Lei Sang, Shuaitao Li, Bin Hu, Kehan Dai, Mark Kraman, Hong Yang, Wen Huang
IMAGE LICENSED BY INGRAM PUBLISHING
This article elaborates on the general design route of stretchable microstrip patch antennas, which are fabricated on polydimethylsiloxane (PDMS) soft substrates. Compared to conventional counterparts on rigid substrates, the stretchability brings about the change of both the overall physical dimensions and the electrical parameters of the materials. Being different from the traditional design route, the deformation parameters are involved into the classical design equations of the microstrip patch antenna. Based on the improved equations, the reconfigurable antenna is able to work at multiple frequency points by using a comprehensive optimization algorithm. For demonstrative purpose, a microstrip patch antenna on PDMS is designed, fabricated, and measured. The demonstrative patch antenna shows nearly the same electrical performance as expected from finite-element method modeling when the center operating frequency is tuned from 6 to 4.9 GHz under a strain of up to 20%. Compared with the simulated results of a conventional design with strain of 5% to 20%, the realized gains have increased by 0.9 dBi (0% strain at 6 GHz), 0.9 dBi (5% strain at 5.7 GHz), 1.9 dBi (15% strain at 5.2 GHz), and 0.8 dBi (20% strain at 4.9 GHz), respectively, by using the strain domain involved design method.
With the rapid development of a diverse variety of electronic technologies, such as bionic robots [1] [2], wearable electronics [3], [4], and artificial organs [5], [6], there is an ever-increasing demand to fabricate electronic systems that are mechanically flexible [7], [8]. However, as a central component in wireless communication systems, high-frequency circuits fabricated on rigid substrates are unable to meet this new standard [9], [10]. Therefore, in the past decade, novel circuits demonstrated on elastomer materials have attracted widespread attention and have been developing rapidly, especially for dc and low-frequency applications [11], [12]. However, trends in technology development require higher operating frequencies to facilitate wider communication bandwidth, which challenges microwave devices and circuit designs on stretchable substrates under complex forms of deformation [13], [14]. For flexible devices, the elasticity of the substrate has the greatest influence on the design of the microwave antenna. Many important issues remain unsolved, such as how to adjust the traditional antenna design paradigm to accommodate the properties of elastic substrates [15], [16], [17].
Naturally, a stretchable microstrip patch antenna is reconfigurable. Narrow-band stretchable antennas can be highly sensitive to substrate deformation and need to be discussed more strictly, while relative insensitivity of wide-band antennas to substrate deformation can be assumed. Considering that mainstream wireless communication systems, such as wireless local area network 5.8-GHz frequency band, is divided into multichannels from 5.15 to 5.85 GHz, a slight deformation of the substrate and the conductive layer could have a significant impact on the performance of the antenna and the electronic system [18], [19]. Therefore, according to the requirements of the above application scenario, it is important to develop a design route for stretchable antennas to properly consider the dynamic dimensions and the dynamic parameters of the material’s properties accordingly [20], [21]. The performance of the antenna will then become a function of not only the frequency, but also a function of the strain. At present, most of the achievements of stretchable antennas are focused on elastic materials, such as in [18], [19], [20], [21], [22], [25], [26], [27], [28], and [29]. Other studies take the change of tensile length into account, but ignore the change of other deformation dimensions or the change of material electrical parameters when the substrate is stretched [22], [23], [24].
Taking into account all of the variations of physical dimensions and the change of material electrical parameters induced by stretching, in this article a general design method involving the strain domain for stretchable microstrip patch antennas is proposed. The theoretical relationship between the antenna performance and the deformation parameters are established. As a result, the initial sizes of the soft antenna are able to be optimized, especially when there are multireconfigurable operating frequency points. Compared to traditional design methods, there are two novel concepts in this article:
With the improved design method, the initial sizes of the soft antenna and the stretching scale is able to be optimized by using the improved equations and design flow in the article.
To demonstrate the design route, the design of a reconfigurable microstrip patch antenna is chosen as an example. As for the choice of substrate materials, PDMS has good tensile property of more than 50%, suitable relative dielectric constants of 2 to 5, and good skin affinity, which make it an excellent material for the fabrication of high-frequency stretchable antennas [25], [26], whereas conventional conductor layers have almost no obvious tensile properties [27], [28]. To improve the tensile property of the conductor layer, the “prestrained†processing is used in the fabrication of the conductive layer [29].
Compared to the design route of a conventional flexible antenna, there is, in addition to the frequency domain, the strain domain that needs to be considered throughout the design of a stretchable antenna. Besides the effect on the physical dimensions of the antenna itself, the strain domain is critical due to the transformation of the dielectric and conductive material properties from constants to strain-dependent values. As the electrical performance of the antenna is related to the structural dimensions, stretchable antennas are characteristically reconfigurable microwave devices. The general design strategy aims to achieve the best overall electrical performance at all desired operating frequencies. By engineering the strain needed at each frequency to achieve the desired performance relative to the initial physical dimensions of the antenna, optimum overall performance can be achieved. As shown in Figure 1, the design route could be divided into five main steps.
Figure 1. General design route for a stretchable patch antenna.
Taking a stretchable patch antenna on a PDMS substrate as an example, the detailed step-by-step design route considering the frequency and the strain domains simultaneously is illustrated below. For the first step, the quantitative relationship among outline dimensions (length L, width W, and thickness H) of the PDMS substrate are calculated by (1) to (3), while the strain is applied uniaxially along the direction of the electromagnetic wave transmission. St is the strain ratio parameter, t is the Poisson coefficient; L0, W0, and H0 are the length, width, and thickness of the PDMS substrate under the normal state, respectively.
Although the outline of the whole soft substrate is linear with the strain ratio, the deformation is not completely uniform on the whole substrate according to the simulated results with Ansys Workbench [shown in Figure 2(a)]. Corresponding to the position of the stretching PDMS substrate, the straining change curves of the antenna structure parameters are derived, as shown in Figure 3.
Figure 2. Schematic view of the structure of a stretchable patch antenna after the tensile is applied in the indicated direction. (a) Simulated displacement of the PDMS substrate under the tensile in Ansys Workbench. (b) The configuration and critical dimensions of the patch antenna.
Figure 3. Straining change curves of the antenna structure parameters.
The next step is to acquire the change curves of the critical material electrical parameters varied with the strain. As metal layer will crack with the stretching, the conductivity of the metal layer will decline rapidly [30]. The numerical values of the conductivity of the stretched conductor layer were tested by using the probe method, as shown in Figure 4(a). Due to the prestrain process, the downward trend of the conductivity is mitigating. The conductivity is about 106 S/m when strain ratio is 20%. Another parameter is the relative dielectric constant of the PDMS. The numerical values of the relative dielectric constant of the PDMS shown in Figure 4(b) were measured using a Keysight dielectric probe kit. The relative dielectric constant is 2.7 under normal state, while it increases to 2.95 when the strain ratio is 35%.
Figure 4. (a) The change of conductivity of the conductor layer versus strain. (b) The change of relative dielectric constant versus strain.
Figure 5 shows the direct observation of the surface morphology of the Au/Ni metal conductor layer under different biaxial poststrain conditions. Under a high-magnification optical microscope, the surface morphology of the Au/Ni metal offers an appearance akin to a “fishing net†at the micrometer scale in Figure 5(a). Under a larger poststrain of 25% as shown in Figure 5(b), the “fishing net†contains smaller crack domains. However, the size of discontinuities between domains changes minimally and is negligibly small compared to the operating wavelength of the antenna in the gigahertz range. Radio frequency (RF) signals are able to pass across the discontinuities between metal domains easily by large electrical field coupling. If we want to repair the cracks and improve the conductivity, we can also brush the stretched surface with an elastic conductive liquid like electrical conductive composites.
Figure 5. The size comparison of cracked microdomains under different strain magnitudes. (a) Biaxial strain of 10%; (b) biaxial strain of 25%.
The next step is to determine the range and initial dimensions of the stretchable patch antenna with consideration of the desired operating frequency, bandwidth, and maximum allowable strain, which, in this work, are set to be within the popular commercial wireless frequency band from 4.9 to 6 GHz, with a step size of ∼0.3 GHz, a bandwidth of 100 MHz, and strain of 35% (permissible maximum strain ratio), respectively. Therefore, the lowest limit of the patch antenna’s initial length Lp,min and width Wp,min are determined with the maximum operating wavelength at 4.9 GHz, when the substrate is strained to 35%, i.e., the maximum strain specification. In this case, the initial patch antenna length ${L}_{{p},{\min}}\,{\times}\,{1.35}$ should be larger than half of the maximum wavelength at 4.9 GHz. Oppositely, the upper limit of the patch antenna length Lp,max and the width Wp,max can be calculated by the minimum operating wavelength at 6 GHz and a strain of 0%. Involving the strain ratio parameters S to the conventional design equations for patch antennas and the above limitations, the values of Lp,min, Wp,min, Lp,max, and Wp,max can be calculated using (4) to (10), shown below. \begin{align*}{L}_{{p},{\min}} & = \frac{1}{{2}{f}_{\max}\,{\times}\,{\left({1} + {St}\right)}{\sqrt{{\varepsilon}_{\text{eff}}{\mu}_{0}{\varepsilon}_{0}}}}{-}{2}{\Delta}{L} \tag{4} \\ {W}_{{p},{\min}} & = \frac{1}{{2}{f}_{\max}{(}{1}{-}{\rho}\,{\times}\,{St}{)}{\sqrt{{\mu}_{0}{\varepsilon}_{0}}}}{\sqrt{\frac{2}{{\varepsilon}_{r}{(}{St}{)} + {1}}}} \tag{5} \\ {L}_{{p},{\max}} & = \frac{1}{{2}{f}_{\min}\,{\times}\,{\sqrt{{\varepsilon}_{\text{eff}}{\mu}_{0}{\varepsilon}_{0}}}}{-}{2}{\Delta}{L} \tag{6} \\ {W}_{{p},{\max}} & = \frac{1}{2{f}_{\min}{\sqrt{{\mu}_{0}{\varepsilon}_{0}}}}{\sqrt{\frac{2}{{\varepsilon}_{r}{(}{St}{)} + {1}}}} \tag{7} \\ {\varepsilon}_{\text{eff}} & = \frac{{\varepsilon}_{r}{(}{St}{)} + {1}}{2} + \frac{{\varepsilon}_{r}{(}{St}{)}{-}{1}}{2}{\left[{{1} + {12}\frac{H(St)}{{W}_{p}}}\right]}^{{-}\frac{1}{2}} \tag{8} \\ {\Delta}{L} & = {0.412}\,{\times}\,{H}{(}{St}{)}\frac{{\left({\varepsilon}_{\text{reff}} + {0.3}\right)}{\left(\frac{{W}_{p}}{H(St)} + {0.264}\right)}}{{\left({\varepsilon}_{\text{reff}}{-}{0.258}\right)}{\left(\frac{{W}_{p}}{H(St)} + {0.8}\right)}} \tag{9} \\ {R}_{c} & = \sqrt{\frac{{{\omega}{\mu}}_{0}}{{2}{\sigma}{(}{St}{)}}} \tag{10} \end{align*} in which, the conductivity v(St) and relative dielectric constant fr(St) change with the strain of the substrate, as shown in Figure 4. Rc is the resistance loss introduced by a metal patch. ΔL is a correction factor for the edge truncation effect of the electromagnetic field. The calculated values of Lp,min, Wp,min, Lp,max, and Wp,max are 12, 16, 16, and 20 mm, respectively. The differences with the traditional equations are as follows:
With a step size of 0.5 mm for patch antenna length Lp and width Wp in the above corresponding range, the desired electrical performance is then evaluated on all possible combinations of values of Lp0 and Wp0 by only modeling the patch structure with two assumptions:
Among typical antenna performances, such as the antenna gain, return loss, radiation pattern, efficiency, etc., the desired performance could be different depending on the application scenario. Therefore, an evaluation parameter ZLpn,Wpn is defined to represent the overall performance of a stretchable patch antenna with the nth initial physical dimension combination of Lp0 and Wp0. \[{Z}_{LpnWpn} = {q}_{1}\,{\times}\,{\text{Return loss}} + {\text{Gain}} + {q}_{3}\,{\times}\,{\text{Efficiency}} + {\ldots}, \tag{11} \] where ${q}_{1},{q}_{2},{q}_{3},{\ldots}$ are weight coefficients. In this work, other than q1 = 1, all of the other weight coefficients are zero to simplify the demonstration. At each desired operating frequency point, the value of the evaluation parameter ZLpn,Wpn is calculated as shown in Figure 6.
Figure 6. The return loss of the demonstrative stretchable patch antenna evaluated with all reasonable combinations of the initial patch length of Lp and width of Wp: (a) 4.9 GHz, (b) 5.2 GHz, (c) 5.4 GHz, (d) 5.7 GHz, (e) 6.0 GHz. (f) Evaluated average added-up results at all frequencies.
Then, an optimum combination of stretchable patch antenna with initial length Lp0 of 14 mm and width Wp0 of 18 mm is found where the ${\mathop{\Sigma}_{{f}1}^{{f}{5}}{Z}_{Lpn,\,Wpn}}{(}{f}{)}$ the maximum value of 19.81 dB, and f represents the desired discrete operating frequency points array of {f1 = 4.9 GHz, f2 = 5.2 GHz, f3 = 5.4 GHz, f4 = 5.7 GHz, f5 = 6.0 GHz}. The corresponding discrete strain points array is {St1 = 20% at f1, St2 = 15% at f2, St3 = 10% at f3, St4 = 5% at f4, St5 = 0% at f5}.
The next critical design step is to determine the type of antenna feedline and its initial physical dimension. Knowing the optimum dimensions of the patch, the input impedance [Zp(f)] at the junction of the patch and feedline shown in Figure 2 can be calculated by (12) to (14): \begin{align*}{Z}_{p} & = \frac{1}{{2}{\left({G}_{1} + {G}_{2}\right)}} \tag{12} \\ {G}_{1} & = \frac{1}{120{\pi}^{2}} \mathop{\int}\nolimits_{0}\nolimits^{\pi}{{\left[{\frac{{\sin}\left({\frac{{k}_{0}{W}_{p}}{2}{\cos}\,{\theta}}\right)}{{\cos}\,{\theta}}}\right]}^{2}}{\left({{\sin}\,{\theta}}\right)}^{3}{d}{\theta} \tag{13} \\ {G}_{12} & = \frac{1}{120{\pi}^{2}} \mathop{\int}\nolimits_{0}\nolimits^{\pi}{{\left[{\frac{{\sin}\left({\frac{{k}_{0}{W}_{p}}{2}{\cos}\,{\theta}}\right)}{{\cos}\,{\theta}}}\right]}^{2}{J}_{0}{(}{k}_{0}{L}_{p}\,{\sin}\,{\theta}{)}}{\left({{\sin}\,{\theta}}\right)}^{3}{d}{\theta} \tag{14} \end{align*} \begin{align*}{S}_{11} & = \frac{\frac{{T}_{11} + {T}_{12}}{{Z}_{0}{-}{T}_{21}{Z}_{0}{-}{T}_{22}}}{\frac{{T}_{11} + {T}_{12}}{{Z}_{0} + {T}_{21}{Z}_{0} + {T}_{22}}} \tag{15} \\ {T} & = {T}_{1}\,{\cdot}\,{T}_{2} = {\left[\begin{array}{cc}{{\cosh}\,{\gamma}{l}_{1}}&{{Z}_{1}{\sinh}\,{\gamma}{l}_{1}}\\{\frac{{\sinh}\,{\gamma}{l}_{1}}{{Z}_{1}}}&{{\cosh}\,{\gamma}{l}_{1}}\end{array}\right]}{\left[\begin{array}{cc}{{\cosh}\,{\gamma}{l}_{2}}&{{Z}_{2}{\sinh}\,{\gamma}{l}_{2}}\\{\frac{{\sinh}\,{\gamma}{l}_{2}}{{Z}_{2}}}&{{\cosh}\,{\gamma}{l}_{2}}\end{array}\right]} \tag{16} \\ {e} & = \frac{\mathop{\sum}\limits_{{f}_{n}}{{\text{abs}}{\left({S}_{11,{f}_{n}}{-}{S}_{11{T}}\right)}}}{N} \tag{17} \end{align*} where k0 is the wavenumber and J0 is the zero-order Bessel function of the first kind. The calculated value of the input impedances Zp(f) array is {Zp(f1) = 400.01 Ω, Zp(f2) = 354.3 Ω, Zp(f3) = 322.6 Ω, Zp(f4) = 281.6 Ω, Zp(f5) = 257.4 Ω}. For the two-order microstrip impedance matching line with a reactance groove chosen as the feedline of the stretchable patch antenna shown in Figure 2(b), six-dimension parameters can be determined by using impedance matching optimization. The return loss S11 at the input port can be derived based on the transmission matrices T of the feedline shown in (15), and the expression of T shown in (16), where T1, T2, Z1, and Z2 are the transmission matrix and the characteristic impedances of the first and the second order of the feedline, respectively. Then, the weighted error function e shown in (17) is defined as the convergence condition with a targeted return loss S11T of 20 dB, where parameter N is the number of discrete sampled frequency points fn.
The optimized initial dimensions of the feedline structure are as follows: MW10 = 1.7 mm, MW20 = 0.8 mm, ML10 = 2.6 mm, ML20 = 7 mm, PW10 = 14.5 mm, and PL10 = 0.6 mm, respectively. After the initial dimensions and the strain ratio calculating, a complete strain involved 3D model in HFSS is still necessary to validate the design.
In conventional designs of a soft antenna, only lengthwise change brought by strain ratio is considered [19], [20], [21]; relative dielectric constant and structure dimensions (W, H) are taken to be unchanged. To validate the proposed strain involved design method, the antenna is also designed by using a conventional method and simulated in HFSS. The simulated S-parameters S11 and the realized gain of the patch antenna under applied strain from 0 to 20% with and without using the proposed design are compared in Figure 7(a) and (b), respectively. In the legend, “ori†means 0% strain, “St5†means 5% strain, “St10†means 10% strain, “St15†means 15% strain, and “St20†means 20% strain, respectively. Prefix C means design using the conventional method.
Figure 7. Comparison of the stretchable patch antenna performance designed by using the proposed method and conventional method. (a) The realized gain of the two patch antennas (in the legend, capital letter “C†means design using the conventional method). (b) The return loss of the two patch antennas. (c) The comparison of the realized gain at the five designed frequency points. (d) The comparison of the return loss at the five designed frequency points.
In the conventional design route, the central frequency point 5.4 GHz (10% strain) is chosen as the main optimized frequency. The simulated result shows that the proposed antenna reliably achieves 2.2 dBi realized gain, which is 0.1 dBi lower than that of the antenna using the conventional design method. However, in other reconfigurable frequency points caused by stretching, except for the shifted operating frequency point, the maximal realized gains are decreased by 0.9 dBi (0% strain at 6 GHz), 0.9 dBi (5% strain at 5.7 GHz), 1.9 dBi (15% strain at 5.2 GHz), and 0.8 dBi (20% strain at 4.9 GHz), respectively, when using the conventional method.
To evaluate the strain domain involved design method, the stretchable antenna was fabricated using the prestrain process and then the metal area was brushed with conductive silver paste. The photo of the stretchable antenna sample with 20% strain is displayed in Figure 8(a).
Figure 8. Stretch testing and radiation properties measurement scenario for the two antennas. (a) The stretchable microstrip patch antenna. (b) Near-field testing system.
The electrical performance of the stretchable patch antenna was tested in a microwave anechoic chamber with a near-field testing system as shown in Figure 8(b). An RF signal was generated at one port of the vector network analyzer (ZNA43 from Rohde & Schwarz) and amplified by a power amplifier, then radiated outside of the stretchable antenna. The RF signal was then received by a standard probe. The fixture was away from the patch and kept out of the primary radiating direction, so its impact could be ignored.
The measured return losses, gains, and radiation patterns of the stretchable microstrip patch antenna under the relaxed and stretched states are shown in Figure 9. As shown in Figure 9(a), the measured patterns have a good agreement with the simulation data in the main beam lobe. As shown in Figure 9 (b) and (c), under different strain magnitudes, the operating frequency can be reconfigured. By stretching the antenna longitudinally, the central operating frequency can be tuned to 6, 5.4, or 5 GHz with the maximum realized gain gradually decreasing from 5.0 dBi to −0.1 dBi. The reason for this reduction is that the equivalent conductivity decreases with the stretching. Compared to the simulated data, there are about ±0.2 dB error in the reconfigured (poststrained) points. The primary reason for this discrepancy is due to the cracking in the Au/Ni metal bilayer caused by the applied strain. Compared to the simulated center frequency points, which are at 6, 5.4, and 4.9 GHz, the measured center frequency points drift slightly to 5.95 GHz (relaxed status), 5.45 GHz (with a strain of 10%), and 4.95 GHz (with a strain of 20%), respectively. As shown in Figure 9(d), the measured total efficiency is higher than the simulated result under 20% strain state. The reason is that we brushed the metal surface with the silver paste, which repaired the cracks and improved the conductivity of the stretchable metal layer.
Figure 9. Experimental data compared with simulation results for the stretchable microstrip patch antenna. (a) Radiation patterns and cross-polarization levels on the XOZ-plane and the YOZ-plane in relaxed states (6 GHz), stretched state with an applied strain of 10% (5.4 GHz), and strain of 20% (4.9 GHz), respectively. (b) Reflection coefficients. (c) Realized gain. (d) Total efficiency.
A comparison of the main performance of the designed stretchable antenna with several reported state-of-the-art works are summarized in Table 1.
Table 1. Comparison with relevant literature.
A general design route involving the strain domain for a reconfigurable microstrip patch antenna on a PDMS soft substrate is proposed and demonstrated. Conductivity of the conductor layer and the relative dielectric constant of the PDMS substrate under varied magnitudes of strain are investigated. Moreover, the deformation parameters of the soft antenna are simulated and analyzed. Then, variations of electrical and structural parameters are integrated into the equations and simulation model. Compared to the conventional patch antenna design, the optimal initial physical dimensions can be calculated with considerations of performance with respect to both frequency and strain change. Following the proposed design route, the measurement results of an example antenna show desired and controlled frequency reconfigurability with strain variation. The electrical performance perfectly matches the simulation data, which validates the reliability of the design route. The strain domain involved design route for soft antennas can also be a good paradigm to the design of other soft microwave devices. The reduction of gain and efficiency caused by the conductivity decline could be improved using more ductile conductive materials like nanotube, graphene, and AgI-based composites.
As a method to realize reconfigurable performance, the stretchable antenna may have some irreplaceable advantages and practical usage, such as the following:
This work was supported by the National Key Research and Development Program of China (2021YFA0715301). Wen Huang is the corresponding author.
Lei Sang (sanglei2008@126.com) is with the School of Microelectronics, Hefei University of Technology, Hefei 230009, China. He is a Senior Member of IEEE.
Shuaitao Li (1275523508@qq.com) is with the School of Microelectronics, Hefei University of Technology, Hefei 230009, China.
Bin Hu (2020111239@mail.hfut.edu.cn) is with the School of Microelectronics, Hefei University of Technology, Hefei 230009, China.
Kehan Dai (2557732213@qq.com) is with the School of Microelectronics, Hefei University of Technology, Hefei 230009, China.
Mark Kraman (mkraman2@illinois.edu) is with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, IL 61801, USA.
Hong Yang (yanghong@cesi.cn) is with the China Electronics Standardization Institute, Beijing 100007, China.
Wen Huang (huangw@hfut.edu.cn) is with the School of Microelectronics, Hefei University of Technology, Hefei 230009, China. He is a Senior Member of IEEE.
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Digital Object Identifier 10.1109/MAP.2023.3301387
