A Flexible Wearable Antenna with Annular Solar Eclipse Structure for ISM/WLAN/WIMAX/Bluetooth Applications

. Tis paper proposes a wearable fexible dual-band antenna that covers the 2.34–2.68GHz and 4.05–5.26GHz frequency bands. Tis antenna employs a novel nested imitation annular solar eclipse structure, where the main radiator is a gradually widening loop, and another loop is coupled inside the radiator. Te antenna, with overall dimensions of 40 ∗ 32 ∗ 0.3mm³, utilizes polyimide as the dielectric material. Te gain, efciency, and cross-polarization of the antenna were tested using a microwave anechoic chamber. Te antenna achieves a maximum gain of 6 dBi and a maximum efciency of 79.6%. We tested the SAR of the antenna at 10mm from the human body, which was signifcantly below the international standard of 2.0W/kg. Te fexible antenna presented in this paper exhibits a broad low-frequency bandwidth, enabling coverage of various communication bands such as ISM, WLAN, WIMAX, and Bluetooth. Te antenna delivers satisfactory simulation and measurement results while meeting the requirements of minimizing radiation exposure to the human body.


Introduction
In recent years, due to the rapid development of society and the continuous innovation of science and technology, traditional fat electronic devices have been difcult to adapt to the current complex and changing environment.Te rapid development of fexible electronic devices is becoming more and more popular.Flexible electronic devices have a certain degree of stretching and bending and can conform to any surface characteristics.In the feld of wireless communication, they are becoming more and more widely used.Te most central component of wireless communication is the antenna used to transmit and receive electromagnetic waves, and every year, many scientists are looking for various new fexible materials to replace conventional materials as the substrate of microstrip antennas in order to break through the antenna with high radiation stability while having large bending.In 2014, Prof. Song et al. [1] designed and fabricated rectangular microstrip antennas using polydimethylsiloxane (PDMS) injected with liquid eutectic gallium indium (EGaIn) as a substrate and measured their center frequency up to 3.4 GHz.Hussain et al. [2] fabricated a fexible wearable antenna by electroplating 4 μm copper (Cu) on polyimide (PI) in 2016, and the antenna was manufactured in an S-shape, and its center frequency was measured to be 2.45 GHz.In 2017, Yan et al. [3] sputtered a layer of metallic Ag with a thickness of 50 nm on PI flm by magnetron sputtering technique, and when the antenna was stretched by 200%, its central frequency still reached 5.6 GHz.It has a series of advantages, such as being fexible, cheap, and reusable [4], so it is suitable to be chosen as the material for the preparation of highly stable fexible antennas.Te combination of monopole antenna and SRR enables the antenna to cover multiple frequency bands [5].Te combination of microstrip gap and SRR plays a significant role in the design of miniaturized antennas for dualband performance [6].Coupling plays a vital role in antenna parameters such as impedance, bandwidth, and resonant frequency [7].
Future industries, including wearable devices, fexible microelectronic products, and fexible integrated circuits, have garnered signifcant attention from society due to their potential for transformative impact and wide-ranging applications.Te demand for fexible antennas and fexible passive devices has experienced a signifcant surge due to the need to develop wireless communication systems that can be seamlessly integrated into fexible materials.Various antenna designs based on diferent fexible materials such as liquid crystal polymers (LCP), polyetherimide (PEI), and polyethylene terephthalate (PET) have been proposed.Tese materials have unique RF properties, such as a low dielectric constant and loss tangent angle.Recently, polyimide has been widely used to make dielectric substrates for fexible devices because of its excellent mechanical and electrical properties.Terefore, in this paper, polyimide is chosen as the dielectric board for the involved antenna.Feasible antenna designs with fexible properties face problems such as excessive design size, low bending degree, and distortion of antenna performance due to bending [8][9][10][11][12][13], so it becomes especially important to study fexible antennas.In [14], a fexible planar monopole antenna with a circular coupling structure is proposed.Te antenna is a toroidal structure based on third-iteration scaling and nesting.Te antenna designed in this paper utilizes a bionic nested structure.Compared to [14], this double circular antenna structure is smaller in size and simpler in structure.Tis idea is derived from the natural phenomenon of an annular eclipse.Tis structure efciently enhances the current path, thereby improving impedance matching and radiation characteristics in the desired frequency bands.
Te performance comparison between the antenna proposed in this paper and the antenna in the reference is shown in Table 1.Te antenna proposed in this paper employs a coplanar waveguide structure to achieve multiband, relatively high gain, and relatively high efciency.
In this paper, a new nested bionic structure is proposed.Te idea is derived from the natural phenomenon of an annular solar eclipse, as shown in Figure 1.A coplanar waveguide antenna is designed based on this unitary mechanism, which efectively increases the current path and improves the impedance matching and radiation characteristics in the target frequency band.Based on the relevant principles of coplanar waveguide antennas, a dual-band fexible antenna is designed in combination with multiband and miniaturization features.Te broadband technology and miniaturization technology of coplanar waveguide antennas are also combined to slot the antenna on the basis of the Archimedean spiral structure [13], and the infuence of parameters such as dielectric material and antenna structure on antenna parameters during the design of the fexible antenna is further explored on the basis of the basic theory and research methods of conventional antenna design.
Te antenna dielectric material is polyimide, which is smaller in size and has fexible bending characteristics compared to traditional microstrip antennas, making it suitable for small smart terminals, especially for devices with more stringent size requirements such as smart watch antennas.Te total size of the dual circular dual-band fexible antenna designed in this paper is 32 × 40 × 0.

Characteristics of the Antenna Structure
When using 3D high-frequency simulation software to build the antenna model, frst, we need to estimate the size of the antenna according to the frequency requirements, and then, according to the calculation results, the parameters will be optimized, and fnally, the antenna model will be selected to meet the design requirements.Te following is a brief introduction to the calculation of some initial dimensions of the microstrip antenna.
When designing the antenna, we frst select the dielectric substrate and need to consider the dielectric constant of the dielectric plate and then combined with the antenna working frequency to estimate the size of the radiation patch.Assuming that the dielectric constant of the dielectric plate is ε r , the operating frequency f of the rectangular microstrip antenna, with the following formula, can be designed to radiate the width of the patch W, that is, where c is the speed of light.Te length of the radiation patch is generally taken to be λ e /2.λ e is the wavelength of the guided wave within the medium, that is, ( After taking into account the edge shortening efect, the actual radiant cell length L should be where ε e is the efective dielectric constant and ∆L is the equivalent radiation gap length, which can be calculated separately using the following equation: Te antenna is printed on a polyimide dielectric plate with a thickness of 0.3 mm, a dielectric substrate size of 32 × 40 mm 2 , a relative permittivity of 3.5, and a dielectric loss rate of 0.008.Te antenna comprises a double circular patch fed using coplanar waveguides and a trapezoidal ground plate on either side of the feed line.Te outer ring of the double ring radiating patch afects the resonant characteristics mainly at the low frequency of 2.489 GHz, while its inner ring radiating patch afects the resonant  2).Te low-frequency bandwidth of the wearable fexible antenna designed in this paper can cover ISM2400 band, WLAN (2402− 2483 MHz), WIMAX (2.3-2.7 GHz), and Bluetooth (2402− 2480 MHz) multiple communication bands; its high-frequency bandwidth can cover the Chinese medium frequency band (4800 MHz-5000 MHz).Te design is based on the theory of loop antenna and coplanar waveguide antenna, using equations ( 1) to (5) to calculate the preliminary rough data, and then, after HFSS simulation parameters optimization, to get the length of the dielectric plate L = 32 mm, width W = 40 mm, H = 0.3 mm, R1 = 13 mm, and R2 = 12 mm.At the same time, based on the advantages of coplanar waveguide compared to microstrip line feed, the antenna adopts the coplanar waveguide feeding method.Due to the broadband characteristics of coplanar waveguides, the antenna exhibits better robustness in frequency range when it is bent.

Simulation Results.
Te simulation was performed using the Ansoft High-Frequency Simulation Software (HFSS) (version 21.0).Te evolution process of the wearable fexible antenna designed in this paper is described as follows: (i) the antenna shown in Figure 3, antenna a, was used as the basis, and after HFSS parameter scan optimization, the resonant frequency point of low frequency 2.489 GHz was obtained by changing the shape of its circular ring, and its structure is shown in Figure 3, antenna b. (ii) In order to increase its high-frequency characteristics, another circular ring was added, as shown in Figure 3, antenna c. (iii) By taking into account the coupling efect between the circular ring and the patch, the internal circular ring is scanned using HFSS to adjust the radius parameter and center position, resulting in the antenna confguration shown in Figure 3, which achieves desirable resonance frequencies of 4.189 GHz and 4.967 GHz at higher frequencies.(iv) At the same time, considering the narrower broadband, the grounding plate is broad banded so that the balance between antenna gain and bandwidth is obtained in Figure 3, antenna e. Trough HFSS simulation analysis and parameter optimization, it  International Journal of Antennas and Propagation can be observed that the electrical parameters of antenna e align with the design requirements.Terefore, this design is considered as the fnal antenna structure, depicted as antenna e in Figure 3. Te return loss of antenna a-antenna e is shown in Figure 4.
Te following is a discussion of the various important parameters afecting the performance of the antenna and to derive the optimal parameters.Te characteristic impedance of a coplanar waveguide antenna without a metal ground plate on the back side is infuenced by the transmission line width L1, ground plate, and thickness, so the infuence of transmission line width L1, ground plate shape, and dielectric plate thickness on the return loss of the antenna is discussed here.
Figure 5 shows the comparison of the results of diferent return loss values from the feed line widths of 0.5 mm, 1 mm, 1.5 mm, and 2 mm by HFSS simulation.From the fgure, it can be found that S11 has signifcant variations in all frequency bands at diferent widths.As the transmission line width increases, the entire frequency band shifts to the right, and with increasing width, the gain in the low-frequency band signifcantly increases.After comparing the diferent return loss values in Figure 5, it can be seen that the frequency band with L1 � 2 mm yields the best performance.
By comparing the diferent return loss values of rectangular and trapezoidal ground plates in HFSS simulation, Figure 6 shows that compared with rectangular ground plates, trapezoidal ground plates have higher gain and bandwidth in the low-frequency band and similar bandwidth but higher gain in the high-frequency band.Terefore, in the antenna design process, the shape and size of the ground plate can be changed appropriately, trying to achieve the best antenna performance with the best gain and bandwidth.
Te bandwidth of the lower band for a dielectric substrate thickness H of 0.3 mm ranges from 2.34 to 2.68 GHz, for a total of 0.34 GHz.Te bandwidth of the high band ranges from 4.05 to 5.26 GHz, for a total of 1.21 GHz.Te bandwidth of the low-frequency band ranges from 2.30 to 2.65 GHz at a thickness H of 0.4 mm, for a total of 0.35 GHz.Te bandwidth of the HF band ranges from 3.94 to 5.18 GHz, for a total of 1.24 GHz.Te bandwidth ranges from 2.27 to 2.63 GHz at 0.5 mm thickness H for a total of 0.36 GHz at low frequencies.Te bandwidth of the HF band ranges from 3.85 to 5.11 GHz, for a total of 1.26 GHz.As shown in the return loss comparison chart with diferent substrate thicknesses in Figure 7, it can be observed that as the substrate thickness increases, the return loss curve of the antenna's high-frequency band (4.05-5.26GHz) shifts to the left, while the displacement range of the low-frequency band (2.34-2.68GHz) is small and negligible; working bandwidth will increase with increase in the thickness of the antenna media substrate.
Te current distribution and current vector direction on the antenna surface are shown in Figures 8(a)-8(c), respectively.As shown in Figure 8(a), at 2.489 GHz, the current is mainly distributed in the left and right sides of the feed line, close to the edge of the feed line grounding plate and the outside of the outer ring.Current through the feed line through the two ends of the outer ring fows to the top of the antenna radiation body, in the inner ring, the current from the feed point farther away from the end of the inner ring on both sides of the fow to the end of the feed point near, and then the grounding plate, the current from the two ends of the fow to the direction of the feed line, the overall direction tends to be parabolic.As can be seen from Figure 8(b), at 4.189 GHz, the current is mainly distributed on the left and right sides of the feeder, near the edge of the grounding plate of the feeder, and on the left side of the outer circular ring.From Figure 8(c), it can be seen that at 4.967 GHz, the current is mainly distributed in the lower half of the feeder, the left and right sides of the inner ring, and the edge of the grounding plate close to the feeder, with a small amount of current distributed on the left side of the outer ring.
Te simulated 3D far-feld radiation pattern and the farfeld normalized E/H surface radiation pattern are shown in Figures 9 and 10.In Figure 10, the red solid line shows the main polarization at Phi � 0 °, and the blue dashed line shows the cross-polarization at Phi � 90 °.Te peak gains are 2.5 dBi, 3.2 dBi, and 5.2 dBi at center frequencies of 2.489 GHz, 4.189 GHz, and 4.967 GHz, respectively.It can be clearly seen that this antenna has good radiation characteristics in the efective frequency band, with good omnidirectionality in the E and H planes and almost no zero point.Tis antenna has a small cross-polarization characteristic.
Te antenna dielectric plate is a fexible material, and the antenna needs to be bent to diferent degrees in the HFSS software.Te antenna is bent at diferent radii in the longitudinal direction to test the return loss value and radiation direction performance under diferent bending degrees.Te structure of the antenna under three diferent bending radii

International Journal of Antennas and Propagation
shows no signifcant resonant frequency shift in the range of 2.34-2.68GHz compared to the unbent return loss.When bent at diferent angles towards the vertical axis, the − 10 dB bandwidth widens in the second frequency band and still meets the communication requirements well.Te diference in return loss between the three diferent bending radii of the antenna is not signifcant.In summary, the antenna can meet its communication requirements well at diferent bending degrees.Te antenna is responsible for several commercial frequency bands used in wearable devices, such as Wi-Fi, WiMAX, and Bluetooth.Terefore, the antenna needs to be simulated for its radiation-specifc absorption rate (SAR) values to the human body and its radiation direction performance when worn.Te antenna will be moved through the axes to the arms of a human model drawn for simulation.Te antenna will be placed 10 mm away from the human body and parallel to the arm, with clothing spaced from the human body, in accordance with an antenna bend radius of 30 mm.Tree central frequency points in the antenna return loss, namely, 2.489 GHz, 4.189 GHz, and 4.967 GHz, were selected to test the SAR values of the antenna to see the absorption ratio of radiation by the human body.Te simulated SAR values of the antenna at these frequencies are shown in Figure 13.Te SAR value of the antenna at 2.489 GHz for the human arm is 0.7684 W/kg, at 4.189 GHz for the human arm is 0.8917 W/kg, and at 4.967 GHz for the human arm is 0.9563 W/kg.Te human simulation SAR value graph shows that although the SAR value of the antenna increases as the resonant frequency point moves towards higher frequencies, the SAR value of the antenna is much lower than the international standard of 2.0 W/kg at 10 mm distance from the human body.Te simulation shows that the antenna is suitable for wearable devices and will not cause radiation damage to the human body, which meets the requirement of minimum radiation exposure to the human body.
Figure 14 shows the radiation direction performance of the antenna after loading the human body.Te gain at the three central frequency points of 2.489 GHz, 4.189 GHz, and 4.967 GHz are 1.6 dBi, 4.9 dBi, and 6.0 dBi, respectively.From the fgure, it can be seen that when the antenna is worn on the human body, the main radiation direction is towards the front of the antenna.Te radiation gain towards the human body is small, while the radiation gain towards the outside is large.In summary, the SAR values of the antenna to the human body are below the national standard, and the antenna has good directionality towards the human body.Terefore, it can be used as an antenna for wearable devices.

Fabrication and Measured Results
. Te antenna was fabricated and tested in a microwave darkroom to verify the correctness of the bandwidth, frequency, and performance of the design.Te antenna was printed on a polyimide dielectric plate with a thickness of 0.3 mm, a dielectric plate size of 32 × 40 mm 2 , a relative permittivity of 3.5, and a dielectric loss rate of 0.008.Figure 15 shows the actual antenna and the experimental test setup.
A comparison between the measured S11 and simulated S11 of the antenna is shown in Figure 16.Te frst frequency point was moved from 2.49 GHz to 2.58 GHz with a return loss of − 19.33 dB.Te second frequency point was moved   Te return loss of the antenna at diferent bending degrees is shown in Figure 17.Te bandwidth of the low-frequency band changes less at diferent bending degrees.As the bending radius decreases, the bandwidth of the high-frequency band of the antenna increases, but it can still cover the required frequency range well.In summary, the diferent bending degrees have less efect on the return loss of the antenna.
Figures 18 and 19 show the 3D far-feld radiation pattern of the antenna at each frequency point and the comparison diagram of the main polarization and cross-polarization of the E/H plane of the antenna, respectively.Te measured and simulated results maintain a good agreement.Te designed antenna shows very good radiation characteristics in all frequency bands, with omnidirectionality in the H plane.However, some discrepancies between the experimental and simulated data can also be found in this case, which are due to unavoidable errors caused by the external environment and the construction of the instrument during the actual measurement.

International Journal of Antennas and Propagation
Te antenna designed for this occasion has two efective frequency bands: the frst band (2.32GHz-2.78GHz) and the second band (4.14 GHz-6.05GHz).Te gain of the actual antenna is shown in Figure 9. Te peak gains are 2.5 dBi, 3.2 dBi, and 5.2 dBi at center frequencies of 2.489 GHz, 4.189 GHz, and 4.967 GHz.As can be seen from Figure 20, the antenna achieved a maximum gain of 6 dBi and a maximum efciency of 79.6%.In the efective frequency band of the antenna, the gain range of the frst band is 1.2-2.62dBi and the efciency range is 37.28%-52.85%.Te second band has a gain range of 0.63-5.41dBi and an efciency range of 26.03%-79.41%.Compared to the simulated antenna's center frequency gain, the gain at the frst frequency point decreased from 2.5 dBi to 1.97 dBi, the gain at the second frequency point increased from 3.2 dBi to 4.08 dBi, and the gain at the third frequency point decreased from 5.3 dBi to 2.06 dBi.Te discrepancy may be attributed to the fact that the simulation process was conducted with ideal feed points and did not account for the losses caused by the SMA connector in the measurement process.However, the antenna still meets the requirements for the desired application frequency range.12 International Journal of Antennas and Propagation

Conclusion
In this paper, a small dual-band fexible antenna with an annular solar eclipse structure, measuring only 32 × 40 × 0.3 mm 3 , was proposed.Te fnal bands and bandwidths of the antenna are 2.32 GHz-2.78GHz (19%) and 4.14 GHz-6.05GHz (37%).Te radiation of the antenna has good omnidirectionality, and the simulated and measured results are in good agreement, verifying the good radiation characteristics of the antenna.Te fexible antenna has the characteristics of miniaturization, high stability, multifrequency band, and wearability.Te antenna covers several commercial frequency bands such as the ISM2400 band, WLAN, WIMAX, and Bluetooth.Te  International Journal of Antennas and Propagation antenna can be used in real-life industrial, scientifc, and medical aspects.

Data Availability
Te data used to support the results of this study are included in the Supplementary Information fle and Figure fles.

2
International Journal of Antennas and Propagation characteristics mainly at the high frequencies of 4.189 GHz and 4.967 GHz.Te trapezoidal ground plate on both sides of the feed line can efectively increase the high-frequency impedance bandwidth of the antenna.On the base model of the antenna in Figure 2, the antenna radiation patch, feed line width, and grounding plate are further optimized to obtain the fnal antenna structure diagram (Table

Figure 12 :
Figure 12: Comparison of return loss of antenna under diferent bending radii.

Figure 17 :Figure 18 :
Figure 17: Comparison between antenna simulation and measurement of diferent curvatures.

Figure 19 :
Figure 19: Cross-polarization of the E/H plane of the antenna at (a) 2.489 GHz, (b) 4.189 GHz, and (c) 4.967 GHz.

Figure 20 :
Figure 20: Gain and efciency of antenna in the measured state.

Table 1 :
Performance comparison of the proposed antenna with recent pioneering state of arts.

Table 2 :
Te dimensions of the proposed antenna design.