilon }_{eff}}}}$$

(2)

$${\epsilon }_{eff}={\displaystyle \frac{{\epsilon }_r+1}{2}}+{\displaystyle \frac{{\epsilon }_r-1}{2}}\left(1+12{\displaystyle \frac{h}{W}}\right)$$

(3)

$$∆L={\displaystyle \frac{0.412h\left({\epsilon }_{eff}+0.3\right)\left(\frac{W}{h}+0.258\right)}{\left({\epsilon }_{eff}-0.258\right)\left(\frac{W}{h}+0.8\right)}}$$

(4)

$$L_a=L4\times 2+L4\times 0.5+L2\approx 53.25\mathrm{mm}$$

(5)

$$L_b=L2\times 0.5+L4\times {\displaystyle \frac{1}{3}}+L4\times {\displaystyle \frac{1}{3}}\approx 15.11\mathrm{mm}$$

(6)

where $f$ represents the center frequency points, $L_a$ and $L_b$ represent the electrical length of the corresponding frequency point, h and W are the thickness of the dielectric substrate and the width of the hexagon, respectively, and $∆L$ is the change in electrical length due to fringing fields.

The surface current distribution diagram shows that the frequency point of the antenna has good frequency controllability, and combined with the S11 diagram when bending, antenna branching more easily directly changes the main frequency point of the antenna, while other resonance points are more difficult to realize. The frequency shift in the high-frequency band may be due to the influence of the resonator sheet coupled with the influence of the outer ring resulting in a shift in the high-frequency band during bending.

Figure 13 and Figure 14 show the simulated radiation direction maps and polarization in the E-plane and H-plane. From the figure, it can be seen that the antenna has good radiation omnidirectional performance at the 1.45 GHz, 3.52 GHz, and 5.54 GHz frequency points. In the E/H normalized radiation direction plots, the solid line represents main polarization and the dashed line represents cross polarization, where the radial coordinates represent the gain and the angular coordinates represent the direction, the angular coordinates of the E-plane (the plane where the electric field vector is located) denote the azimuthal angle, φ, and the angular coordinates of the H-plane (the plane where the magnetic field vector is located) denote the polar angle, θ. The peak gains obtained at 1.45 GHz, 3.52 GHz, and 5.54 GHz are −2.1 dB, 3.81 dB, and 4.08 dB, respectively. Polarization is a voltage characteristic, cross-polarization gradually increases with increasing frequency, and isolation decreases with increasing frequency, but the maximum isolation is less than 20 dB in all cases.

To evaluate the performance of wireless devices when used close to the human body and to avoid causing radiation damage to the human body, the SAR value of a human arm model was simulated with the antenna device close to human skin and radiation directly affecting human tissue. Figure 15 shows the specific absorption rate (SAR) values of the human arm model at 1.45 GHz, 3.52 GHz, and 5.54 GHz. The antenna is 0.2503 W/kg at 1.45 GHz, 0.3859 W/kg at 3.52 GHz, and 0.0823 W/kg at 5.54 GHz, which meets the international standard of human SAR < 1.6 W/kg.

3.2. Measurement Results

Figure 16a,b show the front and back of the antenna model, respectively, and Figure 16c shows the prototype antenna placed in the antenna test system for testing. The simulated and measured S11 are shown in Figure 17.

The reflection coefficients of the antennas that were both simulated and measured are displayed in Figure 17. The simulated −10 dB operating bands are 1.29~1.70 GHz, 3.34~3.66 GHz, and 5.05 ~5.92 GHz, and the three center frequency points of the antenna are 1.45 GHz, 3.52 GHz, and 5.54 GHz, respectively. The actual measured antenna’s operating bands are 1.31~2 GHz, 3.4~4 GHz, and 5.1~5.78 GHz, and the three frequency points are 1.53 GHz, 3.61 GHz, and 5.36 GHz, with relative bandwidths of 42.4%, 16.2%, and 12.5%, respectively. The trend of the measured S11 is basically the same as that of the simulated S11 curves, but the frequency bands are shifted to the left to a certain extent, which is due to the complexity of the electromagnetic environment during the testing process, as well as the errors in the antenna prototype in the manufacturing process.

The antenna is observed to exhibit co-form bending in both directions. The S11 test results obtained on a 40 mm diameter foam cylinder are presented in Figure 18, where the measured S11 after bending is compared with that of the planar antenna. The test results show that after bending along the Y-axis, there is no significant change in the bandwidths and the S11 values of the first and second bands, and the third band’s S11 value decreases, but the bandwidth still covers the effective frequency band, and the original frequency points are not lost. When bending in the other direction, the center frequencies of the first and second bands are shifted to the right, accompanied by a slight increase in bandwidth and S11 values, and the third band is shifted more to the right but still covers the effective frequency points. Overall, the measured and simulated S11 trends are the same, although the performance deteriorates to varying degrees during bending, and the three available frequency bands are still maintained.

Figure 19 shows the S11 values for a test conducted on a human arm. It can be seen that compared with planar antennas, the S11 value of antennas that fit the human body changed to varying degrees. The S11 value of the initial band frequency point fluctuated between −20.25 dB and −23.94 dB, while the S11 value of the subsequent band frequency point exhibited a range of −27.06 dB to −13.29 dB. The S11 value of the third frequency point changed from −15.05 dB to −23.07 dB, and all three frequency bands experienced varying degrees of offset but ultimately still covered the effective available frequency bands. The alteration in the S11 value may be attributed to the coupling effect between the antenna and the human body, which can result in a modification of the input impedance and the surrounding electromagnetic field.

The 3D radiation direction plots and the cross-polarization of the E-/H-planes at the center frequency points of 1.53 GHz, 3.61 GHz, and 5.36 GHz are shown in Figure 20, Figure 21 and Figure 22. As demonstrated in the 3D radiation direction plot, the antenna demonstrates omnidirectional radiation capability at all three frequency points, with the radiation strength increasing with increasing frequency. Polarization is defined as the direction in which the electric field vector vibrates, and cross-polarization is indicative of the voltage characteristics. As demonstrated by the E-/H-plane-normalized directional plot, the gain values at the three available band frequencies are 2.46 dBi, 2.9 dBi, and 3.22 dBi, respectively.

Around the 1.5 GHz frequency point, the antenna exhibits omnidirectional radiation characteristics, which makes the radiation behavior of the antenna more balanced at different angles, which is beneficial for improving the signal transmission efficiency and coverage range. As the frequency deviates from the center frequency point, the cross-polarization characteristics of the antenna radiation pattern gradually become apparent. The cross-polarization increases with frequency in the two frequency bands where 3.5 GHz and 5.5 GHz are the central frequency points. The existence of cross-polarization may cause a decrease in the radiation performance in certain directions, but it also improves adaptability at different frequencies.

Table 3. Comparison of related works and this study.

Ref.	Dimensions (mm3)	Operating Bands (GHz)	Substrate	Gain	Flexible	FBW (%)
[17]	20× 28 × 0.025	3.43–6.29	Polyamide	3.7	Yes	58.84%
[7]	41 × 29 × 1.6	1.51–2.31 3.32–3.8 4.59–5.2	FR4	2.41–3.91	No	64.7% 33.9% 13.4%
[6]	50 × 40 × 1.6	0.79–3.18 3.29–3.98 4.98–7.62	FR4	3.45	No	117.1% 18.9% 41.9%
[18]	60 × 55 × 0.23	1.6–2	Paper	5.3	Yes	——
[19]	70 × 70 × 1.5	1.3–1.8	FR4	——	No	32.3%
[12]	40 × 40 × 1.52	3.18–11.50	Taconic RF-30	——	——	——
[20]	40 × 28 × 0.27	2.36–2.48	Photopaper	1.61	Yes	86%
[21]	40 × 30 × 0.27	2.3–5.3	Photopaper	1.91–3.48	Yes	84.35%
This work	40 × 50 × 0.1	1.29–1.75 3.11–3.65 5.09–5.87	Polyimide	3.3	Yes	27% 9% 16%

presents a comparative analysis of this study with several previous studies.

4. Conclusions

This paper presents the design of a new compact tri-band antenna, which employs a spider web-like structure for the radiator. The dimensions of the antenna are 40 × 50 × 0.1 mm³, and the radiator consists of a simple hexagonal ring resonator. It exhibits three frequency resonance performances at 1.53 GHz/3.61 GHz/5.36 GHz, with main operating frequency bands of 1.29–1.75 GHz, 3.11–3.65 GHz, and 5.09–5.87 GHz, covering GPS, 4G, 5G, and WIMAX frequency bands. The antenna has a small size, a compact structure, and a low specific absorption rate (SAR), and it can still cover available frequency bands under bending conditions, making it easy to integrate and process. Due to the validation of flexible materials, the proposed patch antenna can be conformally designed for wireless devices.