Unobstructive and safe-to-wear watt-level wireless charger

Multiphysics considerations for a wearable WPT hand band

Figure 1a illustrates the multiphysics considerations for the design of the WPT hand band, which was constructed using a 0.5-mm-thin 20% spandex/80% nylon fabric such that it could fit comfortably to the human palm without compromising any hand movement or functionality. A square-shaped pocket, on the hand band houses a flexible planar Cu coil and a stretchable magnetic backplane, as shown at the bottom of the central schematic. The 50-μm-thin Cu coil, serving as a Tx antenna, can inductively couple with an Rx antenna built-in to mobile or wearable devices when the two are in close proximity. The Ferrofabric was positioned beneath the coil to provide magnetic shielding. The three-layer 3M Tegaderm tape made from polyurethane serves as both encapsulation layers for the Ferrofabric and electrical insulation for the Cu coil.

During on-body WPT, a variety of physical phenomena are involved due to the alternating current (AC) flowing through the Cu coil, which are illustrated in the ring of Fig. 1a. Within electromagnetic considerations, the inductive coupling between the Tx and the Rx is influenced by the ferromagnetism of the Ferrofabric. The AC flow leads to variations in current density within the conductor, such as the skin effect and the proximity effect, causing energy losses. Additionally, core loss induced by magnetic backplanes contributes to an increase in effective antenna resistance and a reduction in charging efficiency. Besides, tissue SAR should be quantified to ensure the electromagnetic safety. Within structural considerations, the hand band needs to fit not too tight or too loose to the hand and should not obstruct any hand movement or functionality. To ensure stable charging even under mechanical deformation, the coil strain is purposely isolated from the stretching of the hand band through the pocket insertion. Within thermal considerations, the flow of current through the coil is accompanied by joule heating that can potentially cause skin burns. Blood perfusion and metabolism also affect skin temperature. The subsequent sections provide detailed descriptions of each physical phenomenon and elaborate on the methodologies implemented to address them.

Ferrofabric as a stretchable magnetic backplane

Wireless charging through inductive coupling can benefit from the use of magnetic backplanes placed under the coils to direct the magnetic flux surrounding the coils and therefore improve the inductance of the coils and ultimately, the coupling coefficient⁴⁶. Supplementary Table 1 summarizes state-of-the-art stretchable magnetic materials that have been developed for stretchable/flexible devices such as WPT systems, actuators, micro-electromechanical systems (MEMS), and sensors^{33,46,53,54,55,56,57,58,59,61}. It is evident that while Ferroelastomers have become significantly more stretchable, they continue to suffer from low magnetic permeability.

We, therefore, introduce a new type of stretchable magnetic backplane combining stretchable fabric with ferrofluid, named Ferrofabric, to achieve higher magnetic permeability. A commercial ferrofluid (EMG 900, Ferrotec) consisting of surfactant-coated magnetite nanoparticles (~10 nm) dispersed in hydrocarbon oil was used as the magnetic filler. The surfactant and carrier fluid prevent nanoparticles from agglomerating or settling⁶¹ to enhance magnetic shorting, which leads to a low-reluctance pathway for magnetic circuit and consequently, higher permeability (~19.6)⁶⁵ (Supplementary Fig. 1). Figure 2a illustrates the fabrication process of the Ferrofabric, wherein an oleophilic fabric (Bamboo Rayon 4 Way Stretch with Spandex, APC Fabric Store) with a thickness of 0.5 mm was selected as the ferrofluid absorber. This bamboo fabric was chosen for its high ferrofluid absorption capacity and mechanical compliance (Supplementary Fig. 2). It can also maintain its shape under both wet and dry conditions. To prevent leakage of the ferrofluid from the Ferrofabric, stretchable transparent polyurethane dressings (Tegaderm, 3M) with a thickness of 47 μm were used for encapsulation. The optical micrographs of the unencapsulated bamboo fabric and Ferrofabric did not exhibit any mechanical failure under 50% uniaxial tensile strain (Fig. 2b). In addition to stretching, the encapsulated Ferrofabric is also easy to bend and twist (Fig. 2c). The mechanical properties of the different layers are offered in Fig. 2d. The bare fabric and the Ferrofabric were tested to have a comparably low modulus (57.5 and 75.3 kPa, respectively, Fig. 2d inset). In addition, both Tegaderm encapsulated bare fabric and Ferrofabric exhibited almost identical moduli (3.60 and 3.51 MPa, respectively), indicating that the presence of ferrofluid had minimal impact on the mechanical behaviors of the encapsulated bamboo fabric.

a Fabrication process of the Ferrofabric. b Optical microscope images of bare bamboo fabric and the Ferrofabric in undeformed and 50% stretched configurations. c The Ferrofabric under different deformations: stretching, bending, and twisting. d Stress vs. strain curves of bare fabric and Ferrofabric, with and without Tegaderm encapsulation. e Magnetization vs. magnetic field curves of the bare fabric, the ferrofluid (EMG 900), and the Ferrofabric. f Comparison of mechanical compliance and magnetic permeability with conventional stretchable magnetic composites. g Schematic illustration of the long-term measurement of a Cu coil on Ferrofabric. h Relative changes in resistance and inductance of a Cu coil on Ferrofabric over 91 days.

To investigate the ferromagnetism of the Ferrofabric, magnetization M was measured using a Superconducting Quantum Interference Device (SQUID) by sweeping magnetic field H from −1 T to 1 T at room temperature (Fig. 2e). The H-field induces configurational changes of ferromagnetic nanoparticles in the carrier fluid, aligning them with the field and resulting in higher magnetization (Fig. 2e lower inset). The magnetization of the bare fabric (black) is negligible compared to that of ferrofluid (green) and Ferrofabric (red). The low hysteresis observed in the M–H curves of the ferrofluid and the Ferrofabric indicates low loss and therefore, suitability for AC applications⁶⁶. The relative magnetic permeability of the ferrofluid and the Ferrofabric (\(\mu _r=\chi +1\), where χ is the magnetic susceptibility, i.e., the slope of the M–H curves) is extracted to be 16.6 and 11.3, respectively (Fig. 2e upper inset). The use of the bamboo fabric as the matrix allows the ferrofluid to form continuous magnetic paths, offering more substantial magnetic shorting and hence much higher magnetic permeability (11.3) compared to that of the Ferroelastomers (2.9)⁵⁴. Figure 2f is an Ashby plot that compares the mechanical compliance, i.e., the inverse of Young’s modulus, and the relative magnetic permeability of various stretchable ferromagnetic composites and magnetite, the magnetic filler used in ferrofluid. Notably, our Ferrofabric stands out as a mechanically soft but effective ferromagnetic material, making it particularly suitable for wearable WPT devices. Specifically, higher magnetic permeability helps improve charging performance as it directly affects coil inductance and quality factor. Finite element analysis (FEA) indicates that the Ferrofabric can enhance coil inductance by 21.7% due to better shielding effects whereas Ferroelastomers only made an improvement up to 6.1% (Supplementary Fig. 3).

However, oil molecules can potentially permeate through the Tegaderm encapsulation due to large free volume and high polymer chain mobility of polyurethane⁶⁷. To examine the effect of ferrofluid drying, long-term magnetic properties of the Ferrofabric was tested by measuring the impedance of a Cu coil placed on the Ferrofabric (Fig. 2g) because the complex magnetic permeability µ = µ′ − jµ″ affects both the inductance and effective resistance of a nearby inductor with AC excitation⁶⁸. Supplementary Fig. 4 and Fig. 2h present the long-term changes of the weight and the mechanical and electrical properties of the Tegaderm-encapsulated Ferrofabric. As shown in Supplementary Fig. 4a, b, even though the total weight of the Ferrofabric gradually decreased till Day 20, the effective Young’s modulus of the Tegaderm-encapsulated Ferrofabric remained almost unchanged. This implies that the initial weight loss was mainly due to the drying of the excessive carrier fluid rather than that absorbed by the threads. After 20 days, the effective Young’s modulus of the Ferrofabric started increasing, suggesting that the absorbed ferrofluid began drying. Notably, the impedance of the Cu coil on the Ferrofabric did not show significant change over 90 days (Supplementary Fig. 4c, d and Fig. 2h), demonstrating long-term stability of the electromagnetic properties of the Ferrofabric despite the changes in the mechanical properties due to the oil drying. This surprising discovery can be attributed to the uniform deposition of magnetite nanoparticles onto the bamboo fabric fibers, which can form magnetic paths to maximize magnetic shorting even long after the carrier fluid dried (Supplementary Fig. 5).

Design of the WPT hand band

Existing research in stretchable and wearable WPT systems typically utilizes a unique charging scheme that only works for a specific application and is not widely adaptable to devices where one does not have control of both the Tx and the Rx sides of the system³⁵. Furthermore, they typically have a low amount of power transmitted or received⁶⁹. To create a versatile system capable of charging commercial mobile devices at a watt level as well as a wearable e-tattoo at a microwatt level, our system employs the Qi protocol.

An operating frequency of \(f=130\;\rmkHz\) was chosen since it is the default frequency of the commercial Qi chargers we use (WCT-NXQ1TXH5 & WCT-15W1CFFPD, NXP). Each board came with an MP-A11 transmitter coil complying with the Qi specifications. The operating frequency highly impacts the AC resistance of the coil, the system’s core losses, quality factors, and charging performance⁴⁶. Therefore, optimizing the charging efficiency at this frequency is particularly important in watt-level power transfer to avoid overburdening portable energy sources, prolonging charging time, or compromising human safety due to higher current levels. This requires a comprehensive understanding of all the loss mechanisms within the wearable WPT.

Our wearable Qi-compatible charger consists of a Cu Tx coil with Ferrofabric as the magnetic backplane, as illustrated by Fig. 3a. The Tx coil is a planar spiral with an outer diameter \(d_\rmTx=51\;\rmmm\) (Supplementary Fig. 6), which is designed to be smaller than the size of the user’s palm. The built-in coil in a smartphone or on an e-tattoo would serve as the Rx coil. The circuit diagram of the WPT system is offered in Fig. 3b where each coil is represented by an inductor (\(L\)) and a resistor (\(R\)) connected in series with a negligible parasitic capacitor (C) (phase angle of 85° at 130 kHz). Supplementary Fig. 6c also shows the operating frequency of 130 kHz is far below the coil’s self-resonant frequency of 7 MHz, validating the coil’s parasitic capacitance has a minimal effect on power transfer⁷⁰. For inductive coupling, the maximum coil-to-coil WPT efficiency \(\eta _\max \) can be calculated by

where \(Q=2\pi fL/R\) and \(k\) stand for the quality factor of each coil and the coupling coefficient between them, respectively (Supplementary Note 1 and Supplementary Fig. 7). Equation (1) clearly indicates that higher quality factors and coupling coefficients are desirable to maximize the WPT efficiency. Since the charging distance was measured to be 1 mm for smartphone charging and 0.5 mm for e-tattoo charging, the coupling coefficient k remained close to the maximum value of 1 (0.85 and 0.80, respectively). Hereafter, we keep the WPT frequency, the coil’s planar configuration, and the coupling coefficient unchanged, with a primary focus on optimizing the WPT efficiency through the quality factor, and particularly the coil resistance. In terms of coil materials, Cu and EGaIn are considered, both of which have been widely used as flexible antennas.

a A side view of the model of the transmitter (Tx) and receiver (Rx) coil with magnetic backplanes. \(t_\rmTx\) denotes the Tx coil thickness. \(d_\rmF\) and \(d_\rmTx\) are the diameters of the Ferrofabric and the Tx coil, respectively. h is the coil-to-coil distance or the charging distance. b Circuit diagram of the WPT system with inductive coupling. c–f Comparison of antennas made of two commonly used materials: Cu and EGaIn. c Quality factor vs. Tx coil thickness considering the skin effect. d The effect of various loss mechanisms on the quality factor of the Tx coil inductively coupled to an Rx coil with built-in magnetic shielding of a smartphone. e The quality factor of the Rx coil with respect to the Tx coil thickness. f Maximum charging efficiency vs. the Tx coil thickness. g–j Effects of the Ferrofabric placed under the Tx coil on the charging performance of the Cu and EGaIn Tx coils. g Tx coil inductance vs. the Ferrofabric size. h Changes in Tx coil’s AC resistance vs. the Ferrofabric size. i Relative changes in the quality factor vs. Tx coil thicknesses when the Ferrofabric is the same size as the fabric pocket, i.e., \(d_\rmF/d_\rmTx=1.4\). j Relative changes in maximum charging efficiency vs. Tx coil thicknesses when \(d_\rmF/d_\rmTx=1.4\). k–m Comparison between modeled (hollow markers) and measured (solid markers) maximum charging efficiencies. k Effects of the Ferrofabric size in the smartphone charging case. l Effects of the Ferrofabric size in the e-tattoo charging case. m Effects of the charging distance in the e-tattoo charging case.

At 130 kHz, the effective resistance of a conductor is higher than its DC counterpart due to three different loss mechanisms: the skin effect (\(R_\rmSkin\;\rmeffect\propto 1/\delta\), with skin depth \(\delta =\sqrt1/\left(\pi f\sigma \mu \right)\)), the proximity effect (\(R_\rmProximity\;\rmeffect\propto t_\rmTx,\sigma\)), and the core loss (R_{Core loss} ∝ µ″, d_F), where \(\sigma\) and \(d_{\rmF}\) stand for coil conductivity and Ferrofabric size, respectively. By modeling the skin effect in a straight conductor with a rectangular cross-section using COMSOL FEA (details in “Methods“ section), we found that there is an optimal thickness for Cu to exhibit a local minimum of AC resistance (\(R_\rmAC\)) accounting for the skin effect but not so for EGaIn (Supplementary Fig. 8). In general, thicker coils have lower DC resistance (\(R_\rmDC\)), as indicated by the black markers in Supplementary Fig. 8a, c. However, under AC, the skin effect becomes nonnegligible when the conductor thickness exceeds \(2\rm\delta \). Given that Cu has a much smaller skin depth than EGaIn (δ_Cu =183 μm, δ_EGaIn = 757 μm), the skin effect only affects Cu but not EGaIn in the thickness range we considered. Tx coils made of either Cu or EGaIn with multiple thicknesses were simulated to assess the influence of the skin effect on the quality factor (Fig. 3c). A peak in the quality factor of a Cu Tx coil can be clearly identified but it is not the case for EGaIn. We only carried out experiments for Cu coils and those results are plotted as solid markers in Fig. 3c and the rest of Fig. 3.

When an Rx coil is added to the system and all three loss mechanisms are considered (Fig. 3d), the Cu Tx coil quality factor is generally reduced from Fig. 3c whereas the EGaIn Tx coil quality factor is almost unimpacted. While magnetic shielding improves the inductance of the Tx coil, it also elevates the effective resistance by reducing skin depth and introducing core loss. Moreover, the vicinity of the Tx and Rx coils further increases the effective resistance, primarily due to the proximity effect which affects both coils. Therefore, the quality factor of the Rx coil declines not only due to the presence of the Tx coil but further decreases with more conductive and thicker Tx coils (Fig. 3e). Considering the interplay between the loss mechanisms, Fig. 3f indicates that both the Cu and EGaIn antennas can achieve the maximum coil-to-coil WPT efficiency of ~80% with 50 μm < t_Cu < 100 μm and t_EGaIn > 1200 μm, respectively. However, thicker coils would make the WPT system bulkier and heavier, which clearly hampers wearability. Subsequently, we only consider coil thicknesses that are <100 μm.

To investigate the effects of the size of the Ferrofabric on the charging performance, we placed the Ferrofabric with various sizes under the Tx coil made of either Cu or EGaIn of different thicknesses without the Rx coil (Fig. 3g–i). As evidenced in Supplementary Fig. 4c, d, the Ferrofabric simultaneously increases the inductance and the effective resistance of the antennas. The inductance (Fig. 3g) and the resistance (Fig. 3h) varied when the Ferrofabric size was tuned between the inner and outer diameter of the Tx coil. The inductance of the Tx coil increases with the increase in Ferrofabric size, up to 15% when the Ferrofabric size is 1.4 times the Tx coil size (Fig. 3g). The core loss-induced increase in the effective resistance is independent of the coil materials or thickness (Fig. 3h and Supplementary Fig. 9a, b) because the core loss only depends on the AC frequency and the magnetic flux, which are not affected by the coil material or thickness⁷¹. As the Ferrofabric reduces the skin depth when \(\mu > 1\), the Cu coil that is more susceptible to the skin effect exhibits slightly higher increases in the effective resistance than that of the EGaIn coil when all losses are considered (Fig. 3h). Therefore, the Ferrofabric can impact both the quality factor (Fig. 3i and Supplementary Fig. 9c) and charging efficiency (Fig. 3j and Supplementary Fig. 9d). But it only improves the charging efficiency of a system with less conductive Tx coil, such as those made of EGaIn or ultrathin copper. Although the Ferrofabric eventually turned out to be not helpful to the charging performance of our Cu Tx coils due to its counteracting effects of simultaneously improving the inductance and effective resistance, it still plays a role in protecting the underlying tissue from electromagnetic radiation, which is to be discussed in the safety section.

We evaluated the maximum WPT efficiency while charging a commercially available smartphone as well as a custom-built wireless chest e-tattoo sensor⁶⁴ connected to a Cu Rx coil identical to the Cu Tx coil in the hand band (Fig. 3k–m). For smartphone charging (Fig. 3k and Supplementary Fig. 10), the maximum coil-to-coil efficiency remained above 70%, even with the thinnest Cu coil used (25 μm). However, the efficiency slightly decreases with a bigger Ferrofabric size due to the additional core loss caused by the built-in magnetic backplane of the smartphone. Figure 3l and Supplementary Fig. 11 show that the maximum efficiency when charging a chest e-tattoo is slightly improved by the Ferrofabric when the Tx coil is thin enough. This is because while the resistance change due to the core loss is independent of the coil thickness, the fraction of the core loss-induced resistance increase is smaller in thinner coils. Subsequently, a 50-μm-thick Cu coil with a \(Q_\rmTx\) of 10.9 was adopted in our wearable charger because it has a bending rigidity (\(\propto t_\rmTx^3\)) 70% lower than the 75-μm-thick coils whose \(Q_\rmTx\) is 12.0 while the efficiency is only compromised by <3%. The effect of charging distance was also investigated since clothing can reside between the chest e-tattoo and the hand band charger (Fig. 3m and Supplementary Fig. 12). The measured efficiency increased from 52.8% (without Ferrofabric) to 56.0% (with Ferrofabric) at the charging distance of 5 mm. The measured efficiencies are slightly lower than the modeled ones due to error propagation from a minor discrepancy in resistance and coupling coefficient values (Supplementary Fig. 12a, d, i). The same results for smartphone charging are offered in Supplementary Fig. 13. It is worth noting that in the case of smartphone charging, there is a crossover in the efficiencies with (red) and without (black) the Ferrofabric at the charging distance of 3 mm (Supplementary Fig. 13j), which indicates that the magnetic shielding effect becomes more prominent than the core loss and the proximity effect combined as the charging distance increases. In addition to the vertical distance between two coils, horizontal misalignment also affects charging performance. Supplementary Fig. 14 shows the simulated charging performance when the two coils have horizontal misalignments in the case of smartphone charging and e-tattoo charging. Since horizontal misalignment reduces the coupling coefficient, charging efficiency drops accordingly. Since the internal Tx coil and the UT logo on the surface of the hand band were designed to align, misalignment can be mitigated by aligning the UT logo on the hand band with the Rx coil.

Electromechanical and electrothermal characteristics of the WPT hand band

To ensure wearability and stable charging, a fabric hand band with a pocket over the palm was designed and fabricated through sewing. A 0.5-mm-thin 20% spandex/80% nylon fabric was chosen over other fabrics due to its high flexibility and stretchability (up to 50%). The fabric band was designed to have a snug fit to the wearer’s hand, while the Cu coil and the Ferrofabric were inserted into the fabric pocket which was located at the center of the palm to best align with the Rx coil in a handheld smartphone. Without added adhesives, the free sliding between the coil and the fabric pocket can isolate the stretch of the band from the Cu coil (Fig. 4a). We confirmed that the diameter of the Cu coil remained constant when the band was stretched up to 50% (Fig. 4b), resulting in less than 1% change of the electrical characteristics of the Cu coil (Fig. 4c). The Cu coil and Ferrofabric were subjected to various hand motions such as clenching, hand shaking, and grabbing materials. Although coil deformation and the proximity of conductive and magnetic objects can affect the inductance and resistance of the Cu coil⁷², its electrical properties can recover to the original state, ensuring the electromechanical reliability under practical use (Fig. 4d). The Cu coil inside the hand band showed durability under cyclic loadings such as 20% fabric stretching up to 1000 cycles (Fig. 4e) and palm clenching up to 500 cycles (Supplementary Video 1).

a Strain isolation by means of a non-adhesive hand band pocket. b Demonstration of strain isolation when the hand band was stretched up to 50%. c Relative changes in resistance and inductance of the Tx coil during the hand band stretching. d Recovery of the relative changes in resistance and inductance after various hand deformations: stretching, clenching, warping, hand shaking, and holding a smartphone. e Resistance and inductance of the Cu coil changed <2% after 1000 cycles of 20% stretch of the hand band. f Cross-sectional view of the thermal simulation of the in-hand wireless charging of the smartphone to evaluate thermal safety. g Simulated temperature in the depth direction of the model shown in (f). h Measured palm temperature during smartphone charging. The inset shows the temperature distribution of the palm calculated from the steady-state heat transfer simulation. i Fractions of power division with respect to Tx resistance. j Maximum palm temperature vs. Tx resistance. k Effect of transmitted power on maximum palm temperature.

One of the key concerns to be addressed in the design of a wearable watt-level WPT system is the hand temperature rise caused by coil joule heating. The long-term thermal safety threshold of human skin is 43 °C⁷³. A 3D steady-state heat transfer FEA model was developed using COMSOL for the case of wireless charging of a smartphone (details in “Methods” section), which involves much higher power transfer compared to e-tattoo charging (Fig. 4f). The detailed geometric and material properties are given in Supplementary Fig. 15. This heat transfer model took into account a variety of heat sources including joule heating of both Tx and Rx coils, smartphone operation, tissue metabolism, and the interplay between blood perfusion and tissue temperature⁷³. Figure 4g plots the simulated temperature along the depth direction originating from a point with peak palm surface temperature as indicated by the inset in Fig. 4h. The simulation result indicates that the entire tissue temperature did not exceed 41.6 °C, which is below the safety threshold of 43 °C. This result is further validated through experimental measurements of palm surface temperatures during smartphone charging on the palm. For real-time temperature monitoring, a thermistor was placed at the peak temperature point as indicated by the simulation (see the inset of Fig. 4h). The measured palm surface temperature gradually increased after charging started and reached a steady-state temperature of 41.3 °C, which is in excellent agreement with the simulated value, confirming the thermal safety of our wearable WPT hand band (Fig. 4h).

Considering that joule heating is a major source of energy dissipation in a WPT system, the resistance of the Tx coil and power level can effectively modulate joule heating and enhance the output power delivered to the smartphone battery. Figure 4i sheds light on the influence of the Tx coil resistance on the overall power dynamics within the WPT system. This offers insights into the distribution of active power between each coil and the battery, irrespective of power levels (Supplementary Note 1). Note that the AC resistance of the Tx coil is considered in this context. A Tx coil with higher AC resistance leads to reduced output power to the battery, subsequently diminishing WPT efficiency (Supplementary Fig. 16a). Regarding thermal characteristics, a greater portion of heat dissipation is induced by the Tx coil with higher resistance, ultimately leading to the possibility of surpassing the safety threshold (Fig. 4j). Therefore, a Tx coil with high resistance is detrimental to both charging efficiency and thermal safety. Any coil materials with reduced electrical conductivity (e.g., EGaIn or MXene) or coil geometry with increased total length (e.g., serpentine) need to compromise the power transfer levels to comply with the thermal safety threshold. Additionally, EGaIn is susceptible to resistance increase under mechanical deformation, which leads to unreliable charging performance owing to its high deformability⁴⁵. This relationship can also be understood in terms of quality factor, which exhibits an inverse relationship with resistance (Supplementary Fig. 16b). Through the coupled electromagnetic-mechanical-thermal analysis, we have demonstrated the effectiveness of a 50-μm-thick Cu coil as the optimal Tx antenna for a wearable WPT hand band, capable of safely sending out 5.35 W from the palm charger (Fig. 4k).

On-body wireless charging of mobile and wearable devices

To operate our wearable WPT system, suitable commercial Qi charging boards and power specifications were selected and modified to establish a compatible interface with commercial smartphones (Supplementary Note 3). The Qi charging board needed to connect to a battery which served as the power source. After optimizing the WPT hand band design from components to the system, we demonstrated the wireless charging of both a smartphone (Fig. 1b) and a chest e-tattoo (Fig. 1c) as a daily use scenario. The fabric band was worn on the hand to wirelessly charge a smartphone held in the palm (Fig. 5a and Supplementary Video 2). The in-hand charging performance (1% battery capacity increase every 1 min and 49 s) was found to be comparable to that of a commercial desktop wireless charger (Mi Wireless charger MDY-09-EU, Xiaomi) (1% every 2 min and 9 s) (Fig. 5b). Note that all charging rates decreased after reaching a battery capacity of 95% due to trickle charging, meaning lowering the charging voltage to the battery to avoid damaging the battery.

a Photographs of wireless charging of a smartphone. b Smartphone battery capacity over time, measured with our hand band placed on a table and worn on the palm compared with a commercial desktop wireless charger. c Measured four different power values as labeled in Fig. 3b in the smartphone charging. The horizontal lines on the graph indicate the average power in the normal charging range (0–95%). d Photographs of charging a chest e-tattoo using our device worn on the hand. e Seismocardiogram (SCG) and electrocardiogram (ECG) data collected through Bluetooth without any battery on the e-tattoo. f Battery capacity vs. time during the chest e-tattoo charging with a depleted LiPo battery using our hand band and the commercial wireless charger. g, h Simulated specific absorption rate (SAR) of the human hand during smartphone and e-tattoo charging. (i) A cross-sectional view of the electromagnetic model. (ii) Contour plots of the SAR with and without magnetic backplanes. Comparisons of state-of-the-art wearable WPT systems in terms of (i) stretchability vs. received power and j stretchability vs. charging efficiency. k Charging efficiency remained unchanged after cyclic stretches on the hand band.

To evaluate the WPT and efficiency of our device in real use, voltage and current waveforms were measured to calculate the active power (\(P=V_\rmrmsI_\rmrms\cos \varphi\)) (Supplementary Fig. 17 and “Methods” section). To provide a comprehensive evaluation, our power measurements were conducted at four key locations: DC input power (\(P_\rmIn\)), AC transmitted power (\(P_\rmTx\)), AC received output power (\(P_\rmOut,\rmRx\)), and DC output power (\(P_\rmOut,\rmBat\)), as labeled in Fig. 3b and Supplementary Fig. 7a. Here, we primarily focus on \(P_\rmTx\) to \(P_\rmOut,\rmRx\) efficiency, i.e. the coil-to-coil efficiency as it is what we try to optimize in this work. Figure 5c and Supplementary Fig. 18 illustrate the measured power levels at these four locations during wireless charging of the smartphone with our hand band. Within the normal charging range (0–95% of battery capacity), the \(P_\rmIn\), \(P_\rmTx\), \(P_\rmOut,\rmRx\), and \(P_\rmOut,\rmBat\) were measured to be 7.94, 5.35, 3.81, and 3.41 W, respectively. The ratio of \(P_{\rmOut,\rmRx}\) to \(P_{{\rmTx}}\) renders a coil-to-coil charging efficiency of 71%. The \(P_\rmIn\), \(P_{{\rmTx}}\), \(P_{\rmOut,\rmRx}\), and \(P_\rmOut,\rmBat\) using the commercial Qi charger were measured to be 7.02, 5.64, 4.42, and 2.86 W, corresponding to a coil-to-coil efficiency of 78% (Supplementary Fig. 17b, c), which is only slightly higher than our hand band charger.

In addition to mobile devices, wearable electronics, like e-tattoos^4,22, can also benefit from WPT integrated into fabrics, eliminating or reducing the need for batteries^{7,8,9,10,11,74}. For the charging of these e-tattoos, we demonstrated two modes of operation: battery-free and a depleted battery. Note that our WPT system can be inserted into fabric pockets attached to areas of clothing that are directly over the e-tattoos, extending beyond just the hand band demonstrated in our example. The battery-free case showed that the operation of the e-tattoo, the physiological signals obtained by the e-tattoo, and the Bluetooth transmission of the data were unaffected by the WPT system. The depleted battery case was used to determine the time it would take to recharge a typical LiPo battery used in the chest e-tattoo while also confirming if the WPT system could provide enough power to operate the e-tattoo during the recharging of the device battery. Figure 5d shows a battery-free chest e-tattoo designed to be Qi-compatible with an Rx coil identical to the Tx coil in the hand band. The chest e-tattoo was completely powered by the WPT hand band to measure 3-axis seismocardiography (SCG) and one-channel electrocardiogram (ECG) from the chest⁶⁴ (Fig. 5e) and to transmit the data to a smartphone through Bluetooth Low Energy (Supplementary Video 3). Figure 5f demonstrates the wireless charging of a depleted LiPo battery (LP401230 105 mAh, PKCELL) connected to the chest e-tattoo while under e-tattoo operation, showing charging performance comparable to the commercial charger.

Electromagnetic radiation poses a potential hazard to human tissues, particularly within a wearable WPT system that operates at high frequency and high power. To evaluate the electromagnetic safety concerning the human tissue, we consider the SAR, defined as \(SAR=\sigma E_\rmrms\right^2/\rho\), where \(\sigma\) and \(\rho\) denote the electrical conductivity and mass density of human tissue, respectively, and \(E_{\rmrms}\) represents the root mean square of the electric field within the tissue. It is known that higher operating frequencies tend to yield higher SAR values due to increased tissue conductivity as frequency rises. Specifically, the power transmitted by a WPT operating at a low Industrial, Scientific, and Medical (ISM) frequency (13.56 MHz) and a high ISM frequency (40.68 MHz) must not exceed 2 and 0.3 W, respectively, due to a safety requirement of SAR ≤ 1.6 W/kg imposed by the FCC guidelines⁴⁹. However, this limit presents a challenge for wearable WPT systems transmitting over 5 W as exemplified in our use case of smartphone charging.

It is less of a concern at Qi charging frequencies. A 3D electromagnetic FEA model was constructed to simulate the electromagnetic radiation at 130 kHz into the human tissue for handheld smartphone charging (see Fig. 5g(i), h(i) and “Methods” section)⁷⁵. The maximum local SAR values on the palm turned out to be only 2.14 mW/kg (no magnetic shielding), 1.66 mW/kg (with Ferrofabric), and 0.93 mW/kg (with ferrite). All these values remain far below the safety limit of 1.6 W/kg (Fig. 5g(ii)). Similarly, a 3D FEA model consisting of the hand, our wearable charger, and the chest was built to simulate the e-tattoo charging (Fig. 5h(ii)), which reported maximum local SAR on the chest to be 1.68 mW/kg (no magnetic backplane), 2.25 mW/kg (Ferrofabric), and 3.33 mW/kg (ferrite), all of which are still far below the safety limit. The SAR was lowered by the magnetic backplane in the smartphone charging case but was elevated in e-tattoo charging mainly due to the magnetic layer on the palm concentrating the electric fields toward the chest free of a magnetic layer.

Body-loading effects could also negatively impact the WPT efficiency because the human body is a conductive medium, inducing eddy currents and power loss. However, given the low electrical conductivity of the tissues at the kHz frequency range, the body-loading effect on charging efficiency was found to be negligible by our simulation. Our results indicate that the maximum charging efficiency, with and without human tissue, remains comparable to each other (Supplementary Fig. 19).

Our device demonstrates higher received power and stretchability compared to state-of-the-art on-body WPT systems (Fig. 5i and Supplementary Fig. 20). This kind of watt-level on-body WPT is unachievable through NFC or RF as their SAR are much higher. In addition, alternative wearable transmitters with higher resistance, such as serpentine or wrinkle designs for metal films, or materials choices of EGaIn or MXene, would jeopardize either the charging efficiency or the thermal safety. Figure 5j shows our device is a significant step toward a practical wearable WPT in terms of efficiency and stretchability. A silver nanofiber-based antenna performs well in terms of efficiency (35%) and stretchability (100%) but their system is at a much higher frequency of 10 MHz, which leads to a better quality factor but much lower transmitted power (100 µW) than ours given the SAR limit³². We obtained this outstanding charging performance while ensuring mechanical robustness, thermal safety, and electromagnetic safety (Table 1). Furthermore, we observed no coil-to-coil efficiency degradation for 1000 cycles of 20% stretching on the hand band (Fig. 5k). Finally, it is noteworthy that our charger is easily applicable to wearable microgrid charging for various mobile and wearable devices located across the body, eliminating a separate mobile battery for each device.

We have devised an unobstructive and safe-to-wear WPT hand band capable of efficient charging of both handheld smartphones and wearable e-tattoo sensors via the Qi protocol. We have created a stretchable magnetic backplane, the Ferrofabric, with a unique combination of exceptional magnetic permeability and mechanical compliance. Through a holistic electromagnetic-structural-thermal analysis, we have achieved a fundamental understanding of the effects of coil material, coil thickness, magnetic backplane, and charging distance or misalignment on WPT performance in the kHz frequency range. We have elucidated a variety of loss mechanisms and found that the skin effect led to a critical thickness of the flexible Cu antenna. Further considerations of the proximity effect and the core loss yielded an optimal antenna-magnetic backplane design. We have also evaluated the user safety risks associated with joule heating and electromagnetic radiation. Our wearable WPT system showcases an unparalleled combination of wearability and power delivery to mobile and wearable devices, suggesting a new means of utilizing on-body or portable power sources without the hazards of charging cables. It also marks an exciting step toward the development of wearable microgrids wirelessly powering distributed mobile and wearable devices all over the body.