A New Koch and Hexagonal Fractal Combined Circular Structure Antenna for 4G/5G/WLAN Applications

Abstract

This paper presents a novel double-sided structure multi-band antenna that cleverly combines a Koch snowflake structure with a hexagonal fractal structure; the front of the antenna features a right semicircle minus a half-order Koch snowflake structure, while the back of the antenna showcases a left semicircle minus half of a hexagonal fractal snowflake structure, which are combined together to form a complete circle. The antenna can cover common communication bands such as fourth to fifth generation (5G) commercial bands, ISM, WLAN, and Bluetooth. The structure of the radiator portion of the antenna is designed by iteratively scaling a basic arc shape multiple times based on a certain scale factor, and after simulation and comparison, three iterations can achieve the best antenna performance, and the antenna uses a microstrip line transmission to broaden the antenna bandwidth. The antenna covers three effective frequency bands: 2.38–2.90 GHz (20.3%), 3.35–3.85 GHz (14.1%), and 5.06–5.80 GHz (13.5%). The antenna dielectric sheet is made of RF-35 from Taconic, which has the advantages of high strength, complete surface inertness, and a long service life, with a dielectric constant of 3.5 and actual dimensions of 50 mm × 54 mm × 0.76 mm. The antenna is fractal-iterated in small dimensions, and the approximation of the frequency bands is accomplished by comparing the ratios of each iteration with the current vector map. The antenna was simulated by HFSS software (Version 21). and measured in an electromagnetic anechoic chamber, and the test results were consistent with the simulation results.

1. Introduction

With the rapid development of communication systems, the requirements for antenna performance have become more stringent, and antennas with multi-band [1], a small size [2,3], good radiation characteristics, and a strong radiation gain have become important goals pursued by antenna design, of great significance to the research and development of miniaturized, multi-band and high-gain antennas [4,5].

To enhance the miniaturization and multi-band characteristics of the antenna, a fractal structure was introduced into the antenna design in an electromagnetic field. Fractal geometry provides a new solution for antenna design [6,7]; this is an antenna with spatial filling, self-similarity, fractional dimensionality, and the multi-resonance characteristics of electrical properties [8]. The spatial filling of the fractal structure allows the antenna to occupy the space where the antenna is located in a more efficient way than the traditional Euclidean antenna [9,10], so that the resonant frequency of the antenna moves to the lower frequency band, so as to realize the miniaturization and compactness of the antenna. In addition, the same structure and self-similarity structure at multiple scales exist in the fractal structure [11], which helps to improve the matching characteristics of the antenna and extend the operating frequency band of the antenna, so as to determine that the antenna has multiple resonant frequencies.

To ensure that the antenna has better far-field pattern characteristics of directional radiation, it should also meet various requirements such as a wide frequency band, miniaturization, and pattern stability. The early forms of directional antennas include log-periodic antennas [12], multilayer antenna, and reflective surface antennas [13,14,15,16], which have a wide impedance bandwidth and good directional radiation characteristics, but generally have the shortcomings of excessive volume and are greatly limited in the application of modern communication systems. Dipole antennas usually have the advantage of a small structure size, which can enhance the reception and transmission of signals. In [17], the authors designed a directional antenna with a polyimide and SU-8 polymer using a multilayer coupling technique and Minkowski fractal geometry.

In [5], the authors summarize the design idea of combining antenna fractal and slotting techniques. The antenna’s performance can be considered while realizing multifrequency bands through the slotting and fractal design of the circular monopole patch. In [18], a compact tri–band hexagonal microstrip antenna is designed which initially resonates at 5.2 GHz i.e., the WLAN band. Then, by the introduction of two sawtooth-shaped detected ground structures, the hexagonal microstrip antenna is made to resonate simultaneously at 2.4 GHz, i.e., the Bluetooth band, and 5.8 GHz i.e., the second WLAN band, alongside 5.2 GHz i.e., the first WLAN band. Thus, a compact hexagonal microstrip antenna with tri–band. characteristics is achieved. In [19], a fractal geometry antenna is proposed for achieving the desired miniaturization and multi-band performances. Furthermore, a new hybrid dielectric resonator antenna excited by a new fractal monopole antenna provides a broad bandwidth. In addition, many researchers have combined fractal and array antennas for simulating miniaturized multi-band antennas. In [20], the authors proposed a compact ultrawideband antenna with a dual-band notch character, A Hilbert fractal-shaped slot is etched in the ground plane to enhance the isolation throughout the operational bandwidth. In [21], the authors presented a wideband compact fractal antenna array; it incorporates a Koch snowflake fractal to achieve both miniaturization and a broad bandwidth. In [22], the antenna consists of a crossed floral square-shaped split-ring resonator organized in a Minkowski fractal configuration. In [23], a fractal-shaped metasurface (FSMS) antenna was presented; the MS is made up of a Sierpinski–Knopp fractal-shaped unit cell, which is arranged in a 4 × 6 layout to achieve miniaturization.

In this study, a new bifacial composite snowflake fractal antenna structure is proposed; the front of the antenna features a right semicircular region, showcasing the third-order evolution of the Koch snowflake fractal pattern to enhance its bandwidth through its self-similarity characteristics, while the back of the antenna is based on a left semicircle, displaying a second-order hexagonal snowflake fractal pattern. When these two sides are juxtaposed on the same horizontal plane, they form a complete circular outline, enhancing the design’s integrity and beauty. This design cleverly combines the basic structure of the Koch curve fractal with the core concept of the hexagonal snowflake fractal, aiming to achieve multi-band optimization and antenna performance size reduction. This approach promotes the development of antenna technology towards miniaturization and multi-functionalization. The antenna operates across three frequency bands, 2.38–2.90 GHz, 3.35–3.85 GHz, and 5.06–5.80 GHz, covering ISM2400 (2.42 GHz–2.48 GHz), 4G (2300–2390 MHz, 2555–2655 MHz), 5G (4.8–5.0 GHz), Bluetooth (2400–2483.5 MHz), and WLAN (802.11 b/g/n: 2400–2480 MHz) to meet the requirements for multi-band operation, miniaturization, and high-performance antenna coverage. The antenna offers a simple structure, easy control of the resonator, and a high gain.

2. Antenna Structure and Design Procedure

In mathematics, a fractal is a geometric shape that contains a detailed structure at arbitrarily small scales, usually with a fractal dimension that strictly exceeds the topological dimension.

From the point of view of Euclidean geometry, the definition of dimension must be an integer, whether it corresponds to zero dimensions for points or three dimensions for cubes with a spatial extent. The fractional dimension concept introduced by fractals extends the dimensions from integers to the category of fractions, breaking through the inherent thinking that dimensions can only be integers.

Intuitively, fractal dimensions can be understood in this way: imagine a graph whose size changes regularly as the number of multipliers increases. If the graph were perfectly regular, its fractal dimension would be an integer. But most fractals in nature (e.g., coastlines, mountains, tree canopies) are irregularly shaped, with dimensions between integers 1 and 2. For example, the fractal dimension of a coastline is usually between 1.25 and 1.3, which means that the length of the coastline will increase as the proportion of observations increases, but not as fast as for regular shapes. A set is considered to have a fractal geometry if its theoretical fractal dimension exceeds its topological dimension. Figure 1 shows the common fractal structure of objects in nature.

2.1. Koch Snowflake Fractal Theory

The front of the antenna utilizes the Koch snowflake fractal structure to decrease the size and enhance the radiation efficiency of the antenna. Additionally, the self-similarity and self-loading characteristics of fractals aid in improving the matching properties of the antenna and expanding its working frequency band. Figure 2 depicts the snowflake structure inspired by the Koch curve found in nature.

A fractal curve can iterate infinitely according to specific requirements and scales, constantly twisting and turning to approach the plane that fills the area, known as the spatial filling property of the fractal. Simultaneously, a fractal antenna can never entirely fill this plane, indicating that the fractal dimension can only be a fraction between integers. For instance, the dimension of a fractal curve falls between 1 and 2. The value of the fractal dimension reflects the space-filling capability of a fractal.

There are various methods for calculating fractal dimensions. For a snowflake fractal antenna, the equation can be solved by determining the number of self-similar structures; the state equation can be represented by Equation (1):

$$k_1{\left({\displaystyle \frac{1}{h_1}}\right)}^D+k_2{\left({\displaystyle \frac{1}{h_2}}\right)}^D+\dots +k_n{\left({\displaystyle \frac{1}{h_n}}\right)}^D=1$$

(1)

where D is the dimensionality, n is the scale type, h_n is the nth scale, and k_n is the number of starting element copies according to the scale h_n. As shown in Equation (2), a fractal can contain a variety of different starting element scales. It can be calculated as

$$D={\displaystyle \frac{\mathit{log}\left(\frac{1}{k_1}\right)}{\mathit{log}\left(\frac{1}{h_1}\right)}}={\displaystyle \frac{\mathit{log} k_1}{\mathit{log} h_1}} (\mathrm{n}=1)$$

(2)

For both scale cases, it can be calculated as in Equation (3)

$$k_1{\left({\displaystyle \frac{1}{h_1}}\right)}^D+k_2{\left({\displaystyle \frac{1}{h_2}}\right)}^D=1 (\mathrm{n}=2)$$

(3)

The state equation can be represented by Equation (4). Fractals are fractional-dimensional structures with self-similarity generated by iterative function systems, and the iterative function system is widely used in various fractal structures:

$$K\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}e\\ f\end{array}\right)$$

(4)

where a, b, c, d are real numbers controlling rotation and scaling; e, f are controlling linear translation; x and y are coordinate values of segmented points; and K is the transformation relation matrix K = [a, b, e, c, d, f]. Then, the matrix K is can be represented by Equation (5).

$$K=\left(\begin{array}{cc}{r}_1\mathit{cos} {\theta }_1& -r_2\mathit{sin} {\theta }_2\\ r_1\mathit{sin} {\theta }_1& r_2\mathit{cos} {\theta }_2\end{array}\right)$$

(5)

The K-matrix is given by Equation (6), The contraction ratio of r in the Koch snowflake fractal structure is 1/3, r = r₁ = r₂ = 1/3, θ₁ = θ₂ = 60°:

$$\begin{gathered} K_1=\left[{\displaystyle \frac{1}{3}},0,0,0,{\displaystyle \frac{1}{3}},0\right] \\ {K}_2=\left[{\displaystyle \frac{1}{3}}\mathit{cos} 60^{\circ },-{\displaystyle \frac{1}{3}}\mathit{sin} 60^{\circ },{\displaystyle \frac{1}{3}},{\displaystyle \frac{1}{3}}\mathit{sin} 60^{\circ },{\displaystyle \frac{1}{3}}\mathit{cos} 60^{\circ },0\right] \\ {K}_3=\left[{\displaystyle \frac{1}{3}}\mathit{cos} 60^{\circ },{\displaystyle \frac{1}{3}}\mathit{sin} 60^{\circ },{\displaystyle \frac{1}{2}},-{\displaystyle \frac{1}{3}}\mathit{sin} 60^{\circ },{\displaystyle \frac{1}{3}}\mathit{cos} 60^{\circ },{\displaystyle \frac{\sqrt{3}}{6}}\right] \\ {K}_4=\left[{\displaystyle \frac{1}{3}},0,{\displaystyle \frac{1}{3}},0,{\displaystyle \frac{1}{3}},0\right] \end{gathered}$$

(6)

Koch snowflakes can be built iteratively in a series of stages. They have self-similar properties and are typical fractal graphs. The first stage is an equilateral triangle, and each successive phase is formed by adding outward bends on each side of the previous stage, resulting in smaller equilateral triangles. The area enclosed by successive phases in the snowflake tectonic converges to 8/5 times the area of the original triangle, while the perimeter of the successive phases increases indefinitely. Thus, the snowflakes enclose a finite area but have an infinite circumference, as shown in Figure 3.

2.2. Hexagonal Fractal Iteration

For the antenna miniaturization problem, the proposed hexagonal fractal structure is chosen for the back of the antenna. The antenna features one iteration of a hexagonal structure, resembling the hexagonal snowflake fractal structure found in nature, as illustrated in Figure 4. The process of creating the hexagonal structure involves extending the antenna’s circumference by removing six small hexagons from a larger hexagon. This process leads to a lower antenna frequency, an increase in radiation impedance, and the iterative generation of multiple resonances to achieve compactness, as depicted in Figure 5. The iterative process results in the generation of multiple resonances and the attainment of compactness.

2.3. Characteristics of Antenna Structure

The electromagnetic simulation software HFSS (Version 21)was used to optimize the antenna parameters. The front and back structure parameters of the antenna are shown in Figure 6, and the size table is shown in

Table 1. Dimensions of the proposed antenna.

Dimensions Parameters	W	L	R	S	S1	S2	S3	K	K1
Unit (mm)	50	54	47	1.3	4	12	36	8	0.4
Dimensions Parameters	K2	H	H1	G	G1
Unit (mm)	1	41.8	8.2	21	4.2

. The double-sided circular snowflake fractal antenna is created by combining the basic pattern of the Koch snowflake fractal with the basic pattern of the snowflake fractal based on the hexagon. The back of the dielectric plate forms a left semicircle, serving as the ground plate. Half of the fractal pattern based on a hexagon is also removed from the semicircle. The front of the dielectric plate forms a right semicircle, but with a difference from the previous one as it subtracts half of the fractal pattern based on the Koch snowflake. When the front pattern is viewed on the same plane as the back pattern, a complete circle is observed.

Multi-band applications can be realized with the help of a full ground plane. The partial ground plane was chosen because it increases the level of cross-polarization of the antenna.

The antenna dielectric board adopts Taconic RF-35(tm) with a relative permittivity of 3.5 and a loss tangent of 0.0018. The physical dimensions of the dielectric board are 50 mm × 54 mm × 0.76 mm. The antennas are fed from a 50-coaxial cable through a microstrip-to-fractal-snowflakes-on-both-sides transition.

Equation (7) defines the electric length, and microstrip line width of the antenna is calculated according to this well-known equation:

$$f={\displaystyle \frac{c}{2L\sqrt{{\epsilon }_r}}}$$

(7)

As shown in Formula (8), the size of the patch is calculated according to the relationship between the size of the radiation patch and the resonant frequency:

$$\begin{gathered} W={\displaystyle \frac{c}{2f}}{\left({\displaystyle \frac{{\epsilon }_r+1}{2}}\right)}^{-{\displaystyle \frac{1}{2}}} \\ L={\displaystyle \frac{c}{2f\sqrt{{\epsilon }_e}}}-2\Delta L \\ {\epsilon }_e={\displaystyle \frac{{\epsilon }_r+1}{2}}+{\displaystyle \frac{{\epsilon }_r-1}{2}}(1+12{\displaystyle \frac{h}{w}}{)}^{-{\displaystyle \frac{1}{2}}} \\ \mathsf{\Delta }L=0.412h{\displaystyle \frac{\left({\epsilon }_e+0.3\right)\left(\frac{w}{h}+0.264\right)}{\left({\epsilon }_e-0.258\right)\left(\frac{w}{h}+0.8\right)}} \end{gathered}$$

(8)

where L and W are the size of the patch, c is the speed of light, f is the antenna resonant frequency r, ε is the relative permittivity of the dielectric board, and h is the height of the dielectric board.

3. Results and Discussion

3.1. Simulation Results

The antenna utilizes the Koch snowflake structure as its design inspiration, employing it as the antenna radiator. It incorporates multi-order fractals within a specific space and utilizes a microstrip line structure for feeding. Within this space, the spacing between each small triangle gradually decreases, leveraging electromagnetic coupling effects to generate multiple frequency bands and achieve a multi-band effect. Figure 7 illustrates the evolution process of the antenna.

The simulation was performed using Ansoft High-Frequency Simulation Software (HFSS) (Version 21). By comparing and analyzing the S11 curve in Figure 7, model (c) generates three frequency points and obtains three frequency bands of 2.38–2.90 GHz, 3.35–3.85 GHz, and 5.06–5.80 GHz. At 3.54 GHz, the bandwidth of antenna (c) is 0.16 GHz wider than that of (b) and the reflection coefficient value is low. In the comprehensive comparison, the model antenna (c) demonstrates superior performance in all aspects, leading to its selection as the final antenna model. During the parameter comparison, it was observed that the reflection coefficient value of the two frequency points of model (a) is less than −10 dB at 2.78 GHz and 3.86 GHz. Based on this, the radiator was optimized, and the number of iterations was increased. As shown in Figure 7b, model (b) has an additional frequency to model (a), which at 5.45 GHz. Following a series of parameter optimizations, the structure is depicted in Figure 7c, and the reflection coefficient plots of the three evolution processes are presented in Figure 8.

In the HFSS software, the two feeder width parameters of the bifacial antenna were optimized and analyzed. Ultimately, the optimal frequency band capable of covering 4G, 5G, WLAN, and other commercial frequency bands was determined.

As depicted in Figure 9, sweep the length of K1 from 0.2 mm to 0.8 mm. Observing the figure, it is evident that as the size increases, the center frequency of the low-frequency part has little effect and shifts slightly to the right. With the increase in size of the high-frequency part, the portion larger than 0.4 mm gradually exceeds −10 dB. Regarding the reflection coefficient value, the reflection coefficient of the low-frequency part decreases with the size increment, while the reflection coefficient value of the high-frequency part increases with size growth.

As depicted in Figure 10, the length of K2 is swept from 0.5 mm to 2 mm. The figure illustrates that as the length of K2 increases, the center frequency of the low-frequency part does not change much; all of them are around 2.5 GHz. Meanwhile, the center frequency of the medium-frequency part moves slightly to the right with the increase in length, and the reflection coefficient value of the center frequency of the high-frequency part gradually changes from −15 dB to −20 dB; considering the frequency and bandwidth, the feeder width K2 on the back of the antenna is selected as 1 mm.

Figure 11 shows the final simulated reflection coefficient curve of the double-sided snowflake fractal antenna. The three central resonant frequencies of the bifacial Koch snowflake fractal antenna are 2.56 GHz, 3.54 GHz and 5.45 GHz, respectively. The corresponding reflection coefficient values are −24.84 dB, −11.67 dB, and −16.72 dB, and the corresponding bandwidths are 2.38–2.90 GHz, 3.35–3.85 GHz, and 5.06–5.80 GHz, respectively. The relative bandwidths are 20.3%,14.1%, and 13.5% respectively.

The effect of high-frequency transmission line effects on the antenna can be seen as shown in

Table 2. Antenna impedance table.

Freq	Ang	Mag	RX	Z0	Y
2.56	147.66	0.047	0.923 + 0.046i	46.14 + 2.31j	0.022 − 0.001j
3.54	−117.23	0.191	0.795 − 0.281i	39.77 − 14.03j	0.022 + 0.008j
5.45	−82.21	0.282	0.918 − 0.557i	45.89 − 27.83j	0.016 + 0.010j

, which contains the impedance and conductance at each frequency point.

These frequency bands can cover communication systems such as Bluetooth, TD-LTE, 5G, and WLAN, as shown in

Table 3. Commercial frequency bands covered by the bifacial Koch snowflake fractal antenna.

Band No.	Bandwidth (Simulation)	Covered Commercial Bands
1	2.38–2.90 GHz (20.3%)	WLAN (802.11 b/g/n: 2400–2480 MHZ) Bluetooth (2400–2483.5 MHZ) BDS (2491.75 ± 4.08 MHZ) ISM2400(2.420–2.4835 GHz) WiMAX (2.3–2.7 GHz) TD-LTE (2300–2390 MHz, 2555–2655 MHz)
2	3.35–3.85 GHz (14.1%)	WiMAX (3.3–3.8 GHz) LTE42/43 (3.4–3.8 GHz) 5G band n78 (3.4–3.8 GHz)
3	5.06–5.80 GHz (13.5%)	WLAN (802.11 a/n:5.15–5.35 GHz) 5G (5.725–5.825 GHz)

.

Figure 12 illustrates the surface current distribution of the bifacial snowflake fractal antenna at 2.45 GHz, 3.54 GHz, and 5.45 GHz, respectively. In Figure 12a, the surface current is primarily concentrated at the feeder and the snowflake petals on both sides. In Figure 12b, the surface current is mainly focused at the feeder and the left snowflake petal. In Figure 12c, the surface current is predominantly concentrated at the feeder and at the two snowflake petals in the lower left corner. The fractal structure’s branches visibly elongate the current path of the antenna radiation surface, with a notable current distribution on the resonant ring. In summary, in the low-frequency band, the upper part of the antenna is the primary area of operation, while in the high-frequency band, the lower half becomes the main working region.

Figure 13 illustrates the simulated 3D gain diagram and the E/H cross-polarization of the antenna at 2.56, 3.54, and 5.45 GHz. At the center frequencies of 2.56, 3.54, and 5.45 GHz, the gains of the 3D radiogram are 3.8 dBi, 4.7 dBi, and 2.98 dBi. At the low-frequency point of 2.56 GHz, the antenna’s orientation performance is good with no side lobes. However, at the middle-frequency point of 3.54 GHz and the high-frequency point of 5.45 GHz, there are side lobes without a zero point, yet the antenna still maintains good radiation characteristics. As depicted in Figure 12, the overall cross-polarization degree of each frequency band of the antenna is good. However, with the increase in frequency, the cross-polarization of the antenna gradually increases relative to the main polarization. Nevertheless, the isolation degree of the overall cross-polarization from the main polarization remains within an acceptable range.

3.2. The Simulation of a Reflector on the Back of an Antenna

In order to enhance the directionality of the fractal snowflake antenna, n 80 mm × 80 mm metallic copper reflector was added 250 mm from the back of the antenna, as illustrated in Figure 14.

Figure 15 shows the S11 curve of the reflection coefficient for the double-sided snowflake fractal antenna and the antenna with an added reflector at the back. Upon comparing and analyzing the S11 curve in Figure 14, it is observed that the center frequency of the antenna with the reflector tends to shift to the left, albeit with a minor offset frequency. Specifically, at 2.56 GHz, the reflection coefficient value ranges from −24.84 dB to −28.1 dB, and the bandwidth at 3.54 GHz is widened, increasing by 0.24 GHz, from 3.35–3.85 GHz to 3.06–3.80 GHz; the resonant frequency point of the antenna is almost constant at 5.45 GHz at high frequency, the reflection coefficient value is from −16.71 dB to −14.80 dB, and the bandwidth is relatively consistent.

Figure 16 shows the 3D gain of the center frequency with the addition of a metal reflector on the back of the bifacial snowflake fractal antenna, with the gain of the 3D gain diagram at the center frequencies of 2.56, 3.54, and 5.45 GHz, respectively, of 8.7 dBi, 8.8 dBi, and 6.5 dBi, respectively. On the whole, the gain of the retroreflector on the back of the antenna is significantly increased compared with before, and the directivity is better.

4. Fabrication and Measurement Results

4.1. Antenna Measurement

In order to verify the correct bandwidth, frequency, and performance of the designed antenna, the antenna prototype was fabricated and tested using a vector analyser and microwave darkroom. The antenna prototype was fabricated using Taconic RF-35(tm) material with a relative dielectric constant of 3.5 and a dielectric loss tangent of 0.0018 as the dielectric sheet; the antenna had dimensions of 50 mm × 54 mm and a thickness of 0.76 mm. Figure 17 illustrates the front and back physical view of the antenna, the diagram of the antenna being placed in an electromagnetic microwave darkroom for testing, and the antenna being tested using a vector analyzer.

Figure 18 shows the comparison between the actual antenna S11 and the simulated antenna S11, and the comparison with the simulated antenna data clearly shows that the first band and the second band are fused into a wider band, and the band range is fused from the first band of 2.38–2.90 GHz and the second band of 3.35–3.85 GHz to 2.33–3.78 GHz in the simulation, and the reflection coefficient value of the real antenna is also lower at −29.52 dB. Comparing the second band of the antenna with the simulated antenna, the bandwidth is moved from 5.06–5.80 GHz to 4.75–5.99 GHz, and the reflection coefficient value is changed from −16.72 dB to −32.5 dB. Additionally, the simulation results are in good agreement with the actual test results, but there is still a certain degree of error, which is related to the antenna’s fabrication and soldering process. Electromagnetic interference around the vector analyzer during the measurement process can affect the measurement results.

The frequency bands corresponding to the actual measured antennas can cover Bluetooth, TD-LTE, 5G, WLAN, and other communication systems, as shown in

Table 4. Measured bandwidth and frequency bands covered by the antenna.

Band No.	Bandwidth	Covered Commercial Bands
1	2.33–3.78 GHz	WLAN (802.11 b/g/n: 2400–2480 MHZ) Bluetooth (2400–2483.5 MHZ) BD S(2491.75 MHZ ± 4.08 MHZ) ISM2400 (2.420–2.4835 GHz) WiMAX (2.3–2.7 GHz) TD-LTE (2300–2390 MHz, 2555–2655 MHz) LTE42/43 (3.4–3.8 GHz) WiMAX (3.3–3.8 GHz) 5G band n78 (3.4 GHz–3.8 GHz)
2	4.75–5.99 GHz	WLAN (802.11 a/n:5.15–5.35 GHz) 5G (5.725–5.825 GHz)

.

Figure 19 (1) depicts the three-dimensional far-field radiation direction map of the antenna at each frequency point, and the cross-polarization of the E\H plane by the antenna at 2.56, 3.54, and 5.45 GHz is shown in Figure 19 (2,3). From the figure, it can be seen that the antenna has good directional characteristics; with the increase in frequency, a side flap begins to appear in the three-dimensional radiation, and the cross-polarization of the antenna gradually increases; the antenna test results and the simulation results have a small difference, which is attributed to errors in the artificial manufacturing process of the antenna.

4.2. The Measurement of a Reflector on the Back of an Antenna

An 80 mm × 80 mm metallic copper reflector was added 250 mm from the back of the antenna as shown in Figure 20a, Figure 20b shows the antenna in a microwave darkroom for 3D radiation direction map measurements, and Figure 20c shows measurements of the antenna using a vector analyzer.

Figure 21 shows the comparison between the measured and simulated antennas at 250 mm of the antenna example, and the comparison with the simulated antenna clearly shows that the overall band becomes wider and the performance becomes better. The first band is changed from 2.21–2.59 GHZ to 2.16–2.67 GHZ; the second band is changed from 3.07–3.83 GHZ to 3.35–3.95 GHZ, and the measured reflection coefficient is also lowered to −20.6 dB; and the third band is expanded from 5.10–5.73 GHz to 4.63–6.03 GHz. This is due to the internal structure of the antenna material and the antenna welding process.

Figure 22 (1) depicts the three-dimensional far-field radiation direction map of the antenna at each frequency point, and the cross-polarization of the E\H plane by the antenna at 2.56, 3.54, and 5.45 GHz is shown in Figure 22 (2,3). From the figure, the antenna has a good directivity after adding the reflector plate, and with the increase of frequency, the antenna’s far-area radiation field begins to appear as a sidelobe. and the cross-polarization increases. The antenna’s measured and simulated differences are small; this is due to the surrounding environment during the antenna is tested in an anechoic chamber.

5. Discussion

In this paper, we present a double-sided snowflake fractal antenna with 2.38–2.90 GHz, 3.35–3.85 GHz, and 5.06–5.80 GHz frequency bands, which can cover multiple communication systems such as 5G, WLAN, and Bluetooth. The antenna has a good appearance and performance, and has a good directivity in all frequency bands. The simulation and actual measurement results have a good agreement.

In future research, it is hoped that the antenna can be designed as a flexible material in order to be applied to wearable terminals. The conductivity of flexible materials tends to be lower than that of conventional metallic materials, which affects the radiation efficiency and bandwidth of antennas. Therefore, flexible materials with specific electrical properties are chosen to avoid changes in the antenna’s performance. In addition, human activities (e.g., bending, twisting) can further affect the stability of the antenna’s performance, and the material needs to be flexible and adaptable enough to increase the stability of the antenna structure and reduce deformation under certain shapes or stresses. The challenges of adapting antennas to flexible materials include, but are not limited to, the conductivity of the material itself, the coefficient of thermal expansion, the mechanical strength, and the manufacturing process. Using advanced composites that combine the benefits of multiple materials, it is possible to fabricate antennas that are both flexible and electrically conductive.

In conjunction with the above discussion, if antennas are to be fabricated as flexible materials in the future, it is likely that a flexible material with high strength and durability will be selected, such as polyimide and polyester. They have a good flexibility, abrasion resistance, and heat resistance, being flexible materials with a high strength and durability.

The performance comparison between the antenna proposed in this paper and the antennas in the reference is shown in

Table 5. Performance comparison of the proposed antenna with the recent pioneering state of art.

Ref.	Size (mm2)	Centre Frequency (GHz)	Maximum Gain (dBi)	Substrate Material	Applications
[1]	80 × 80	1.56/2.49/3.5/5.24	2.45	Rogers AD255C	2G/3G/4G
[5]	85 × 70	1.6/2.35/3.8/5.85	4.99	FR4	5G/WLAN/Navigation
[11]	150 × 80	3.6	5.3	FR4	Sub-6 GHz band
[13]	83 × 56	2.47/3.55/5.55	3.73	FR4	Navigation, WLAN
[18]	35 × 27.4	5.2	4.14	FR4	WLAN band
[20]	30 × 41	5.5/8.1	4	FR4	/
[21]	58.45 × 58.45	14.6	3.81	FR4	Ku-band
[22]	74 × 70	4.5/7.7	2.05	FR4	5G Sub-6 GHz
[23]	26 × 26	4.89	1.56	FR4	Public Protection
Prop	50 × 54	2.5/3.5/5.5	4.7	Taconic RF-35(tm)	4G/5G/WLAN/Navigation

.