Introduction
Flexible, wearable, and compact electronics have rapidly evolved over the last decade, transforming diverse applications and technological interactions [Reference Kazanskiy, Khonina and Butt1]. With the ability to bend, stretch, and conform to various shapes, wearable electronic devices are revolutionizing both medical and nonmedical industries [Reference Sayem, Lalbakhsh, Esselle, Buckley, O’Flynn and Simorangkir2].
On the other hand, compact electronics are crucial in health-care field where small size and precision are essential [Reference Chan, Iyer, Wang, Lyness, Kooner, Sunshine and Gollakota3]. In Internet of things (IoT) applications, they can be easily embedded into various objects and environments, enabling seamless connectivity and data collection. Additionally, smaller devices can lower overall costs by using fewer materials and simplifying production processes [Reference Perwej, Omer, Sheta, Harb and Adrees4]. For instance, the study in [Reference Hong, Mehlman and Katti5] presents a smartphone device equipped with six different antennas, catering to various standards (GPS, Bluetooth, WiFi, GSM, etc.).
To achieve a compact and high-performing antenna in wireless body area network (WBAN) and energy harvesting applications, the antenna dimensions are primarily governed by electrically small antenna (ESA), which was firstly introduced by Wheeler in 1947 [Reference Wheeler6]. Several ESA techniques are highly effective, including geometric alterations such as adding slots or slits, folded antennas, and short circuits [Reference Khan, Sharawi and Mittra7]. Additionally, the use of magneto-dielectric materials and the integration of metamaterials, particularly in patch antennas, were explored [Reference Tadesse, Acharya and Sahu8]. Another approach involved adding localized loads or segments of conductive line (capacitive or inductive) to artificially increase the electrical length of the antenna, thus lowering its resonant frequency [Reference Rowell and Murch9, Reference Sarrazin, Pflaum and Delaveaud10]. However, these miniaturization techniques often result in significant performance drawbacks, especially in the sub-GHz bands [Reference Kumar, Moloudian, Simorangkir, Gawade, O’Flynn and Buckley11]. The complexity and non-planarity of folded antenna geometries frequently result in reduced gain and directivity. Furthermore, their low efficiency increases the back-lobe levels, as demonstrated in various studies [Reference Khan, Sharawi and Mittra7, Reference Sarrazin, Pflaum and Delaveaud10]. This is primarily due to the absence of a standardized design procedure. In addition, the use of high dielectric material substrates for low-frequency designs significantly limits bandwidth and incurs high costs [Reference Xu and Wei12]. Metamaterial integration also results in very low gain and impedance bandwidth [Reference Alibakhshikenari, Ali, Soruri, Dalarsson, Naser-Moghadasi, Virdee, Stefanovic, Pietrenko-Dabrowska, Koziel and Szczepanski13]. Consequently, most ESAs exhibit limited bandwidths and radiation efficiency, while those with wider bandwidths, higher gain, and improved efficiency tend to have lower miniaturization factors.
To address these challenges, integrating artificial reflectors based on metasurfaces offers a balanced solution by maintaining performance while reducing electrical size. These structures consist of periodic arrays of sub-wavelength scatterers, which significantly enhance antenna performance in terms of gain, impedance bandwidth, and front-to-back ratio (FBR) [Reference Yi, Mu, Han and Li14]. Moreover, artificial magnetic conductor (AMC) structures are particularly beneficial for improving antenna performance and reducing electromagnetic absorption by the human body [Reference Dey, Kumar, Arif and Anguera15].
In this work, we demonstrate a parasitic element (PE) behavior inspired by AMC properties, combining the advantages of both PEs and AMCs, an approach rarely exploredin current research. For instance, recent studies [Reference Malekpoor16, Reference Malekpoor and Abolmasoumi17] have demonstrated novel AMC unit cells utilizing rhomboid coupled parasitic patches and techniques involving planar parasitic patches and stacked elements.
This article proposes a compact, flexible dual-band antenna design with a PE-inspired AMC, covering the GSM band (880–990 MHz) and the WiFi band (2.25–3.22 GHz). The Section “Comparison of Two Proposed Antenna Configurations” compares the performances of two compact monopole antennas fed by a coplanar waveguide (CPW). The Section “Two Proposed AMC Variants” focuses on the configuration of the proposed AMC designs. In addition, this Section conducts a parametric study of the designed single element to identify the AMC and PEC (perfect electric conductor) phase regions. The fabrication process of the designed system is thoroughly detailed in the Section “Fabrication Steps for Antenna with AMC”, while the Section “Measurement and Analysis” characterizes the complete system with the AMC and under bending conditions. The final section discusses the contribution of the novel prototype to the concept of ESA comparing it with the classical approach and existing works.
Comparison of two proposed antenna configurations
The design of a conformable and wearable dual-band antenna on polymer substrates necessitates meticulous selection of a miniaturization technique, ensuring optimal performance at both operating frequencies. Figure 1 shows two selected designs for the dual-band monopole antennas, labeled N#1 and N#2. These designs are inspired by the conventional CPW monopole antenna [Reference Foroozesh and Shafai18].
Figure 1. Comparison of the two CPW-fed monopole antenna configurations and their geometrical dimensions (in mm): 
$L_{1,6}$ = 50, L 2 = 48, L 3 = 48.5, L 4 = 15.5, 
$L_{5,8}$ = 21.83, L 7 = 33.5, L 9 = 14.7, l 1 = 50, 
$l_{2,5}$ = 20.75, l 3 = 3.7, l 4 = 40, l 6 = 3.7, l 7 = 2, e 1 = 2, 
$e_{2,3,6,7}$ = 1.5, 
$e_{4,10}$ = 0.25, 
$e_{5,9}$ = 5.84, e 8 = 0.5, 
$h_\mathrm{copper\,foil}$ = 0.06, 
$h_\mathrm{Kapton}$ = 0.05, 
$h_\mathrm{PDMS}$ = 0.5.
The two compact antennas, each consisting of two resonant paths, are designed to operate at low frequency using 
$L_{2,7}$ and at high frequency using 
$L_{4,9}$. The theoretical values of the aforementioned parameters are determined using the following equation:
\begin{equation}
L_{2,4} = \frac{c}{4f_{1,2} \sqrt{\epsilon_r}}
\end{equation} where 
$f_{1,2}$, c, and ϵr represent the low and high frequency, the speed of light, and relative permittivity of the polydimethylsiloxane (PDMS) substrate, respectively. The theoretical lengths of L 2 and L 4 are 49.90 and 18.33 mm. After optimization with a high frequency structure simulator (HFSS) Optimetrics, L 2 and L 7 were set to 48 mm and 33.5 mm at 900 MHz and L 4 and L 9 to 15.5 mm and 14.7 mm at 2.45 GHz, respectively.
The parameters 
$e_{1,6}$, 
$e_{2,7}$, 
$e_{5,9}$, and 
$l_{2,5}$ were optimized to increase the impedance bandwidth of each antenna while maintaining a compact electrical size. Antenna N#1 is a threefold monopole antenna with a length of 0.285
$\lambda_{900\mathrm{M}}$ to which a stub of 0.13
$\lambda_{2.45\mathrm{G}}$ is added. However, antenna N#2 is a meander antenna with a length of 0.66
$\lambda_{900\mathrm{M}}$ and a spacing e8 of 0.5 mm, connected to a stub of 0.12
$\lambda_{2.45\mathrm{G}}$. The antenna structures are fed using a 50 Ω CPW line, with theoretical calculations based on paper [Reference Simons19]. The flexible substrate is made of PDMS, a transparent polymer with well-characterized dielectric properties of ϵr = 2.8 and tanδ = 0.008. A 65 µm-thick polyimide, adhesive Kapton is then added above the PDMS layer to improve the cohesion robustness of the overall antenna.
The radiation patterns and surface current distribution were plotted in Fig. 2 for each compact antenna. The folded design presents a classical omnidirectional radiation pattern in the H-plane at 900 MHz and 2.45 GHz. The E-plane radiation pattern at the lower frequency is asymmetrical due to the influence of the designed folded arm, which is oriented to one side of the surface, and the optimized length of the CPW line. At higher frequency, the antenna’s radiation is more symmetry radiated in the both planes.
Figure 2. Radiation patterns and current distribution of the folded and meander antennas in both planes: (a) & (c) at 900 MHz; (b) & (d) at 2.45 GHz, respectively.
The reduced electrical size of the antenna design N#1 (ka = 0.66, where a is the radius of the minimum enclosing sphere and k is the wave number) limits its radiation performance before integrating the single AMC element, particularly at sub-GHz frequencies. The results thus show a maximum gain (E-plane) of −1.25 and 3.33 dBi, a reflection coefficient S 11 of −20.3 and −36.5 dB, and an impedance bandwidth of 100 and 970 MHz for the two operating resonant frequencies, respectively. Nevertheless, the meander antenna N#2 exhibits an insufficient maximum gain of −1.61 and −0.58 dBi, with a matched S 11 and narrower impedance bandwidths of 60 and 35 MHz at 0.896 and 2.47 GHz. This is due to the proximity of the meander line to the 2.45 GHz stub, which induces undesired electromagnetic coupling, represented by parasitic capacitors. This results in reduced antenna efficiency (80%) and gain, a narrower bandwidth, and a disruption of radiation pattern symmetry within the 2.45 GHz frequency range. This is confirmed by the weak current concentration on the 2.45 GHz resonant stub, as illustrated in Fig. 2d. The FBRs, measured from the main lobe (
$\theta = 0^\circ$) to the back-lobe (
$\theta = 180^\circ$), are below 2 dB for both antenna designs. As shown in Table 1, this limitation poses a significant challenge for future advancements in on-body applications.
Table 1. Comparison of two compact dual-band antennas with different parameters
Two proposed AMC variants
Once the folded CPW monopole antenna is selected, two AMC patterns are proposed: AMC design #1 consists of a parasitic octagonal ring that affects the lower resonant frequency, centered by a patch octagon to resonate at the higher frequency. On the other hand, a second variant, AMC design #2, forms two octagonal rings, as shown in Fig. 3.
Figure 3. Configuration of the two AMC cells: octagonal ring centered with a patch octagon (AMC design #1) and two octagonal rings (AMC design #2). Geometrical dimensions (in mm): Lx = Ly = 60, 
$l_{y1}$ = 37.48, 
$l_{y2}$ = 
$l'_{y3}$ = 58.94, 
$l'_{y1}$ = 20.18, 
$l'_{y2}$ = 30.67, tx = 4.62, ty = 7.3, 
$t'_{x}$ = 7.85, 
$t'_{y1}$ = 5.15, 
$t'_{y2}$ = 6.28, a 1 = 15.3, a 2 = 18.37, a 3 = 
$a'_{4}$ = 24.41, 
$a'_{1}$ = 8.36, 
$a'_{2}$ = 12.7, 
$a'_{3}$ = 19.21.
The adjustment of the truncated corners aims to reduce the period of the cell surface to 60 × 60 mm2 with Lx = Ly less than 
$\lambda_{900\mathrm{M}}$/4. Adjusting the tx gap between the two octagonal patterns induces slight rightward shifts in the frequency of S 11 phase. This shift is linked to variations in the ty parameter, resulting in instability of zero phase of S 11 around 900 MHz. Remarkably, no such instability is discerned at 2.45 GHz. The reverse case involves adjustments to the 
$l_{y1}$ parameter. The thickness of the AMC substrate (5.5 mm 
$ \lt \lt \lambda$) impacts the 
$\pm90^{\circ}$ bandwidth of the S 11 phase, particularly at lower frequency. For pattern #2, the optimization primarily targeted the parameter 
$l'_{y1}$, which has the most pronounced impact on the performance of S 11 phase at 2.45 GHz, along with the gap 
$t'_x$, and the width 
$t'_{y2}$ for optimal performance at 900 MHz.
Each AMC cell was simulated independently in Ansys HFSS using periodic boundary conditions. As a result, the S 11 phases of the two AMCs overlap at around 900 MHz, as depicted in Fig. 4. Both patterns fall within the AMC phase range of 
$\pm 90^{\circ}$, as illustrated in Table 2, at both low and high frequencies. At 2.45 GHz, AMC #1 exhibits a broader bandwidth (8.57%) compared to AMC #2 (4.3%). This bandwidth sensitivity is influenced by variations in the thickness of the AMC substrate (
$h_\mathrm{PDMS}$) and parameters such as the widths of the octagonal patch and ring: 
$l_{y1}$, ty, 
$t'_{y1}$, and 
$t'_{y2}$.
Table 2. Comparison of two AMC variants with different parameters
λ 0: free-space wavelength computed at low-frequency band.
Figure 5 illustrates a comparison of the effect of oblique incident angles on the S 11 phase of AMC designs #1 and #2 in TE/TM polarizations. At 2.45 GHz, as the angle of incidence increases from 0∘ to 45∘, both patterns exhibit a similar frequency shift, with slight variations of 0.45% for AMC #1 and 0.53% for AMC #2. The stability of the zero phase at 2.45 GHz is evident in the dispersion diagram for AMC #1 pattern, as depicted in Fig. 6. It is observed in the dispersion diagram, Fig. 6, where the curves remains nearly flat along Γ-X around 2.45 GHz. The bandwidth decreases by approximately 2.95% (Fig. 5a) and 1.43% (Fig. 5b) with increasing oblique incidence angles.
Figure 4. S11 phase and magnitude followed by the surface current distributions of the two dual-band AMC cells.
Figure 5. Effect of the variation of oblique incidence angles (θ) on the S11 phase behavior of (a) design #1 and (b) design #2 in TE/TM polarization at both frequencies. (a) AMC design #1 and (b) AMC design #2.
Figure 6. Dispersion diagrams for TE and TM modes at 900 MHz and 2.45 GHz, centered on Γ.
However, at 900 MHz, AMC #2 falls out of the AMC phase at 
$\theta = 30^{\circ}$ and 45∘, causing a frequency shift of the S 11 zero phase by 60 and 86 MHz, respectively. This phenomenon is attributed to the movement observed in the dispersion diagram, where the branch corresponding to 900 MHz shifts toward higher frequencies, greater than 1 GHz, with an increase in the angle, along Γ-X. This shift also impacts the AMC bandwidth, resulting in a decrease of 1.21% and 0.86% for AMC #2, respectively. These previous results suggest that the octagonal ring centered with a patch octagon offers stable performance and is, therefore, preferred for combining with the folded monopole antenna.
The operating frequencies of the AMC #1 structure have been further investigated through the analysis of the dispersion diagram, as shown in Fig. 6. The electric field magnitude was plotted for two specific branches, encompassing TE and TM modes at 900 MHz and 2.45 GHz at Γ. At the first branch, there is a nearly degenerate behavior on Γ-X-M-Γ. Conversely, in the case of the 2.45 GHz branch, the lifting of degeneracy began after the second third of Γ-X, and the frequency dispersion remains low over the first third of X-M. Consequently, it can be deduced that for angles less than 60∘, Fig. 5a, the phase shift for these modes is expected to undergo only marginal changes. The absence of band gaps is attributed to the absence of the vias.
Parametric study of the PE inspired by AMC
This parameter study reveals the behavior of the designed single AMC element under ideal periodic conditions. It identifies which cell geometry, operating at 900 MHz and 2.45 GHz, is more sensitive to AMC phase perturbations.
The parameter p represents the distance between the edge of the cell and the AMC pattern, as shown in Fig. 7. This parameter exhibits a smooth impact at 2.45 GHz on the 
$\pm 90^{\circ}$ bandwidth within which the frequency of the S 11 zero phase remains in the AMC phase throughout the variation of p, as shown in Fig. 8. However, a parasitic behavior is detected at the outer octagonal ring operating at 900 MHz, where the S 11 zero-phase frequency shifts by 60 MHz, exceeding the AMC phase bandwidth and thus entering the PEC phase when p surpasses the range of 0.1–4 mm.
Figure 7. Study of the impacts of parameters p and x on AMC phase characteristics.
Figure 8. Impact of parameter p on frequency shift and bandwidth of the S 11 phase in a single AMC cell.
Further parametric analysis of the AMC structure, illustrated in Fig. 7 as a 3 × 3 AMC array, investigates the effects of the parameter x, which denotes the equidistant gaps between adjacent cells. As shown in Fig. 9, the variation of parameter x from 0.1 to 10 mm introduces a notable degree of sensitivity, particularly at a frequency of 900 MHz. The frequency shift of the S 11 phase exceeds the AMC phase 
$\pm 90^{\circ}$ to PEC phase by 4.4% when x surpasses 4 mm. However, at 2.45 GHz, the AMC phase exhibits a slight fluctuation in frequency shift, with a variance of 
$\pm 3\%$. Conversely, at 900 MHz, the AMC phase bandwidth is minimal at x = 0.1 and 0.5 mm (
$\pm0.5\%$) but increases to 4% when x exceeds 1 mm.
Figure 9. Impact of parameter x on frequency shift and bandwidth of the S 11 phase in the AMC array.
Therefore, this analysis reveals that the outer octagonal ring geometry of the AMC cell operating at 900 MHz shows greater sensitivity in the AMC phase compared to the performance at 2.45 GHz. Thus, to ensure the AMC phase of the designed cell, the parameters p and x should remain within the range of 0.1–4 mm.
Experimental results
A 4 × 4 AMC prototype was fabricated using a Xurography machine [Reference Yang, Huang, Dai, Barber, Wang and Lu20]. The measurement process of the S 11 phase for the AMC array was conducted in an anechoic chamber [Reference Sievenpiper, Zhang and Broas21], as illustrated in Fig. 10a, starting with a PEC metallic plate of identical dimensions (240 mm × 240 mm) as the reference.
Figure 10. Measurement setup of the S 11 phase of 4 × 4 AMC array: (a) in anechoic chamber; (b) comparison of S 11 phase between measured and simulated results.
According to Fig. 10b, the measured resonance frequencies are 0.871 GHz and 2.37 GHz, while the simulation predicts frequencies of 0.896 GHz and 2.44 GHz, resulting in deviations of −2.8% for both resonant frequencies. The measured AMC’s operational bandwidths, with differences of 15% and 5%, exhibit a high degree of concordance with the simulation results. The discrepancy between the measured and expected results can be attributed to two main factors. First, the two horns were not positioned strictly at normal incidence but at an incidence angle of approximately 10∘. Secondly, mechanical challenges occur when a given small support is not entirely attached to the fabricated 4 × 4 AMC array substrate composed of adhesive Kapton and PDMS.
Fabrication steps for antenna with AMC
As mentioned in Section II, PDMS is the chosen material with measured ϵr = 2.80 and tanδ = 0.008 that allows us to overcome the challenges of communicating with wearable and conformable object. In addition, due to its mechanical adaptability, ease of manufacturing, and stable chemical properties [Reference Alqadami, Jamlos, Soh and Vandenbosch22], the PDMS layer of the PE inspired by AMC also serves as an alternative substrate to foam, reducing the distance between the AMC scatterer and the ground plane. In contrast, the PDMS is recognized for being hydrophobic and chemically inert material. Hence, this polymer substrate demonstrates limited adhesion to metallic surfaces and conductive inks. The single element backed-antenna is thus assembled by bonding the antenna, fabricated on an adhesive Kapton film (65 µm), with 
$\epsilon_r = 3.2$ and tanδ = 0.0017 [Reference Technical23], to the top surface of the PDMS, Fig. 11.
The PDMS substrate (Sylgard 184) is a mixture consisting of the monomer and the curing agent in a ratio of 10:1. Before curing, a degassing step is necessary to remove all bubbles from the solution. The desired thicknesses are 5.5 mm and 0.5 mm for the AMC and the antenna patterns, respectively. To achieve these thicknesses, molds were created using a 3D printer, specifically the Ultimaker, with a polylactic acid (PLA) substrate having ϵr = 2.22 and tanδ = 0.005. All dielectric substrates employed in this study were characterized using the resonant cavity technique at both resonant frequencies [Reference Kassem, Vigneras and Lunet24].
Figure 11. Fabrication process of the antenna system.
The conductive parts are produced by etching a 60 µm-thick adhesive copper foil with an electrical conductivity of 5.96 × 107 S/m using the Xurography technique [Reference Yang, Huang, Dai, Barber, Wang and Lu20]. On top of the PDMS layer, a 65 µm-thick adhesive Kapton® is applied as an intermediate surface to which the copper foil is bonded. Figure 11 briefly illustrates all the steps in sequence and highlights the stacking of all the layers. The CPW is connected to the antenna feed point via a subminiature version A (SMA) connector.
Measurement and analysis
The folded antenna is coaxially fed and tested in the anechoic chamber, as shown in Fig. 12. The antenna system is placed at a far-field distance of 2.5 m to the Tx-horn antenna connected to an Agilent E4428C power generator.
Figure 12. Measurement setup of the folded monopole antenna with a single element backing in anechoic chamber.
The effect of the S 11 performance is studied in Fig. 13 by positioning the single element in closer proximity to the antenna (
$\Delta H$). The measured S 11 exhibits an unstable response at 2.45 GHz. The frequency shift of S 11 remains 106 MHz for 
$\Delta H$ of 5 cm. Subsequently, it gradually decreases to 102 and 25 MHz as 
$\Delta H$ decreases to 3 and 1 cm, respectively, which 
$\Delta H$ is less than 
$\lambda_{2.45\mathrm{G}}$/4, as shown in Fig. 13. Moreover, the bandwidth decreases from 858 MHz without AMC to 220 MHz at 
$\Delta H$ of 1 cm, which is considered sufficient to cover the higher frequency. Nonetheless, the appearance of a third resonant frequency at 2.15 GHz can potentially be attributed to the proximity of the AMC cell at a distance of 1 cm, a scenario that does not occur for 
$\Delta H$ values greater than 1 cm. This is attributed to the close interference between electromagnetic waves from the radiator and the PE inspired by AMC, resulting in undesired resonant frequencies. Due to the fact that 
$\Delta H$ is less than 
$\lambda_{900\mathrm{M}}$/4, the frequency shift of the S 11 is stabilized. It shifts slightly around 37.5 MHz at 900 MHz, with a bandwidth of around 130 MHz for all the tested 
$\Delta H$. With a 
$\Delta H$ of 1 cm, the overall antenna system exhibits a good impedance match (
$S_{11} \lt -10$ dB), while maintaining a distance of less than λ/4 at both frequencies.
Figure 13. Measured S 11 of the antenna system design with varying spacing 
$\Delta H$ beneath the antenna.
Figure 14 shows a good agreement of the simulated and measured S 11 of the overall antenna system design. The folded antenna exhibits a 20 MHz left shift with an impedance bandwidth of 100 MHz at 900 MHz for both without and with AMC-backing. At higher frequency, the 10 dB bandwidth diminished from 970 to 170 MHz, this still encompasses the 2.45 GHz. However, the frequency shift of S 11 is considered negligible. The slight discrepancy between the simulation results and measurements can be explained by the imperfections in the various stages of realization and soldering.
Figure 14. Simulated and measured S 11 of the CPW-fed monopole antenna without/with AMC cell backing.
As illustrated in Fig. 15, the simulated and measured FBR are in agreement at both planes and frequencies. The measured FBR increased from less than 2 dB to 12.3 and 19.9 dB, with measured realized gains of 1.88 and 5.66 dBi and simulated radiation efficiencies of 95% and 88% at both frequencies, respectively. The undesired third frequency at 2.15 GHz exhibits an impedance bandwidth of 132 MHz, a maximal gain of 6.01 dBi, and FBR of 14 dB. As seen in Fig. 15, the distribution of surface current on the antenna system is also depicted at frequencies of 900 MHz, 2.15 GHz, and 2.45 GHz.
Figure 15. Comparison of the simulated and measured radiation patterns and current distribution of the antenna without/with AMC in both planes at 0.9 and 2.45 GHz and at the corresponding third resonant frequency of 2.15 GHz.
The impact of bending test on the S 11 performance of the complete system design was measured, as shown in Fig. 16. The antenna system was tested on the fabricated PLA objects with different radii, considering their dielectric properties during the simulation and measurement. A frequency shift of 60 MHz (6.66%) and 120 MHz (4.89%) in the x-direction and 50 MHz (5.55%) and 100 MHz (4.08%) in the y-direction was observed at 900 MHz and 2.45 GHz, respectively, when the antenna system was bent till a radius of 30 mm. However, for bending radii greater than 60 mm, most S 11 frequency shifts were less than 20 MHz, ensuring that S 11 remained well-matched.
Figure 16. Measurement of S 11 frequency shift under bending effects in both directions.
As a result, the impact of a 60 mm bending radius shows stability in gain measurements and consistency with simulations, with peak measured gains of 1.45 and 5.44 dBi at 900 MHz and 2.41 GHz, respectively. However, a difference of ±1 dBi between the free space and bending tests is observed in Fig. 17a, particularly at the lower frequency. This discrepancy is attributed to unwanted mutual coupling between the antenna and the AMC single element caused by bending, which distorts the radiation pattern and reduces gain. This effect is also reflected in the FBR values, Fig. 17b, which are reduced by ±2–4 dB compared to those in free space at both frequencies. With FBR values exceeding 10 dB at both resonant frequencies, we can proceed to test our final prototype on the human body for potential health-care applications.
Figure 17. Simulated and measured peak realized gain (a) and FBR (b) in free space and during the bending test (R = 60 mm).
Discussion and results
As demonstrated previously, a single AMC-backed antenna on two polymer substrates has demonstrated effective performance and significant size reduction, making it ideal for wearable health-care devices. Therefore, our prototype serves as a viable alternative to the classical approach (antenna + ground plane), as depicted in Fig. 18. The objective is to highlight the advantages of this alternative method compared to the classical approach in terms of electrical size and performance metrics.
Figure 18. Simulation setup of the antenna system for the classical and alternative approaches with two manufactured prototypes. (a) Classical approach constructive interference and (b) alternative approaches.
In the classical approach, the antenna achieves constructive interference at a minimum space of 
$\lambda_0/4 = 83.3$ mm, with a GND ranging from 60 to 500 mm, where λ 0 is the free-space wavelength at 900 MHz. The frequency shift of S 11 remains relatively constant, within an impedance bandwidth (dashed curves) of ±100 MHz at 0.9 GHz and ±900 MHz at 2.45 GHz, as illustrated in Fig. 19a. Furthermore, in Fig. 19b and 19c, the maximum gain and FBR increase significantly as a GND reaches approximately 250 mm at 2.45 GHz and 300 mm at 900 MHz.
Figure 19. Comparison of the two approaches performance at different a GND at 900 MHz (blue) and 2.45 GHz (orange): (a) frequency shift of peak S 11; (b) maximum realized gain; (c) FBR. The diamond red shapes represent the measured results for a single element and a 2 × 2 AMC array at both frequencies.
On the other hand, a 10 mm spacing (
$\lambda_0/33$) between the antenna and the AMC cell (60 × 60 mm2), both simulated and measured, does not negatively impact the frequency shift of S 11 compared to the classical approach. However, this spacing reduces the bandwidth from 11.7% to 6.1% at 900 MHz and from 39.2% to 11.4% at 2.45 GHz. As shown in Fig. 19b, the maximum realized gain at 900 MHz is significantly lower than that of the classical approach, primarily due to the use of a single AMC element and the sensitivity of the octagonal ring design on the antenna. However, there is a significant impact on the gain at 2.45 GHz compared to the classical approach, when ground size is increased to 175 mm. Lastly, the close proximity of the antenna and AMC cell results in a significantly higher FBR, as observed at 60 mm of a GND.
Increasing the surface area of the artificial reflector, as illustrated in Fig. 18b, with [n × n] arrays, maintains a well-matched S 11 and enhances the impedance bandwidths by more than 50% at 900 MHz and 11% at 2.45 GHz compared to a single AMC cell (Fig. 19a). The increased number of AMC cells results in notably higher FBRs at both frequencies. However, the maximum gain does not improve as much, particularly at 900 MHz, remaining below the classical approach. This is due to the proximity sensitivity of 10 mm, which causes electromagnetic noise and performance disturbances. Therefore, a single AMC cell can effectively cover the entire antenna, achieving a reduced electrical size of 
$ka = 0.79 \lt 1$ while maintaining satisfactory performance.
To complete the comparison of our final work with the existing studies summarized in Table 3, we have introduced figures of merit, FOM
$_{\{Gain,FBR,Q\}}$, which quantify the trade-offs between the gain, FBR, and the quality factor (Q) performances of the antenna system relative to its electrical size. These FOMs are defined in the following equation:
\begin{equation}
\mathrm{FOM}_{\{Gain,FBR,Q\}} = \frac{\{Gain,FBR,f_r/BW\}}{(k\cdot a)^2 \cdot (k \cdot h)}
\end{equation}Table 3. Comparison of reference antenna systems for wearable applications
MTM
$^*$: metamaterial inspired AMC, AMC
$^*$: PE-inspired AMC.
with fr being the resonant frequency at 900 MHz and 2.45 GHz, 
$k = 2\pi/\lambda_0$ the wavenumber, a the radius of the minimum sphere enclosing the antenna system, and h the air gap between the antenna and the AMC. In addition, 
$(k \cdot a)^2$ provides a measure of the effective aperture of the antenna system. The three FOMs are crucial for comprehensive antenna design and performance optimization, in terms of bandwidth efficiency, high directional gain, and effective suppression of back-lobes.
According to the table, our compact antenna system exhibits the smallest electrical size of 0.79, compared to the previous works. The FOMQ shows a satisfactory value, particularly in the sub-GHz range, although it is lower than those reported in [Reference Sharma, Tripathy and Sharma29]. Nevertheless, using AMC properties have shown an improvement in FOM
$_{Gain}$ and FOM
$_{FBR}$, achieving values of 15.85/47.71 and 103.75/167.89 at both frequencies, respectively, compared to other types of metasurface employed in the previous works such as [Reference Velan, Sundarsingh, Kanagasabai, Sarma, Raviteja, Sivasamy and Pakkathillam25, Reference Khajeh-Khalili, Haghshenas and Shahriari27–Reference Sharma, Tripathy and Sharma29].
Conclusion
A novel compact CPW-fed monopole antenna for IoT applications, featuring a single AMC cell, has been investigated through simulation, fabrication, and characterization in the GSM and WiFi bands. A parametric study showed that for parameters p and x beyond 4 mm, the AMC cell transitions to the PEC phase only at 900 MHz. Thereafter, the antenna system, with 
$(ka = 0.79)$, was compared to a classical approach and to existing works in terms of electrical size and performance. The comparison has demonstrated superior FOM
$_{\{Gain, FBR, Q\}}$, corresponding to the reduced electrical size at 0.9 and 2.45 GHz, respectively. The next phase involves testing our prototype under real-world conditions, including off-body constraints, for wearable health-care applications.
Acknowledgements
The author gratefully appreciates Jean-Luc Lachaud from the IMS Laboratory and David Bedenes from Bordeaux INP for their valuable contributions to fabrication techniques and measurement methods.
Competing interests
The authors report no conflicts of interest.
Elie Zaraket is a Ph.D. student. In 2020, he received a Master’s degree in Microsystems and Embedded Systems in the Faculty of Sciences in Lebanese University, Lebanon. In 2021, he works on the modeling, Design and Characterization of Energy-Data Hybrid Transition Device at EnergyLab of the University of La Réunion in collaboration with NUIST, Nanjing, China. Currently, he is pursuing his thesis in radiofrequency field at IMS Laboratory of the University of Bordeaux, France.
Ludivine Fadel received the Ph.D. degree in Electrical Engineering from the University of Bordeaux, France, in 2004. She is an Associate Professor at Bordeaux University and her main research interests include wireless power transfer and energy harvesting, materials and printing technologies for RF application.
Yéro Dia is currently pursuing his thesis in electromagnetic energy harvesting on flexible substrates for powering WBAN networks. In 2021, he received a Master’s degree in Microsystems, Instrumentation and Robotics in University of Franche-Comté, in Besançon, France.
Valérie Vignéras is a full professor in the Polytechnic Institute of Bordeaux and conducts research in the IMS Laboratory on complex structures (mixtures, structured media, and self assembled media) both by simulation to predict or optimize their properties and by characterization before their integration in high-frequency systems (antennas, electromagnetic compatibility, and radar shieldness).
Laurent Oyhénart received the Ph.D. degree in Electrical Engineering from the University of Bordeaux, Bordeaux, France, in 2005. Currently he is an Associate Professor with the University of Bordeaux and develops his research activities in the IMS Laboratory. His research interests include computational electromagnetics, photonic crystals, and antenna synthesis.
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