Design and performance evaluation of a compact radiation absorber for 5G applications

Introduction: The emergence of electromagnetic wave pollution as a new form of pollution in human society is attributed to the advancements in communication technology and the electronic information business. In addition to harming priceless electronic equipment, these electromagnetic radiation and interference issues brought on by electrical and electronic devices have a major negative influence on human productivity and wellbeing. The secret to getting rid of electromagnetic radiation interference (EMI) and improving performance is electromagnetic shielding technology. Metamaterial absorber is a type of metamaterial that absorb EMI radiation. The benefits of metamaterial absorbers include their lightweight, simple construction, and excellent absorptivity.

Methods: This paper proposes a novel metamaterial absorber for EMI radiation absorption. It consists of dielectric layers, metamaterial shielding layer and transmission line. The reflection of radiation is reduced by miniaturization of metamaterials.

Results and Discussion: Simulation results show that the proposed design has better performance as compared to existing methods. The operating frequency range is from 23.1 to 28.3 GHz. The values of S₂₁ with and without shielding are −5 dB and −0.05 dB, and the shielding effectiveness is 10.10 dB and a maximum of 12.63 dB.

1 Introduction

With the development of mobile communication technology, electronic systems continue to move towards miniaturization, high integration and high speed. In this process, flexible electronic technology has received widespread attention due to its excellent flexibility and has promoted wearable electronics (Shallah et al., 2024). The realization and rapid development of flexible electronic devices such as foldables and foldable electronic devices have been widely used in education, medical and industrial fields. However, as the signal frequency and the integration of electronic components increase, the intensity of electromagnetic interference (EMI) between components increases, and the electromagnetic environment on the printed circuit board (PCB) becomes more complex. If the electromagnetic radiation reaches a certain limit, it may even cause the entire circuit to collapse (Fu et al., 2023). The main device for signal transmission between PCBs or PCB on-board devices is the transmission line. Unlike when transmitting low-frequency signals, when the transmission line transmits high-frequency signals, the intensity of electromagnetic radiation generated in the space is greater, and the impact on other components is also worse (Lei et al., 2022). In traditional rigid PCBs, vias and metal films are usually used on transmission lines to form shielding cavities to suppress electromagnetic radiation and achieve good shielding performance. However, in flexible PCB, this solution will affect the flexibility of the transmission line, and is prone to produce parasitic capacitance and inductance, etc., causing signal integrity problems (Albawri et al., 2020; Norouzi et al., 2023). Thus, it is imperative to provide a method for suppressing electromagnetic radiation for flexible high-frequency transmission lines (Gupta et al., 2020).

The phenomenon of electromagnetic interference in transmission lines becomes more and more serious as the frequency increases. In recent years, domestic and foreign scholars have conducted a lot of research to solve this problem (Chien et al., 2020; Xie et al., 2022). The authors in (Suarez et al., 2020) proposed using ferrite materials to solve the problem of PCB board-level electromagnetic interference (EMI), that is, using the characteristics of ferrite materials to effectively absorb electromagnetic waves to reduce the interference caused by transmission lines in PCBs, and the electromagnetic radiation in the MHz frequency class. The authors in (Liu et al., 2023) proposed using magnetic electroplating alloys instead of ferrite materials to suppress electromagnetic radiation in PCBs, and conducted a test on shielding effectiveness with 4F1 ferrite materials at 500 kHz and 3 MHz frequencies. In comparison, similar shielding effectiveness is achieved with a thinner thickness. The authors in (Zhuang and Lin, 2023) studied the impact of the spacing and position of PCB edge vias on the electromagnetic radiation shielding effectiveness, and verified it in the range of 0–3 GHz. In rigid PCBs, vias are still widely used as the main space radiation suppression technology. However, as the frequency increases, due to the influence of parasitic parameters and impedance discontinuities, vias will inevitably cause signal transmission problems in the PCB. Causes signal integrity issues. Moreover, this problem is also inevitable in flexible PCB. The authors of (Wang et al., 2021) proposed a technique for shielding radiation from transmission lines and other PCB components by employing materials with high dielectric constants rather than vias. They tested it in the range of 0–10 GHz and found that with the frequency The shielding efficiency of high dielectric constant materials is better than that of via holes, but these materials are thicker and less flexible, so they are not suitable for flexible PCBs. Therefore, there are certain limitations in using the above technologies for electromagnetic radiation suppression in ultra-thin flexible high-frequency transmission lines, and most of them are reflective shielding solutions. In high-frequency application scenarios, reflected waves will affect the transmission performance of the transmission line. The use of low-reflective shielding technology can solve this problem.

Low-reflective shielding materials can effectively absorb electromagnetic radiation and improve electromagnetic compatibility near disturbed equipment. Early research on low-reflective materials mainly focused on ferrite and magnetic metal materials. Ferrite materials have the characteristics of strong absorption loss and low cost, but have low absorption frequency and high density. The authors in (Perdigones and Quero, 2022) proposed a ferrite material composed of CoFe₂O₄, with an absorption frequency band of 8.2–10.2 GHz, a thickness of 2 mm, and performance at 9.25 GHz with maximum reflection loss of −55 dB. Compared with ferrite materials, magnetic metal materials have stronger magnetism and greater absorption loss, but they have the disadvantages of high density and narrow absorption bandwidth. Reference (Tian et al., 2023) proposed a magnetic metal material composed of Ho-Ce-Co alloy with an effective absorption bandwidth of 1.6 GHz and a thickness of 2 mm, which can reach −42.99 dB at 6.48 GHz with maximum reflection loss. New low-reflection shielding materials are carbon-based, conductive polymer-based and metal sulfide-based materials. Carbon-based materials have the advantages of low density, large dielectric loss and adjustable conductivity, but they have the disadvantage of narrow absorption bandwidth. Reference (Chen et al., 2018) proposed a carbon-based material composed of graphene microflowers, which can absorb electromagnetic waves at 6.0–8.9 GHz. The thickness is 4 mm and can reach a maximum of −42.9 dB at 6.9 GHz. Conductive polymer-based materials have the advantages of large dielectric loss and strong conductivity, but they also have the disadvantage of narrow absorption bandwidth. Reference (Wang et al., 2018) proposed a conductive polymer-based shielding material composed of Ni/SiO₂/polyaniline. The operating frequency range is 16.0–17.9 GHz and the thickness is 8.7 mm. It can reach 17.1 GHz with reflection loss of −41.5 dB. Metal sulfide-based materials have large dielectric losses and good electrical conductivity, but they also have the problem of large thickness. Reference (Wu et al., 2020) proposed a metal sulfide-based material composed of Fe₃O₄/Fe₃S₄, with an absorption frequency band of 5.8–8.4 GHz, a thickness of 3.3 mm, and a −45.3 dB at 7.1 GHz. The above low-reflection shielding materials used in high-frequency transmission lines have problems such as large thickness and narrow absorption bandwidth. Disadvantages: It is difficult to adapt to flexible transmission lines. The emergence of metamaterials has given new ideas to solve this problem.

Metamaterial is an artificially designed periodic sub-wavelength structure that has extraordinary physical properties that natural materials do not have, such as negative dielectric constant, negative magnetic permeability and negative refractive index, and has good control and absorption capabilities for electromagnetic waves. It has high application potential in electromagnetic stealth (Gao et al., 2023) and anti-jamming communications (Yang et al., 2020). Metamaterials are ultra-thin, and the thickness can be reduced to a few tenths of the operating wavelength. Due to its periodic array structure, the scale can be flexibly adjusted for application in various scenarios, and it can adapt to the trend of miniaturization of electronic systems (Ali and Alhindawi, 2021; Dai et al., 2023). The authors in (Hossain et al., 2023) proposed the concept of a perfect metamaterial absorber. They used hard FR4 material as the dielectric substrate and designed metal strip resonant structures on both sides to achieve electromagnetic wave amplitude control at 11.5 GHz. Reference (Araujo et al., 2020) proposed a flexible metamaterial structure, using PET material as the dielectric substrate to achieve good flexibility, and coating one side of it with a layer of conductive material with a square resistance of 74 Ω. The film is printed with a pattern, achieving effective absorption of electromagnetic waves in a wide frequency band of 4.1–19.3 GHz, that is, adjusting the amplitude. The authors in (Chung et al., 2022) deploys the Pancharatnam-Berry phase theory and introduced the propagation phase to design a metasurface that can achieve complete phase control when circularly polarized incident, and in the range of 9–11 GHz. The authors in (Wu et al., 2022) proposed a metamaterial design method with full control of amplitude, phase and polarization. By introducing the concept of “metamaterial atoms” constituting “metamaterial molecules”, they realized the control of electromagnetic wave amplitude, control of phase and other parameters. Due to the significant advantages of metamaterials in volume, form and function compared to traditional materials in regulating the amplitude, phase and polarization of electromagnetic waves, they are not only widely used in perfect lenses, electromagnetic stealth and other scenarios, but their miniaturization characteristics make them at high research value in improving the electromagnetic compatibility of micro-devices such as mobile terminals.

In response to the aforementioned problems, this paper proposes a low-reflection scheme that uses miniaturized metamaterial structures to shield electromagnetic radiation for high-frequency flexible transmission lines.

The main contributions are as follows.

1) By coupling the transmission line to the metamaterial structure, the metamaterial’s regulation and absorption characteristics of electromagnetic waves are used to suppress electromagnetic radiation, and the equivalent parameter theory and equivalent circuit theory are used to analyze and verify the designed miniaturized metamaterial structure.

2) A segmented transmission line with coplanar characteristics is designed for simulation and testing that operates in the FR2 frequency of 5G.

3) By comparing the S-parameters and electromagnetic radiation intensity of the segmented coplanar waveguide transmission line before and after adding the metamaterial shielding structure, the performance of the metamaterial in maintaining transmission quality and suppressing electromagnetic radiation of the transmission line was verified, and the actual product was processed for testing.

2 Model design

2.1 Electromagnetic shielding mechanism

Metamaterials are composed of artificially designed periodic subwavelength structural units, with carefully designed structural patterns on a single structure. When the radiated electromagnetic wave is incident on the surface pattern, if it matches the working frequency band of the metamaterial structure, a strong electromagnetic resonance will be generated. Therefore, the metamaterial has good control and absorption capabilities for electromagnetic waves. By coupling it with a high-frequency flexible transmission line, it can be used in regulate and absorb radiated electromagnetic waves within a wide frequency band to achieve electromagnetic shielding.

The suppression of electromagnetic radiation from transmission lines by metamaterial structures, that is, the regulation of electromagnetic waves, can be analyzed from multiple angles. Specifically, it mainly includes the control of three aspects: amplitude, phase and polarization.

First, the metamaterial structure regulates the amplitude of electromagnetic waves mainly through electromagnetic loss, which is mainly divided into two parts: dielectric loss and ohmic loss. The dielectric substrate of the metamaterial structure is usually a lossy material. When electromagnetic waves are incident into the medium, if magnetic resonance occurs, the surface pattern and the metal backing plate will generate anti-parallel currents, and a certain displacement current will be generated in the medium. This part is called dielectric loss (Holloway et al., 2012; Ding et al., 2016; Li Y. et al., 2023). Ohmic loss is mainly caused by the incident electromagnetic wave exciting the resonance of the metal structure on the surface of the metamaterial. Since the metamaterial can electrically resonate with the electromagnetic wave at a certain frequency point or within a certain frequency band, this part of the electromagnetic wave will be converted into current and lost. When the high-frequency electromagnetic wave radiated by the transmission line is incident on the surface of the metamaterial structure, if it matches the working frequency band of the metamaterial, it will enter the interior of the structure and be partially transmitted. Define the transmittance $T\left(\omega \right)$, and partially be reflected, reflection rate is $R\left(\omega \right)$, and the rest is lost inside the metamaterial. The loss rate is defined as $L\left(\omega \right)$, that is, the metamaterial suppresses electromagnetic radiation as an absorbing structure. The corresponding loss rate calculation formula is expressed in Eq. 1

$L\left(\omega \right)=1-T\left(\omega \right)-R\left(\omega \right)(1)$

Second, metamaterials can effectively control the phase of electromagnetic waves in the microwave band. For a reflective metamaterial structure with a complete metal backplate on one side of the medium, assuming that the dielectric constants before and after the electromagnetic wave is incident (the metamaterial dielectric layer) are ${\epsilon }_1$ and ${\epsilon }_2$ respectively, and the magnetic permeabilities are ${\mu }_1$ and ${\mu }_2$ respectively, the boundary conditions are (Li Y. et al., 2023) expressed in Eq. 2

$\left\{\begin{array}{l}{A}_1+B_1=A_2+B_2\\ Y_1\left(A_1-B_1\right)=Y_2\left(A_2-B_2\right)+Y_{\mathrm{s}}\left(A_2+B_2\right)\end{array}\right.(2)$

In the formula: $A_i$ and $B_i$ represent the electric field components in the forward and reverse directions in each layer of media respectively; $Y_1$, $Y_2$ and $Y_{\mathrm{s}}$ respectively represent the equivalent admittance of the medium in which the electromagnetic wave is located before and after incidence and the surface structure of the metamaterial. When incident on the metamaterial from free space, $Y_1=Y_0$, $Y_0$ is the admittance of free space, its value is $\sqrt{{\epsilon }_0/{\mu }_0}=1/377$ S, where ${\epsilon }_0$ and ${\mu }_0$ are the dielectric constant and magnetic permeability of free space respectively (Silva et al., 2020; Ardeshana et al., 2024). The metamaterial dielectric layer admittance $Y_2=\sqrt{{\epsilon }_2}{Y}_0$.

On this basis, the reflection phase of the metamaterial structure can be expressed in Eq. 3

${\varphi }_{\mathrm{r}}=\arg \left(\frac{B_1}{A_1}\right)=\arg \left(\frac{1-\sqrt{{\epsilon }_2}-Y_{\mathrm{s}}/Y_0-\left[1+\sqrt{{\epsilon }_2}-Y_{\mathrm{s}}/Y_0\right]e^{2jkd}}{1+\sqrt{{\epsilon }_2}+Y_{\mathrm{s}}/Y_0-\left[1-\sqrt{{\epsilon }_2}+Y_{\mathrm{s}}/Y_0\right]e^{2jkd}}\right)(3)$

In the formula: $k$ is the wave number of electromagnetic waves in metamaterial media; $d$ is the thickness of the medium. When the radiated electromagnetic wave enters the metamaterial structure, the reflected part will produce a phase change, which is different from the electromagnetic wave before the incident, that is, the electromagnetic wave signal transmitted by the transmission line (Wang et al., 2023a; Dai et al., 2024). Therefore, compared with traditional vias and metal shielding films, metamaterials have less impact on the signal integrity of transmission lines.

Third, the control of the polarization of incident electromagnetic waves is also an important part of the structural properties of metamaterials. Generally speaking, the polarization of electromagnetic waves can be divided into three categories: linear polarization, circular polarization and elliptical polarization (Sun et al., 2021; Dai et al., 2022). Metamaterials can effectively convert the polarization of electromagnetic waves by changing characteristics such as amplitude and phase through specific design.

Therefore, compared with the traditional reflective shielding structure, the metamaterial structure reduces the reflection component and changes the characteristics of the reflected wave when suppressing the high-frequency radiation of the transmission line, which can effectively maintain the transmission performance of the transmission line.

2.2 Structure design

To comply with the trend of high integration of electronic systems, the designed metamaterial structure has the characteristics of miniaturization and uses flexible materials to ensure matching with flexible transmission lines. The front and three-dimensional views of the designed metamaterial structural unit are shown in Figures 1A,B respectively. The main structure consists of metamaterial patterns, dielectric substrates and metal back plates. The unit size is 0.079λ₀ × 0.079λ₀ (λ₀ is the wavelength corresponding to the lowest cutoff frequency in the operating bandwidth), and the thickness is only 0.04λ₀.

Figure 1

Figure 1. Proposed design. (A) Front view; (B) side view.

As can be seen from Figure 1A, the metamaterial pattern consists of three square open split rings of different sizes. The coupling between the three resonant rings is used to increase the resonance points (Cao et al., 2021; Xu G. et al., 2023; Zhang et al., 2023), and finally achieves electromagnetic wave response in a wide frequency band.

The metamaterial pattern and the metal backplane are both made of metallic copper, with a conductivity of 5.8 × 10⁷ S/m and a thickness t¹ of 0.018 mm. The dielectric substrate is made of polyimide material, with a dielectric constant of 3.5, a loss tangent tan δ of 0.0027, and a thickness t₂ of 0.48 mm. One side of the dielectric substrate is completely covered by a metal backplane, so the transmittance of electromagnetic waves is zero. The complete geometric parameters are shown in Table 1.

Table 1

Table 1. Design parameters.

2.3 Electromagnetic characteristic analysis

When conducting research on the electromagnetic properties of metamaterial structures, commercial simulation software CST was used for modeling. The boundary conditions in the x and y directions were set to the “unit cell” periodic boundary, and the z direction was set to an open boundary. A frequency domain solver was used for modeling electromagnetic parameters.

The comparison of the S-parameters of the metamaterial structure when TE and TM polarized electromagnetic waves are vertically incident is shown in Figure 2A. In the frequency range of 23.10–28.30 GHz, S₁₁ is lower than −10 dB, showing that it is sensitive to electromagnetic waves having hood control and absorption performance, with the best reflection loss of −44 dB at 27.56 GHz. The reflection phases of the two polarized waves when they are vertically incident are shown in Figure 2B. Within the metamaterial operating frequency band (Yang M. et al., 2023), the phase undergoes multiple mutations, and incident waves of different frequencies show different reflection phases. On the other hand, for TE and TM polarization waves, the designed metamaterial structure shows consistent electromagnetic control performance, and therefore has polarization insensitivity.

Figure 2

Figure 2. Vertical incident electromagnetic waves evaluation. (A) S-parameter; (B) reflection phase.

2.4 Equivalent parameter evaluation

When conducting research on the regulation and absorption of electromagnetic waves in metamaterial structures, impedance matching is an important aspect. Impedance matching refers to the degree of reflection and absorption of electromagnetic waves by metamaterials when electromagnetic waves are incident on the surface of a metamaterial structure (Gao et al., 2024; Xu and Shin, 2024), so it is closely related to the performance of metamaterials. After the incident electromagnetic wave interacts with the metamaterial, it is divided into three parts, namely, reflected, transmitted and absorbed electromagnetic waves. When designing a metamaterial structure, a metal conductor is usually used as a backplane to ensure that the transmission coefficient is 0. In this case, reducing the reflection coefficient S₁₁ can increase the absorption rate (Liu et al., 2022). The reflection coefficient is calculated by Eq. 4

${\mathrm{S}}_{11}=\frac{Z_{\text{in}}-Z_0}{Z_{\text{in}}+Z_0}(4)$

In the formula: $Z_0$ represents the impedance of free space, its value is 120π Ω; $Z_{\text{in}}$ represents the surface impedance of the metamaterial structure, and the calculation formula for its equivalent value is (Ding et al., 2016) expressed in Eq. 5

$Z_{\text{in}}=\sqrt{\frac{{\left(1+S_{11}\right)}^2-S_{21}^2}{{\left(1-S_{11}\right)}^2-S_{21}^2}}=\frac{1+S_{11}}{1-S_{11}}(5)$

It will be normalized and compared with the equivalent impedance of the metamaterial. Impedance matching can be achieved when $Z_{\text{in}}=Z_0$ (Li M. et al., 2023). The metamaterial structure has better control and absorption effects on electromagnetic waves.

In the designed metamaterial structure, one side of the dielectric substrate is completely covered by the metal backplane, and the transmission coefficient S₂₁ is 0. The S-parameters are extracted from the CST simulation software, and the equivalent impedance is calculated using the programming software. The results are shown in Figure 3. The real part of the equivalent impedance of this structure is close to 1 and the imaginary part is close to 0 in the operating frequency band, so it matches the free space impedance well.

Figure 3

Figure 3. Equivalent impedance evaluation with real and imaginary parts.

Metamaterial is a composite artificial material that is microscopically inhomogeneous, but can be regarded as a uniform dielectric material from the subwavelength scale. Therefore, equivalent medium theory can be used for analysis. The calculation formulas of equivalent dielectric constant and equivalent magnetic permeability are as follows (Holloway et al., 2012) in Eqs 6, 7

$\epsilon \left(\omega \right)=1+\frac{2\mathrm{j}}{k_{0}h}\left(\frac{1-S_{11}}{1+S_{11}}\right)(6)$

$\mathrm{\mu }\left(\omega \right)=1+\frac{2\mathrm{j}}{k_{0}h}\left(\frac{1+S_{11}}{1-S_{11}}\right)(7)$

In the formula: $k_0$ represents the wave number of free space; h represents the thickness of the metamaterial structure dielectric substrate. The equivalent dielectric constant and equivalent magnetic permeability of the designed metamaterial structure were analyzed. Based on the S-parameter simulation results, the formula was used to perform inversion calculations. The results are shown in Figures 4A,B, where the real part of the equivalent dielectric constant and the equivalent magnetic permeability represents the matching degree of the metamaterial and free space (Hu et al., 2019; Alves et al., 2023; He et al., 2023), and the imaginary part represents the energy loss. It can be seen that the real parts of the two equivalent parameters are close to 0 within the operating frequency, so the structure matches the free space well. The imaginary parts of both are greater than 0 in the working frequency band, indicating that they have a certain loss capability for electromagnetic waves.

Figure 4

Figure 4. Evaluation of real and imaginary parts of equivalent parameters. (A) Dielectric constant; (B) permeability.

2.5 Circuit equivalent structure

When electromagnetic waves are incident on the metamaterial surface structure, an induced current will be excited, and the metamaterial structure will form a current path, which forms an equivalent circuit model. Among them, each open split ring structure can be equivalent to an RLC branch, and the equivalent parameters can be calculated according to the following formula (Silva et al., 2020) in Eqs 8–14

$F\left(k,w,\lambda \right)=\frac{k}{\lambda }\cos \theta \left(\ln \left(\text{cosec}\frac{\pi w}{2k}\right)+G\left(k,w,\lambda \right)\right)(8)$

$G\left(k,w,\lambda \right)=\frac{1}{2}\frac{{\left[1-{\beta }^2\right]}^2\left[\left(1-\frac{{\beta }^2}{4}\right)\left(A_{+}+A_{-}\right)+4{\beta }^2{A}_{+}{A}_{-}\right]}{\left(1-\frac{{\beta }^2}{4}\right)+{\beta }^2\left(1+\frac{{\beta }^2}{2}-\frac{{\beta }^4}{8}\right)\left(A_{+}+A_{-}\right)+2{\beta }^6{A}_{+}{A}_{-}}(9)$

$A_{\pm }=\frac{1}{\sqrt{1+\frac{2k\sin \theta }{\lambda }}-{\left[\frac{k\cos \theta }{\lambda }\right]}^2}-1(10)$

$\beta =\frac{\sin \left(\pi w\right)}{2k}(11)$

$\frac{L}{Z_0}=\frac{p}{k}F\left(k,2m,\lambda \right)(12)$

$\frac{C}{Z_0}=4\frac{p}{k}F\left(k,s,\lambda \right)(13)$

$R=\rho \frac{L_c}{S}(14)$

Where, $k,m,s$ and $p$ are respectively the period length of the resonant ring in the metamaterial surface structure, the width of the metal strip, the distance between the two resonant rings and the length of the resonant ring on the lateral scale; $\lambda$ represents wavelength; $\theta$ represents the incident angle of electromagnetic waves; L, C and R respectively represent the equivalent inductance, capacitance and resistance of each open split ring; $Z_0$ represents the impedance of free space; $\rho$ represents the electrical conductivity of the material (Chen et al., 2022; Jiang and Li, 2022; Wang et al., 2023b); $L_c$ and represent the length and cross-sectional area of the conductor respectively.

The three square resonant rings of the designed surface pattern of the metamaterial structure can be equivalent to three sets of RLC series branches, in which the capacitance is composed of the equivalent capacitance at the opening of the three resonant rings and the coupling capacitance between the inner and outer rings, C₁, C₂ and C₃ are respectively generated by the mutual coupling of three rings from outside to inside in the metamaterial surface pattern and the opening of each ring itself (Zhang et al., 2024; Zhao et al., 2024). The inductance is excited by the induced current generated when electromagnetic waves are incident into the structure. L₁, L₂ and L₃ are respectively induced by the three rings from the outside to the inside in the metamaterial surface pattern when electromagnetic waves are incident. Resistors R₁, R₂ and R₃ are equivalently generated by the metal strip opening structure of three rings from outside to inside in the surface pattern. Therefore, the equivalent circuit model is shown in Figure 5. Among them, Z₀ represents the free space impedance, Z_h represents the equivalent impedance of the metamaterial dielectric substrate, and the three groups of parallel RLC branches correspond to the equivalent impedance parameters of the three resonant rings in the metamaterial surface structure.

Figure 5

Figure 5. Circuit equivalent structure of metamaterial.

The metamaterial structure is analyzed based on the equivalent circuit theory. In order to simplify the calculation, all parameters are obtained based on the incident angle of 0°. The resistances R₁, R₂, and R₃ calculated by the formula are 0.053 Ω, 0.033 Ω, and 0.013 Ω respectively. Inductors L₁, L₂, and L₃ are 20.20 nH, 25.85 nH, and 19.00 nH respectively (Liao et al., 2022; Xu H. et al., 2023; Mou et al., 2023). Capacitors C₁, C₂, and C₃ are 2.30 fF, 1.26 fF, and 0.95 fF respectively. Using the calculated parameter values combined with ADS software for optimization, the obtained simulated S-parameter curve is shown in Figure 6, which is basically consistent with the results obtained by CST simulation software.

Figure 6

Figure 6. S-parameter evaluation using ADS and CST simulators.

3 Shielding performance evaluation

3.1 Transmission line model for segmented coplanar waveguide

To verify the effectiveness of high-frequency flexible transmission lines loaded with metamaterial structures for electromagnetic shielding, an SCPW transmission line operating in the 5G FR2 frequency band was designed for testing.

The segmented coplanar waveguide transmission line is redesigned based on the traditional coplanar transmission line, and a half-wavelength resonator is added to adjust the operating frequency of the transmission line (Ding et al., 2021), making the coplanar waveguide structure more suitable for high-frequency application scenarios.

The segmented coplanar waveguide transmission line is mainly composed of a coplanar waveguide part and a dielectric substrate, as shown in Figure 7A. The coplanar waveguide part consists of a signal line (I), a ground plane (II), and a half-wavelength resonator (III). As shown in Figure 7B, increasing the number of segmented coplanar waveguide units can freely adjust the overall length of the transmission line. In the segmented coplanar waveguide transmission line structure (Liu, 2021; Yang Y. et al., 2023), the coplanar waveguide part is made of metallic copper, the conductivity is 5.8 × 10⁷ S/m, the thickness is 0.018 mm, the dielectric substrate (IV) uses a dielectric constant of 3.5, and the loss tangent tan δ is 0.0027 Polyimide material, thickness is 0.05 mm, and other structural parameters are shown in Table 2. Because the SCPW transmission line uses ultra-thin copper film and flexible polyimide materials, it has good flexibility and can meet the needs of flexible electronic devices.

Figure 7

Figure 7. Illustration of segmented coplanar waveguide model. (A) Transmission line; (B) unit structure.

Table 2

Table 2. Segmented coplanar waveguide parameters.

3.2 Performance evaluation when loaded with metamaterial structures

3.2.1 Design structure

Metamaterial structures have good control and absorption capabilities for electromagnetic waves due to their extraordinary physical properties. By changing the constituent materials, they can also meet the flexibility needs of flexible electronic devices. Since high-frequency metamaterials can easily achieve ultra-thin thickness, they are closely related to high-frequency transmission lines have good adaptability. Unlike most traditional electromagnetic shielding methods that suppress radiation through reflection (Li et al., 2021; Jiang and Xu, 2023), the metamaterial structure has characteristics such as negative magnetic permeability and negative dielectric constant, and can control the transmission line by regulating and absorbing electromagnetic waves. It can achieve good shielding performance at high frequencies while reducing transmission loss and ensuring signal transmission quality.

The flexible transmission line shielding structure loaded with metamaterial structure consists of three parts, as shown in Figure 8, which are the transmission line, the dielectric spacer layer and the metamaterial shielding layer. Among them, the transmission line is placed at the bottom of the overall structure. The metamaterial shielding layer is located on the top layer and consists of an array of metamaterial structural units. Between the two is a dielectric spacer layer, which is used to isolate the upper and lower parts and form a certain distance between the transmission line and the metamaterial array to ensure that the metamaterial shielding structure can work normally.

Figure 8

Figure 8. Transmission line model with metamaterial loading.

The metallic copper used in the metamaterial pattern and metal backplane has a conductivity of 5.8 × 10⁷ S/m and a thickness t₁ of 0.018 mm. Polyimide material, having a thickness of t₂ 0.48 mm, a dielectric constant of 3.5, and a loss tangent tan δ of 0.0027, makes up the dielectric substrate. Since a metal backplane entirely encloses one side of the dielectric substrate, there is no electromagnetic wave transmission.

The overall structure of the segmented coplanar waveguide transmission line loaded with metamaterial is depicted in Figure 9A. From bottom to top are the segmented coplanar waveguide transmission line, dielectric spacer layer and metamaterial shielding layer. Among them, the segmented coplanar waveguide transmission line is consistent with the structural parameters introduced previously. The dielectric spacer layer is made of polyimide material with the same structure as the upper and lower layers, with a thickness of 0.15 mm, ensuring the flexibility of the overall structure. The metamaterial shielding layer is composed of 12 metamaterial units arranged along the signal transmission direction of the transmission line, as shown in Figure 9B.

Figure 9

Figure 9. Segmented coplanar waveguide with metamaterial. (A) Segmented coplanar waveguide transmission line; (B) shielding layer of metamaterial.

3.2.2 Electromagnetic parameter analysis

The metamaterial structure can absorb the radiation of high-frequency flexible transmission lines and change the electromagnetic properties such as the amplitude, phase and polarization of the reflected components, so it has less impact on the transmission performance (Huang et al., 2023). The S-parameter comparison of the segmented coplanar waveguide transmission line before and after adding a metamaterial shielding structure is shown in Figure 10. Since the metamaterial structure regulates and absorbs the radiated electromagnetic waves of the transmission line, it effectively reduces the reflection component of the radiation wave. Compared with the segmented coplanar waveguide without a shielding structure, due to the parasitic capacitance and parasitic inductance generated by the coupling of the transmission line and the metamaterial structure, the operating frequency band of the metamaterial structure will be shifted to a certain extent, which in turn affects the transmission characteristics of the transmission line at 32–34 GHz. Moreover, the loss of the segmented coplanar waveguide transmission line increases significantly in some frequency bands, and the resonance point also moves toward the low frequency band. There is a certain offset, but it still maintains good transmission performance in the wide frequency bands of 23.49–30.96 GHz and 32.98–38.00 GHz.

Figure 10

Figure 10. Performance comparison of S-parameters with and without metamaterial. (A) S₁₁; (B) S₂₁.

3.2.3 Shielding effectiveness analysis

The designed metamaterial structure has a certain loss capability for electromagnetic waves, so in the working frequency band, it can efficiently suppress the electromagnetic radiation of flexible high-frequency transmission lines. Set up an electric field probe in the CST simulation software to simulate a 3 m far-field radiation test, and calculate the average value of the peak values in each radiation direction to analyze the shielding effectiveness (Huang et al., 2019; Huang et al., 2022). The comparison of the 3 m far-field electric field radiation intensity of the segmented coplanar waveguide transmission line before and after adding the metamaterial shielding structure is shown in Figure 11. To match the operating frequency of the metamaterial structure, the frequency range was limited to 22–29 GHz during the simulation test. It can be seen that, in this frequency band, the radiation intensity of segmented coplanar waveguide transmission lines without shielding structures is higher than −15 dB V/m, and the highest value is distributed near 22 GHz, which can reach −13.5 dB V/m. Therefore, when no shielding structure is loaded, the flexible segmented coplanar waveguide transmission line has a high radiation level in the operating frequency band. High-frequency radiation will have an irreversible impact on other components in the flexible PCB and affect the electromagnetic characteristics of the entire electronic system. A shielding structure needs to be designed to effectively suppress the radiation from segmented coplanar transmission lines. Use the following formula to calculate shielding effectiveness in Eq. 15

$\text{SE}=\log \left[\frac{E_0}{E_{\mathrm{s}}}\right](15)$

Figure 11

Figure 11. Electric field radiation intensity evaluation with and without metamaterial.

In the formula, $E_0$ and $E_{\mathrm{s}}$ are the electric field radiation values at the same position before and after shielding respectively. The shielding effectiveness of segmented coplanar waveguide transmission lines in the metamaterial operating frequency range can reach an average of 10.10 dB and a maximum of 12.63 dB. Therefore, the metamaterial structure can effectively reduce the electromagnetic radiation of high-frequency flexible segmented coplanar waveguide transmission lines.

The metamaterial structure has a good inhibitory effect on the electromagnetic radiation of the transmission line. On the one hand, the metamaterial may modify the transmission line’s surface electric field distribution and effectively control electromagnetic waves. Figure 12 compares the segmented coplanar waveguide transmission line’s surface electric field distribution before and after the metamaterial shielding structure was added. Without shielding, the surface electric field value is still higher in the edge area of the ground line of the transmission line, and the amount of outward radiation is larger. After adding the shielding structure, the surface electric field distribution range has been reduced and is limited to the ground area of the segmented coplanar transmission line. Moreover, at the three frequencies of 23 GHz, 25 GHz and 27 GHz, the surface electric field peak value of the segmented coplanar waveguide transmission line was reduced by 3.0 dB mV/m, 2.6 dB mV/m and 0.8 dB mV/m respectively. On the other hand, cavities can be formed to confine electromagnetic waves within a shielding structure. The electric field distribution of the overall structure of the transmission line after loading the shielding structure was calculated, and the results are shown in Figure 13 (the frequency is set to 27 GHz). It can be seen that the electromagnetic waves are bound in the whole structure composed of the transmission line and the shielding array. The metamaterial structure utilizes the electromagnetic resonance effect regulates and absorbs electromagnetic radiation. As can be seen from Figure 13, the electric field distribution is confined to the desired level after utilization of metamaterial structure in the transmission line.

Figure 12

Figure 12. Surface electric field distribution at different frequencies with and without metamaterial. (A) 23 GHz (no shielding); (B) 25 GHz (no shielding); (C) 27 GHz (no shielding); (D) 23 GHz (with shielding); (E) 25 GHz (with shielding); (F) 27 GHz (with shielding).

Figure 13

Figure 13. Overall structure electric field distribution when frequency is 27 GHz.

4 Actual measurement and performance evaluation

After theoretical analysis and simulation, in order to further verify that the metamaterial structure has little impact on the flexibility and transmission properties of the segmented coplanar waveguide transmission line before and after loading the metamaterial shielding structure was processed, and the conductor copper was printed on the dielectric polyimide material with a constant of 3.5, the actual object is shown in Figure 14. Flexibility analysis was conducted on the actual object, and the images of the bending test proved that the flexibility of the flexible transmission line can still be maintained after using the metamaterial structure of the flexible dielectric substrate. To weld the high-frequency SMA adapter to connect the vector network analyzer for S-parameter measurement, a test transition structure is designed when processing various high-frequency flexible transmission lines.

Figure 14

Figure 14. Proposed prototype. (A) no shield; (B) with test 1 bend; (C) with metamaterial; (D) with test 2 bend.

The processed segmented coplanar waveguide transmission line was tested, and the actual measurement environment is shown in Figure 15. The comparison of the measured and simulated S-parameters before and after adding the metamaterial shielding structure and with bending is shown in Figure 16. It can be seen that the transmission bandwidth of the two is basically the same, but the measured transmission loss has increased significantly. There are certain differences between the simulation and actual measurement results. On the one hand, there is a certain processing error due to insufficient process accuracy, which will cause parasitic parameters and impedance discontinuities in the transmission line structure, causing an increase in transmission loss. This effect occurs at high frequencies. On the other hand, the transition structure designed by welding SMA adapters, as well as high-frequency SMA adapters, will bring certain transmission losses. Furthermore, Figure 16 depicts that the measured and simulated reflection and transmission coefficients with and without bend (with shielding and without shielding) have approximately similar results which validated that the proposed structure enable stable performance in bending or none-bend position.

Figure 15

Figure 15. Experimental setup and analysis. (A) no shielding; (B) with metamaterial.

Figure 16

Figure 16. Comparison of simulation and measured results of the proposed structure with and without bend and shielding. (A) S₁₁; (B) S₂₁.

In addition, as shown in Table 3, compared with existing metamaterial structures, the structure designed in this paper is smaller in size and achieves good control over electromagnetic waves in a wide frequency band, so it has the characteristics of miniaturization and wide frequency band.

Table 3

Table 3. Performance comparison of proposed and existing designs.

5 Conclusion

This paper proposes a low-reflection radiation shielding solution to address the electromagnetic interference problem of high-frequency flexible transmission lines, which uses metamaterial structures to regulate and absorb radiation waves. The overall structure consists of transmission lines, dielectric spacers and metamaterial shielding layers. The media are all made of flexible materials to ensure flexibility. To verify the effectiveness of the solution, a miniaturized broadband metamaterial structure operating at 23.10–28.30 GHz and a high-frequency transmission line with segmented coplanar waveguide characteristics operating were designed and tested. The results show that the metamaterial shielding array is effective for segmented coplanar waveguide transmission lines. The electric field radiation in the 3 m far field achieves an average shielding efficiency of 10.10 dB and a maximum shielding efficiency of 12.63 dB, with little impact on transmission quality. It can maintain transmission performance in the wide frequency bands of 23.49–30.96 GHz and 32.98–38.00 GHz. The metamaterial structure can also be miniaturized at high frequencies, with a thickness of only 0.04λ₀, and the use of flexible dielectric substrates can ensure the flexibility of flexible transmission lines. Therefore, using metamaterial structures to suppress electromagnetic radiation has great application potential in high-frequency flexible electronic devices. Follow-up work can further study high-frequency transmission lines loaded with metamaterial shielding structures from the perspective of building theoretical models.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

Author contributions

IK: Data curation, Project administration, Software, Supervision, Visualization, Writing–original draft. AA: Formal Analysis, Investigation, Methodology, Resources, Validation, Writing–original draft. P-CW: Conceptualization, Data curation, Formal Analysis, Visualization, Writing–original draft. IH: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing–original draft.

Funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP 2024R435), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. National Science and Technology Council 112-2811-E-005-011-MY2 and 112-2634-F-005-001-MBK.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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