State-of-the-Art Power Transfer Methods in Triboelectric Energy Harvesters

Abstract

Triboelectric nanogenerators (TENGs) are attracting increasing attention as viable power sources for self-powered systems, due to advantages such as material and form-factor versatility, compatibility with low-frequency mechanical stimuli, and scalable, low-cost fabrication. Unlike conventional harvesters, TENGs exhibit two device-level characteristics that critically shape interface-circuit design: (i) a time-varying internal capacitance that induces a strongly dynamic source impedance, and (ii) a significantly high effective source impedance that yields very high open-circuit voltages at low currents. These characteristics directly affect impedance matching, rectification, voltage conversion, and maximum power point tracking (MPPT) strategies for maximum power transfer. While TENGs and piezoelectric energy harvesters (PEHs) share similar lumped electrical models, the time variance and voltage/current operating regime of TENGs fundamentally limit the portability of PEH-oriented power transfer methods. This paper provides two contributions. First, we introduce a figure-of-merit (FoM) that serves as an energy-extraction coefficient: the fraction of the ideal maximum power of the TENG device (under instantaneous impedance tracking) that appears at the rectifier input, typically the first stage of a power management unit (PMU). The FoM exposes losses arising from mismatch at the device–PMU boundary, thereby helping circuit designers localize dominant loss mechanisms (e.g., impedance mismatch, rectifier topology or suboptimal MPPT policies) and guiding device researchers to prioritize physical parameters (e.g., dielectric thickness, displacement, electrode area) with explicit awareness of interface constraints. Secondly, we conduct a thorough evaluation of the suitability of advanced PEH-derived methods, such as rectifiers (both passive and active configurations), DC–DC conversion, and MPPT, for application to TENGs. We derive theoretical upper bounds on extractable power for representative rectifier families under TENG-specific operating conditions, and we analyze technology-imposed voltage limits and their implications for architecture and control. We also survey recent TENG demonstrations together with their PMU interfaces and interpret reported performance through the proposed FoM. Overall, the analysis highlights that the unique characteristics of TENGs and technology limits for the voltages must be explicitly accounted for while developing interface circuits to realize maximum power extraction. This process can significantly benefit from coordinated device–circuit co-design via system-level metrics such as the proposed FoM.

I. Introduction

Self-powered systems enabled by energy harvesting technologies have become a popular method to address existing challenges in traditional battery-powered systems. Harvesting ambient mechanical energy has emerged as a promising solution to power autonomous sensor networks [1]–[3], wearable and implantable electronics [4]–[11], and Internet-of-Things (IoT) devices [12], [13].

For decades, piezoelectric energy harvesters (PEHs) dominated the mechanical-to-electrical energy conversion landscape due to their relatively high power density and well-established fabrication processes [14]–[21]. However, the introduction of triboelectric nanogenerators (TENGs) in 2012 by Wang et al. [22] offered a paradigm shift in how mechanical energy can be converted to usable electrical power. Unlike their piezoelectric counterparts, TENGs demonstrate remarkable versatility by utilizing an extensive range of flexible, lightweight, and cost-effective materials while accommodating diverse structural configurations tailored to specific mechanical input scenarios. This inherent design flexibility, combined with simplified fabrication requirements and broad material compatibility, has increased the adoption of TENGs in many application domains [23]–[35]. These distinctive advantages of TENG systems are illustrated in Fig. 1, providing a comprehensive overview of their technological benefits in multiple dimensions.

Fig. 1.

Key Advantages of triboelectric nanogenerators (TENGs) in terms of design flexibility, fabrication requirements, material compatability, and system integration.

The design optimization of TENG-based energy harvesting systems has traditionally employed a segmented approach, where researchers have focused on advances at the harvester level (aimed at enhancing the conversion of mechanical energy to electrical energy through triboelectric and electrostatic effects [36]–[39]) or on power management methods that condition the generated electrical output into a DC signal suitable for powering electronic loads or charging energy storage elements [40]–[48]. Researchers working on TENG devices typically focus on optimizing the physical parameters of the harvester (such as electrode area, dielectric properties, and contact surface characteristics) by connecting a fixed resistive load to the TENG output and empirically identifying the load resistance that maximizes the average power transferred to the load [49]–[52]. Alternatively, circuit designers independently optimize individual power management components (such as a rectifier, DC–DC converter, and control circuits) often analyzing each block in isolation under idealized conditions [53]–[56]. This decoupled design methodology overlooks the critical interdependence between the TENG and the power management unit, typically resulting in reduced power transferred to the load.

The core of this challenge arises from the impedance matching requirements imposed by the electrical behavior of the TENG [57]–[59]. The maximum transfer of power from the TENG to an external load occurs only when the load impedance matches the internal impedance of the TENG at each instant in time. Importantly, the internal impedance of a TENG dynamically varies due to the TENG’s time-dependent internal capacitance. Thus, the optimal load impedance is inherently time-dependent, a condition that cannot be fulfilled by a simple resistive load. Furthermore, since the TENG produces an alternating output, a rectifier is typically used as the primary interface between the TENG device and the power management unit [41], [43], [60]. The nonlinear characteristics of the rectifier and the time-varying internal impedance of the TENG introduce a coupled dynamic that cannot be accurately captured when the TENG device and interface circuits are analyzed independently. Thus, achieving maximum power transfer requires a holistic approach that jointly considers the characteristics of the TENG device and the power management circuits.

This paper addresses these challenges through two primary contributions. First, unlike prior studies that independently optimize either the TENG device or the power management circuits, we present an evaluation framework and introduce a figure-of-merit (FoM) that reveals the efficiency gap between the intrinsic energy conversion capability of the TENG and the practically extractable power. Conventional evaluations of power efficiency typically compare the DC output power to the power measured at the rectifier input, implicitly assuming that this input power represents the total energy available from the harvester. This assumption neglects the power lost due to the impedance mismatch between the TENG’s time-varying internal capacitance and the input impedance of the rectifier. To quantify this loss, we introduce a theoretical benchmark, referred to as the ideal maximum power, which represents the power that could be extracted if the load impedance perfectly followed the instantaneous optimal impedance of TENG throughout each mechanical cycle. Although such a condition is physically not feasible, this benchmark provides a meaningful reference that exposes the power loss that occurs before the power management unit, arising due to the rectifier’s inability to adapt to the dynamic impedance of the TENG. The FoM introduced in this paper compares the rectifier input power with the ideal maximum power, thereby quantifying how much power is lost due to the impedance mismatch caused by variable internal capacitance of the TENG.

Second, we critically assess the applicability of power transfer techniques originally developed for piezoelectric energy harvesters (PEHs) to triboelectric nanogenerator (TENG) systems. The transduction mechanisms underlying these two technologies, as illustrated in Fig. 2(a) for piezoelectric and Fig. 2(b) for triboelectric harvesters, differ fundamentally, leading to distinct electrical characteristics. PEHs operate based on the piezoelectric effect, where mechanical stress induces lattice deformation and dipole polarization, resulting in charge separation and bidirectional electron flow as the material undergoes cyclic deformation and relaxation [61]–[63]. This process produces alternating current with relatively moderate voltage levels. In contrast, TENGs are based on the contact electrification effect, where friction between dissimilar materials generates triboelectric surface charges that remain after mechanical separation [64], [65]. The subsequent variation in electrostatic potential as the surfaces move apart drives charge redistribution through the external circuit to balance the surface charge disparity, producing current pulses synchronized with the mechanical motion.

Fig. 2.

Transduction mechanisms in (a) piezoelectric and (b) triboelectric energy harvesters.

These distinct transduction mechanisms between the PEH and TENG devices result in significantly different electrical characteristics. Although both PEHs and TENGs can be represented by a voltage source with a reactive internal impedance, there are two important differences. First, TENGs produce open-circuit voltages on the order of hundreds to thousands of volts, which are several orders of magnitude higher than the output voltages of typical PEHs [66], [67]. Second, the internal capacitance of a TENG varies dynamically with electrode separation during mechanical motion, whereas the capacitance of a PEH remains practically constant, determined primarily by the fixed geometry and material properties of the piezoelectric crystal [68]. These differences have significant implications for the choice of rectifier topology, voltage conversion strategy, and control algorithms required to achieve maximum power extraction, as highlighted throughout this paper.

The remainder of this paper is organized as follows. Section II provides an overview of the electrical modeling of TENG devices, highlighting some of the unique TENG characteristics. The proposed system-level FoM is introduced in Section III. The implications of this FoM for maximum power transfer are also highlighted. Section IV explores various methods for power extraction and their compatibility with the characteristics of TENGs. For each method, a theoretical analysis is provided to determine the maximum power that can be extracted from the harvester. In Section V, experimental results from existing TENG-based energy harvesting systems are presented. The implications of the proposed FoM for these results are also discussed. Finally, Section VI concludes the paper and outlines directions for future research.

II. TENG Electrical Model

One of the most widely adopted approaches in TENG design is the vertical contact-separation configuration, as depicted in Fig. 3(a) [58], [69], [70]. In this configuration, two plates of conductive electrodes are used. One of the plates is fixed and coated with a dielectric material, while the other plate moves vertically in a periodic cycle. When the plates come into contact, an exchange of charge occurs, creating opposing charge on the moving electrode and the dielectric surface. This charge remains trapped because at least one of the materials is an insulator.

Fig. 3.

A contact-separation TENG: (a) the cross-section of the device, (b) the equivalent electrical model and (c) the final electrical model.

The equivalent electrical model of this TENG, shown in Fig. 3(b), consists of a voltage source ($V_{\mathrm{o}\mathrm{c}}$) and a fixed capacitor ($C_{\mathrm{d}\mathrm{e}\mathrm{v}}$) in series with a variable capacitor ($C_{\mathrm{a}\mathrm{i}\mathrm{r}}$) [59], [71], [72]. The voltage generated by the device can be expressed as

$$V_{\mathrm{o}\mathrm{c}}\left(t\right)=\frac{\sigma x\left(t\right)}{{ϵ}_0},$$ (1)

where ${ϵ}_0$ is the permittivity of free space, $\sigma$ is the charge density, and $x\left(t\right)$ is the distance between the two plates. In addition, the TENG internal capacitors can be expressed as

$$C_{\mathrm{d}\mathrm{e}\mathrm{v}}=\frac{S{ϵ}_0{ϵ}_r}{d},C_{\mathrm{a}\mathrm{i}\mathrm{r}}\left(t\right)=\frac{S{ϵ}_0}{x\left(t\right)},$$ (2)

where $S$ is the area of the plates, ${ϵ}_r$ is the relative permittivity and $d$ is the effective thickness of the coating material. Consequently, the combined internal capacitance of the TENG ($C_T$) can be expressed as

$$C_{\mathrm{T}}=\frac{S{ϵ}_0{ϵ}_r}{d+{ϵ}_{r}x\left(t\right)}.$$ (3)

Thus, the electrical model of a contact-separation TENG can be simplified, as illustrated in Fig. 3(c).

According to (3) and considering a periodic movement of the dielectric plate from zero (full contact mode) to $x_{\text{max}}$ (fully separated plates), $C_{\mathrm{T}}\left(t\right)$ in the electrical model of TENG varies between $C_{\mathrm{T},\text{max}}$ in full contact mode at the beginning of each cycle and $C_{\mathrm{T},\text{min}}$ when the plates are fully separated at each half cycle. Thus, $C_{\mathrm{T},\text{max}}$ and $C_{\mathrm{T},\text{min}}$ are

$$C_{\mathrm{T},\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{S{ϵ}_0{ϵ}_r}{d},$$ (4)

$$C_{\mathrm{T},\mathrm{m}\mathrm{i}\mathrm{n}}=\frac{S{ϵ}_0{ϵ}_r}{d+{ϵ}_r{x}_{\mathrm{m}\mathrm{a}\mathrm{x}}}.$$ (5)

Considering the commonly used motion profile for TENG characterization [59], [72], the displacement $x\left(t\right)$ is modeled as a sinusoidal motion,

$$x\left(t\right)=\frac{x_{\mathrm{m}\mathrm{a}\mathrm{x}}}{2}(1-cos\omega t),$$ (6)

where $\omega$ is the angular frequency of the motion and $x_{\text{max}}$ represents the maximum separation distance between plates. Based on this motion pattern, the open-circuit voltage $V_{\mathrm{o}\mathrm{c}}\left(t\right)$ and the equivalent time-varying capacitance of the TENG $C_{\mathrm{T}}\left(t\right)$ over one period $T$ are shown in Fig. 4.

Fig. 4.

The behavior of the triboelectric harvester illustrating the movement of the electrode, $x\left(t\right)$, open circuit voltage, $V_{\mathrm{o}\mathrm{c}}\left(t\right)$, and the variable capacitor, $C_{\mathrm{T}}\left(t\right)$ in one harvester cycle $T$.

Based on this electrical model, TENGs exhibit three distinctive characteristics that fundamentally differentiate them from other energy harvesting technologies and create unique design challenges. The first characteristic is the variable internal capacitance, where unlike PEHs with fixed internal capacitance [73], TENGs feature time-dependent capacitance $C_T\left(t\right)$ that varies with mechanical motion according to (3). This dynamic impedance characteristic significantly complicates power optimization as the optimal load impedance continuously changes during operation, requiring sophisticated matching strategies that cannot be achieved with fixed impedance approaches.

The second characteristic is the low internal capacitance, typically in the picofarad to nanofarad range [36], [74]. A low internal capacitance yields a high source impedance, which becomes particularly large at the low excitation frequencies (approximately 1–10 Hz) associated with human motion and ambient vibrations [11], [75]. Without appropriate impedance matching, the disparity between this source impedance and the load (or rectifier input) can substantially degrade power transfer efficiency, leading to significant losses at the interface between the harvester and the power management unit.

A third distinguishing characteristic is the high open-circuit voltage. TENGs typically produce voltages from hundreds to thousands of volts, which are orders of magnitude larger than those of PEHs [73], [76]. Although such levels can, in principle, enhance the power density and reduce the relative impact of diode forward drops in rectification, they simultaneously impose practical challenges for the design of the power management unit. When connected to practical loads or rectifiers, TENGs typically deliver output currents in the range of microamperes to milliamperes depending on the load impedance and device parameters. High-voltage rectification, start-up, and regulation typically require transistors and passive devices with elevated breakdown voltages. Reliability and leakage power also emerge as important considerations at high voltages. These technology and implementation constraints are often not considered in theoretical studies, yet they have a significant influence on practical realizations. Standard digital CMOS processes are limited to much lower voltages (typically 1.8 V to 5 V) and cannot accommodate TENG output voltages. However, there are specialized high-voltage CMOS fabrication processes that support transistors with voltage ratings from tens to hundreds of volts [77].

The electrical behavior of TENGs is commonly represented by using an electrical model similar to that of PEHs. A typical electrical model for a PEH device comprises a periodic Thevenin voltage source (which represents the mechanical vibration of the piezoelectric material) in series with a fixed capacitance that captures transducer parasitics. Due to this model-level similarity, numerous studies review the two technologies together [10], [11]. Several recent studies have also developed hybrid nanogenerators that leverage both PEHs and TENGs [78], [79]. However, circuit techniques developed for PEHs are not directly transferable to TENGs because of the fundamental differences summarized above. In particular, TENG interfaces must accommodate time-varying internal capacitance and the resulting dynamic source impedance, low-frequency operation with pronounced frequency dependence, and elevated open-circuit voltages with associated device and safety constraints. These factors require specialized power management unit architectures and control strategies that consider the unique TENG characteristics.

III. Evaluation of Power Transfer Efficiency

A. Conventional Methods and Limitations

In standard approaches, power transfer efficiency is evaluated by treating the TENG device and power management unit (PMU) as two distinct domains. The time-averaged power measured at the rectifier input (i.e., the PMU input) is adopted as the reference for subsequent efficiency calculations. Many integrated TENG systems employ maximum power point tracking (MPPT) to adjust the effective load and maximize this input power [80]–[82]. The controller perturbs or estimates the operating point by modulating, for example, the duty cycle of a downstream DC–DC converter or the rectifier switching frequency [56], or by regulating a targeted rectifier voltage [55], [83], thereby varying the impedance presented to the harvester. The operating point that maximizes the input power averaged over a mechanical cycle is then identified and treated as the available power from the harvester. End-to-end efficiency is computed as the ratio of the power delivered to the final load to this maximum input power.

Although widely used and effective for comparing PMU topologies under identical harvesters, this evaluation method has an important limitation that becomes more pronounced as $\beta$ (ratio of $C_{\mathrm{T},\text{max}}$ to $C_{\mathrm{T},\text{min}}$) increases. Specifically, due to the internal impedance that varies over time described by (3), the instantaneous power transfer capability can fluctuate significantly within each mechanical cycle when $\beta$ is large. MPPT schemes that maximize cycle-averaged input power necessarily consider a single effective loading profile and therefore cannot realize the time-dependent impedance required for instantaneous optimal transfer. As a result, for large $\beta$, intervals associated with low capacitance may support orders of magnitude higher instantaneous available power than those with high capacitance, yet the averaging-based method spreads the loading effect across the entire cycle.

Furthermore, conventional evaluation approaches do not provide a basic means of determining whether the maximum measured time-averaged input power reflects an intrinsic device limit or results from an imperfect impedance matching at the device–PMU interface. In the absence of a theoretical upper bound on extractable power, device researchers lack a quantitative basis for prioritizing physical parameters (such as dielectric thickness $d$, maximum displacement $x_{\text{max}}$, and electrode area $S$) that most constrain harvestable power. Similarly, circuit designers cannot adequately attribute observed losses among rectifier inefficiencies, suboptimal MPPT policies, and fundamental mismatches between the dynamic device impedance and the realizable loading profile of practical PMU architectures.

B. Ideal Maximum Power and Impedance Matching

To establish a more accurate theoretical foundation for the optimization of the TENG system, we define the ideal maximum power as the power that would be extracted if the TENG were terminated by a time-varying impedance that achieves a perfect conjugate matching with the internal capacitance of the device at each time instant. For the simplified TENG model shown in Fig. 3(c), the internal impedance is purely capacitive with magnitude

$$Z_{\mathrm{T}}\left(t\right)=\frac{1}{C_T\left(t\right)\omega }.$$ (7)

Maximum instantaneous power transfer would occur when the load presents an inductive reactance whose magnitude equals the magnitude of the capacitive reactance of $C_T\left(t\right)$ at each moment, as shown in Fig. 5(a). In this case, the optimal inductive load would be

$$L_{\mathrm{o}\mathrm{p}\mathrm{t}}\left(t\right)=\frac{1}{C_T\left(t\right){\omega }^2},$$ (8)

which cancels the capacitive reactance, resulting in resonance and maximum power transfer. Inductive matching is impractical at low operating frequencies of typical TENG devices (on the order of Hz), as it requires inductors on the order of mega Henries. Therefore, we consider a resistive load for power extraction, as illustrated in Fig. 5(b).

Fig. 5.

Ideal impedance matching options between a TENG device and its load: (a) conjugate impedance matching and (b) resistive matching.

For a resistive load ${\mathrm{R}}_L$, the instantaneous power delivered to the load is

$$P_{\mathrm{L}}\left(t\right)=\frac{V_{\mathrm{o}\mathrm{c}}^2\left(t\right)R_L\left(t\right)}{R_L^2\left(t\right)+Z_T^2\left(t\right)},$$ (9)

as $Z_T$ is a pure reactance. When the load is a time-varying resistor that continuously matches the instantaneous impedance of ${\mathrm{C}}_T$, the optimal resistance $R_{\mathrm{L},\text{opt}}\left(t\right)$ and voltage $V_{\mathrm{L},\text{opt}}\left(t\right)$ across the load are given by

$$R_{\mathrm{L},\mathrm{o}\mathrm{p}\mathrm{t}}\left(t\right)=\frac{1}{C_T\left(t\right)\omega },V_{\mathrm{L},\mathrm{o}\mathrm{p}\mathrm{t}}\left(t\right)=\frac{V_{oc,AC}\left(t\right)}{\sqrt{2}}.$$ (10)

When the load connected to a TENG differs from the optimal load resistance $R_{L,\text{opt}}\left(t\right)$, power loss occurs due to impedance mismatch. With this time-dependent optimal resistive load, the maximum available power is

$$\begin{gathered} P_{\text{harv,ideal,avg}}=\frac{1}{T}{\int }_0^T{V}_{\mathrm{L},\mathrm{o}\mathrm{p}\mathrm{t}}\left(t\right)\times I_{\mathrm{L},\mathrm{o}\mathrm{p}\mathrm{t}}\left(t\right)dt \\ =\frac{S{\sigma }^2{ϵ}_r\omega }{2T{ϵ}_0}{\int }_0^T\frac{{\left(x\left(t\right)-x_{avg}\right)}^2}{d+{ϵ}_{r}x\left(t\right)}dt \end{gathered}$$ (11)

where $T$ is the harvester period and $x_{avg}$ is the average displacement. The power delivered to this load, given by (11), constitutes the upper bound on the extractable power from a fixed harvester connected to an optimally matched load. Thus, this bound represents the maximum harvestable power determined solely by the physical parameters ($S$, $d$, ${ϵ}_r$, $\sigma$) of the harvester and the mechanical input characteristics ($x_{\text{max}}$, $\omega$). Reductions in extracted power relative to this bound arise from impedance mismatch at the device–PMU interface, rectifier losses, or inefficiencies in subsequent power conditioning stages. By quantifying this theoretical maximum, we establish a topology- and control-agnostic reference against which practical implementations can be evaluated.

In practical implementations, the load resistance is typically fixed rather than time-varying. For a fixed resistor $R_L$, the average power over one cycle is obtained by integrating (9). The optimal fixed resistance that maximizes the average power is obtained by maximizing

$$P_{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{v},\mathrm{a}\mathrm{v}\mathrm{g}}=\frac{1}{T}{\int }_0^T\frac{V_{oc}^2\left(t\right)R_L^2}{{\left(R_L^2+Z_T^2\left(t\right)\right)}^2}dt.$$ (12)

C. Figure of Merit for TENG Systems

To assess how effectively a given PMU topology extracts power from a specific TENG device, we introduce a figure of merit (FoM) that serves as an energy-extraction coefficient. The FoM is defined as the percentage of the ideal maximum power of the device that appears at the input of the rectifier, thus quantifying the quality of impedance matching between the harvester and the PMU,

$$\mathrm{F}\mathrm{o}\mathrm{M}=\frac{P_{\mathrm{P}\mathrm{M}\mathrm{U},\mathrm{i}\mathrm{n},\mathrm{a}\mathrm{v}\mathrm{g}}}{P_{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{v},\text{ideal,avg}}},$$ (13)

where $P_{\mathrm{P}\mathrm{M}\mathrm{U},\mathrm{i}\mathrm{n},\mathrm{a}\mathrm{v}\mathrm{g}}$ is the time-averaged power delivered to the PMU input under a given loading condition, including MPPT methods, and $P_{\text{harv,ideal,avg}}$ is given by (11). The proposed FoM quantifies the impedance matching performance at the device–PMU interface. A FoM equal to unity denotes perfect (though impractical) tracking of the device's time-varying optimal impedance, whereas smaller values indicate an increasing mismatch between the device impedance and the effective load presented by the PMU. Note that the suggested (FoM) distinctly isolates the power loss that occurs specifically due to imperfect impedance matching, distinguishing it from the losses occurring in subsequent PMU components such as the rectifier, DC-DC converter, and control circuitry. To assess the entire system, we describe the power transfer efficiency of the system as

$$\begin{gathered} {\eta }_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}}=\mathrm{F}\mathrm{o}\mathrm{M}\times {\eta }_{\mathrm{P}\mathrm{M}\mathrm{U}} \\ =\frac{P_{\mathrm{P}\mathrm{M}\mathrm{U},\text{in,avg}}}{P_{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{v},\text{ideal,avg}}}\times \frac{P_{\mathrm{o}\mathrm{u}\mathrm{t}}}{P_{\mathrm{P}\mathrm{M}\mathrm{U},\text{in,avg}}}=\frac{P_{\mathrm{o}\mathrm{u}\mathrm{t}}}{P_{\text{harv,ideal,avg}}} \end{gathered}$$ (14)

where ${\eta }_{\text{PMU}}$ is the conventional PMU efficiency (ratio of PMU output power to PMU input power) and $P_{\text{out}}$ is the power delivered to the final load. Thus, the efficiency of the system is evaluated by comparing the actual useful output power with the theoretical maximum power that can be extracted.

The power transfer efficiency of the system given by (Equation 14) provides a useful metric that considers each source of loss throughout the entire energy harvesting process, allowing fair comparisons between various TENG systems. For example, a high PMU efficiency ${\eta }_{\text{PMU}}$ does not guarantee a high overall system efficiency if the FoM is poor. Consider a system where an MPPT algorithm successfully maximizes the average input power to the PMU, achieving $P_{\text{PMU,in,avg}}=10\mathrm{m}\mathrm{W}$. A well-designed PMU delivers this power to the load with efficiency 90%, producing $P_{\text{out}}=9\mathrm{m}\mathrm{W}$. Thus, according to standard metrics, the system functions effectively. However, if the device's ideal maximum power output for the same mechanical input is $P_{\text{harv,ideal,avg}}=50\mathrm{m}\mathrm{W}$, the FoM is only 0.2, indicating a system efficiency of only 18%. Theoretically, the device could supply five times greater power. However, failure of the PMU to follow the dynamic optimal impedance, particularly during high-power phases when $C_T\left(t\right)$ approaches its minimum, leads to 80% of potential power being dissipated at the device-PMU interface, even before factoring in any inefficiencies of the PMU itself. As another example, according to the harvester parameters described in [40], the internal capacitance ranges from 20 pF when the plates are fully separated to 245 pF when in contact ($\beta \approx 12$). Upon connecting the PMU to the device, the rectifier's input voltage reaches 48 V, while the device generates an open-circuit voltage of 500 V. Assuming a sinusoidal waveform for the movement of the plates, the device can produce 291.6 μW during each harvester cycle. This corresponds to an average output current of approximately 18 μA at the 48 V rectifier voltage. However, only 88 μW of power is transferred per cycle to the PMU. In this scenario, the FoM is determined to be 0.3. These examples illustrate the importance of the proposed FoM in evaluating the system-level power transfer efficiency of TENGs.

It is important to note that the proposed FoM is most applicable to energy harvesters with time-varying internal impedance. For harvesters with constant internal impedance, such as piezoelectric devices, static impedance matching can achieve near-optimal power transfer [84], and the FoM provides limited additional insight beyond conventional efficiency metrics [61].

D. Design Implications

The FoM given by (13) and system efficiency given by (14) offer useful insights for both circuit and device designers, facilitating the co-optimization of the TENG system rather than focusing solely on component-level enhancements. For those working on circuits, the FoM quantifies the efficacy of a specific PMU topology and its control strategy when integrated with a TENG device. By evaluating the FoM across various rectifier topologies, as well as differing switching strategies and MPPT algorithms, designers can determine which configurations best address the device’s time-varying impedance properties. Crucially, FoM indicates when further PMU efficiency improvements, like minimizing conduction losses, enhancing switching speeds, or refining control algorithms, will have minimal impact on overall system performance due to the predominant power loss caused by impedance mismatches at the device-PMU interface. In these situations, attention should pivot towards creating PMU topologies that better track the device’s dynamic impedance, albeit with a slight compromise in PMU efficiency.

In the development of the harvester device, researchers should consider the dependence of the ideal maximum power, as defined by (11), on physical parameters and how different design decisions impact the power that can be collected. Importantly, this evaluation indicates that simply increasing open-circuit voltage or capacitance variation does not necessarily lead to greater extractable power when considering the constraints of practical PMU configurations. In particular, enhancing $\beta$ by reducing the dielectric thickness or increasing the maximum displacement can raise the theoretical maximum power; however, it concurrently decreases the FoM achievable with real-world PMU designs, which can ultimately result in a decrease in the actual output power. The framework described in this section establishes a basis for the comprehensive analysis of particular PMU topologies described in Section IV.

IV. Power Management Unit (PMU) Circuitry

Energy harvesting circuit for a TENG device comprises the same building blocks as the conventional interface with PEHs: rectification, DC-DC converter and control unit, as shown in Fig. 6. This figure also illustrates the impedances at the device-PMU interface: the time-varying TENG impedance ${\mathrm{Z}}_{\mathrm{T}}$ and the PMU input impedance ${\mathrm{Z}}_{\mathrm{P}\mathrm{M}\mathrm{U}}$. The mismatch between these impedances leads to power loss, as discussed in Section III, where we introduce the FoM. However, the high voltage signal and the time-varying capacitance in the electrical model of TENG lead to unique challenges in the design of the interface circuit and optimization of the energy extraction.

Fig. 6.

Block diagram of a triboelectric energy harvesting system.

A. Rectifier Design for TENGs

The rectifier is the first stage at the interface with both types of energy harvesters, PEH-based devices, and TENG-based devices. For rectifier intefacing PEH, the primary focus in the design is minimization of the forward voltage drop across the diodes and reduction of the reverse leakage current. In TENG systems, the diode conduction loss is less critical due to orders of magnitude higher operating voltage. However, high and variable internal impedance of the TENG along with the high voltage introduce considerable challenges in the design of an efficient charge extraction rectifier, especially in the case of active rectifier.

1). Passive Rectifiers:

The full-wave rectifier (FWR) topology utilizes bidirectional charge flow and doubles the usable energy compared to a half-wave rectifier. Since the TENG behaves as a high-voltage AC source with capacitive impedance, the FWR provides symmetric conduction paths that minimize charge accumulation on the electrodes and prevent polarization imbalance that can occur with single-direction conduction. Additionally, the diode-based FWR requires no control or auxiliary power, which is essential for self-driven architectures where the TENG is the sole energy source. Therefore, the choice of a full-wave rectifier reflects a balance between simplicity, bidirectional energy harvesting, and compatibility with autonomous operation.

For rectifier interfacing PEH with constant internal capacitance, the extracted charge from the harvester is equal for the rising and falling half-period of the open-circuit voltage signal and the same output rectifier voltage. When rectifier is interfacing TENG device, there is an asymmetry in the charge transferred during two cycles due to variable internal capacitance, as given by

$$\begin{gathered} \mathrm{\Delta }{Q}_p=C_{T,min}\left(V_{oc,max}-\mathrm{\Delta }V-(1+\beta )\left(V_{rec}+2V_d\right)\right) \\ \mathrm{\Delta }{Q}_n=C_{T,min}\left(V_{oc,max}-\beta \mathrm{\Delta }V-(1+\beta )\left(V_{rec}+2V_d\right)\right) \end{gathered}$$ (15)

where $\mathrm{\Delta }{Q}_p$ and $\mathrm{\Delta }{Q}_n$ represent the rising and falling half-period of the periodic open-circuit voltage signal. $V_{\mathit{\text{rec}}}$ is the rectifier output signal at the beginning of the half-cycle, $V_d$ is the voltage drop across the diode and $\mathrm{\Delta }V$ is the change in the output voltage at the end of the half-cycle. From (15), we observe that the extracted charge is suboptimal and a function of the rectifier voltage due to precharging of the internal capacitance. Fig. 7 illustrates the schematic of a FWR connected to a TENG, along with the time waveforms at the terminals of the TENG interfacing full-wave rectifier, under the assumption that the displacement of the electrodes in the TENG follows a sinusoidal function.

Fig. 7.

The schematic of a FWR is shown in (a). The waveforms in (b) are voltages $V_{oc}$ (blue) and $V_c$ (red), the voltage at terminals of internal capacitor of TENG. The time waveforms shown in (c) are voltages $V_p$ (blue) and $V_n$ (red) at terminals of TENG.

From (15), we obtain the energy per cycle as a function of the output voltage. For a fixed output capacitance $C_{\mathit{\text{rec}}}$, the optimal voltage that maximizes the extracted energy per cycle from TENG using FWR is

$$V_{rec}^{\mathrm{o}\mathrm{p}\mathrm{t}}=\left(\frac{V_{oc,max}}{2(1+\beta )}-V_D\right)\left(1-\frac{C_{T,min}+C_{T,max}}{C_{rec}-C_{T,min}}\right).$$ (16)

When the rectifier capacitance is much larger than the internal capacitance of TENG and the output voltage of the rectifier is kept almost constant, the optimal voltage becomes

$$V_{rec}^{\mathrm{o}\mathrm{p}\mathrm{t}}=\frac{V_{oc,max}}{2(1+\beta )}-V_D.$$ (17)

In this case, the maximum power extracted by a FWR connected to a TENG is

$$P_{FWR}^{\mathrm{m}\mathrm{a}\mathrm{x}}=2f{C}_{T,min}(1+\beta ){\left(\frac{V_{oc,max}}{2(1+\beta )}-V_D\right)}^2,$$ (18)

where $f$ is the frequency of the periodic displacement of the electrodes. From (18), we note that the maximum power obtainable using FWR is highly dependent on the variation of the internal capacitance.

FWR as a passive rectifier has been used primarily in the discrete implementations of energy harvesting systems [42], [54]. The reverse bias voltage of discrete diodes matches the high open-circuit voltage of TENG. However, if the diode voltage increases beyond 500 V, the reverse leakage current becomes comparable to the output current of TENG, severely limiting the extracted energy.

Unlike piezoelectric harvesters, the extracted charge in two half-cycles of TENG open-circuit voltage is asymmetric. From (15), with increase of the rectifier output voltage and for TENGs with high $\beta$ (ratio of the maximum and minimum internal capacitance), the charge can be reversed. In this case, the half-wave rectifier demonstrates higher extracted energy than the FWR [41], [55]. To still utilize the charge that can be extracted in the falling half-cycle, dual output rectifier that separately extracts the positive and negative half-waves into two independent output nodes is implemented [55], as illustrated in Fig. 8. The output of the negative voltage side is kept at a lower value than the voltage on the positive side in order to optimize charge extraction, leading to improvement of the efficiency over FWR [55]. However, the dual output of the rectifier introduces complexity into the design of the following DC-DC converter. Due to imbalance between two sides, the energy can be harvested from the positive path, while the energy stored on the output capacitor of the negative side can be used for powering the control logic in the power management unit [41].

Fig. 8.

The schematic of a dual-output rectifier.

2). Synchronized-Switched Harvesting (SSH) Rectification:

The loss in the charge transfer from TENG in one cycle using FWR is due to precharging of the internal capacitance. This negative bias voltage introduces a phase difference between the voltage and current of TENG and reduces the on-time of diodes in the rectifier. To eliminate the phase difference and off-time of diodes, a synchronized-switched harvesting (SSH) for reversing the biasing voltage of the internal capacitor has been introduced for PEHs [85]. The polarity reversal is implemented by introducing an inductor or switched-capacitor in FWR architecture, as discussed by the following.

Inductor-based SSH.

In synchronized-switched harvesting on inductor (SSHI) technique, an inductor is introduced to change the polarity of the bias voltage [85]. The charge flow is controlled through an in series switch that ensures that the energy-transfer between internal capacitance and inductor happens at the end of each half-cycle and the polarity of the bias voltage is reversed. The series connection of inductor and switch can be in parallel or series connection with TENG. In the parallel SSHI (P-SSHI)–based rectifier, a series inductor–switch branch is connected in parallel with TENG. When the switch is briefly turned on for half the resonant period of the $LC$ circuit, it inverts the voltage across the TENG's internal capacitance, $C_T$ [86], as shown in Fig. 9(a). By synchronizing the switch activation with the turn-off moment of one diode pair, the polarity of the voltage across $C_T$ is reversed, prompting the other diode pair to conduct after half of the $LC$ resonance cycle. Because the $LC$ resonant frequency is significantly higher than the operating frequency of the TENG, the off-time of the diodes becomes negligible, thereby resolving the issue of diode recovery delay [87]. Fig. 9(b) and (c) illustrate the voltage waveforms at the TENG terminals and across the internal capacitor. From the waveform of the voltage across the internal capacitor, we obtain the extracted charge from TENG in both half-cycles as

$$\begin{array}{r}\mathrm{\Delta }{Q}_p=C_{T,min}\left(V_{oc,max}-\mathrm{\Delta }V+(\beta -1)\left(V_{rec}+2V_d\right)\right)\\ \mathrm{\Delta }{Q}_n=C_{T,min}\left(V_{oc,max}-\beta \mathrm{\Delta }V-(\beta -1)\left(V_{rec}+2V_d\right)\right).\end{array}$$ (19)

Fig. 9.

The schematic of a P-SSHI rectifier is shown in (a). The waveforms in (b) are voltages $V_{oc}$ (blue) and $V_c$ (red), the voltage at terminals of internal capacitor of TENG. The time waveforms shown in (c) are voltages $V_p$ (blue) and $V_n$ (red) at terminals of TENG.

For a large value of $C_{\mathit{\text{rec}}}$, the total charge extracted in one cycle becomes optimal,

$$\mathrm{\Delta }Q=2C_{T,min}{V}_{oc,max}.$$ (20)

We observe that the extracted charge is a function of only the TENG parameters. From (1) and (5), the total charge is

$$\mathrm{\Delta }Q=\frac{\sigma S}{1+\frac{d/ϵr}{x_{\mathrm{m}\mathrm{a}\mathrm{x}}}}=\sigma S\left(1-\frac{1}{\beta }\right).$$ (21)

The efficiency of charge extraction from the TENG is proportional to the maximum displacement of the moving electrode and inversely proportional to the effective thickness (i.e., thickness divided by the relative permittivity) of the dielectric layer. We observe that the increase in $\beta$ increases the extracted charge, but the increased asymmetry adds complexity to the circuit design. The theoretical maximum extractable power for a TENG connected to a P-SSHI based rectifier is then obtained by multiplying the extracted charge by the output voltage of the rectifier [83],

$$P_{PSSHI}^{\mathrm{m}\mathrm{a}\mathrm{x}}=2f{C}_{T,min}{V}_{oc,max}{V}_{rec}.$$ (22)

With an increase of the rectifier voltage, the extracted power can go to infinity, similar to the P-SSHI technique applied to PEH (assuming there is no limit on the voltage). Similar to the PEH method, the loss in extracted charge is due to loss in charge transfer between the internal capacitor and the inductor [88].

Although P-SSHI-based rectifier offers significantly higher energy extraction efficiency compared to FWR, the gain is reduced when the output voltage of the rectifier is limited by the technology. The reduction is significant for a high ratio of the maximum open-circuit voltage of TENG, $V_{oc,\mathit{\text{max}}}$ and the rectifier voltage limit, $V_{\mathit{\text{max}}}$, as seen from (15) and (21). The relative charge loss in (15) is a function of the ratio of $V_{oc,max}$ and $V_{\text{max}}$. Given the stringent voltage limitation in IC implementations, with a $V_{\text{max}}$ value of 70 V, for TENGs $V_{oc,max}$ greater than 1 kV, P-SSHI rectifiers become less effective compared to PEH harvesters. In one more scenario, the performance of P-SSHI when interfacing TENG is different compared to PEH due to the asymmetry in the extracted charge in two half-cycles (19). When the ratio of $V_{oc,max}$ and $V_{\mathit{\text{rec}}}$ becomes comparable to $\beta$, the direction of the charge in the negative half-cycle can be reversed, calling for a similar solution as the dual-output rectifier in FWR.

Implementation of a P-PSHI rectifier requires a precise time control circuit to activate the high-voltage switches, which poses significant challenges in discrete designs due to the large leakage current. For IC implementation, the required bulky inductor is impractical for on-chip integration and must be implemented as an external component.

Switched-capacitor based SSH.

The Electrostatic Charge Boosting (ECB) rectifier is an inductor-less interface designed to enhance energy extraction from TENG. The ECB rectifier introduces a switched-capacitor (SC) architecture that synchronizes charge extraction and redistribution according to the capacitance variation. Fig. 10 shows the schematics of this technique. Its operation consists of three main phases—extraction, flipping, and charging. During the extraction phase, when the TENG capacitance reaches its minimum, energy is extracted and temporarily stored in a capacitor array. Discharging $C_T$ in this phase will prevent the rectifier diodes from turning off. In the flipping phase, voltage flipping aligns the TENG voltage with the current direction to maximize charge transfer, and in the charging phase, the stored charge is dumped back to the TENG at a lower voltage level, preventing the rectifier diodes from turning off again. This synchronized charge-return process boosts the net electrostatic charge ($Q_T$) on the TENG electrodes, achieving a charge-boosting coefficient greater than one, which leads to a quadratic increase in output power with rectified voltage [89]. The extracted power from an ECB rectifier is

$$P_{ECB}^{\mathrm{m}\mathrm{a}\mathrm{x}}=(\alpha -1)f{C}_{T,min}{V}_{rec}^2+\left({\eta }_f+1\right)f{C}_{T,min}{V}_{rec}{V}_{oc,max}$$ (23)

where ${\eta }_f$ is the flipping efficiency and $\alpha$ is the charge storage efficiency during the temporary storage. The theoretical maximum power achievable by this rectifier under ideal conditions is

$$P_{ECB}^{\mathrm{m}\mathrm{a}\mathrm{x}}=2f{C}_{T,min}{V}_{rec}{V}_{oc,max}$$ (24)

which is similar to the maximum power achievable by P-SSHI technique. Although ECB and P-SSHI lead to the same amount of maximum theoretical power, the absence of inductors in the ECB method enables full CMOS integration, making the ECB approach a compact and efficient power management solution for self-powered TENG systems. However, increasing $\alpha$ in the ECB technique requires a considerable number of precise high voltage switching, making the controlling circuit more complicated and reducing the efficiency.

Fig. 10.

The schematic of rectifier with implemented electrostatic charge boosting.

3). Synchronized Electric Charge Extraction Rectification:

The synchronized electric charge extraction (SECE) rectifier aims to maximize the energy transfer efficiency of TENGs by actively controlling the timing and pathway of charge extraction from the output of the rectifer, as opposed to the SSH technique. In this topology, as shown in Fig. 11, the rectifier operates under open circuit conditions and is only discharged when the internal capacitance reaches the minimum and the maximum value. This leads to the total extracted charge per cycle to be the same as in the SSH technique, as given by (21). The charge is transferred to the inductor connected to the output of rectifier in a fashion similar to that of the buck DC-DC converter. An important difference compared to the SSH technique is that charge transfer occurs when the rectifier voltage is equal to the maximum open-circuit voltage of TENG, $V_{oc,\mathit{\text{max}}}$. This leads to a higher extracted power compared to (22),

$$P_{SECE}^{\mathrm{m}\mathrm{a}\mathrm{x}}=2f{C}_{T,min}{V}_{oc,max}^2.$$ (25)

Fig. 11.

The schematic of synchronized electric charge extraction rectifier.

However, in the SECE implementation, the voltage across the switch and diodes is as high as $V_{oc,max}$. This greatly limits the applicability of this method for TENG devices. Thus, the SECE implementation has been limited only to discrete implementation of the harvesting circuit that interfaces TENG with comparable $V_{oc,max}$.

B. DC-DC Conversion for TENGs

To maximize the efficiency of the rectifier in an energy harvesting system that interfaces with TENG, the output voltage of the rectifier should be high, as discussed in Section IV-A. To convert the high output voltage of the rectifier to a lower power supply voltage, the DC-DC converter following the rectifier should have a low conversion ratio (defined as $V_{\mathit{\text{out}}}/V_{\mathit{\text{in}}}$).

The conventional choice for a DC-DC converter is an inductor-based buck converter. The inductor used in the TENG DC-DC converter has a high value (typically in the range of millihenries) due to the low frequency of operation. Thus, it is a bulky external component that cannot be implemented on an IC. The primary challenge in designing a DC-DC converter for a TENG PMU is minimization of the loss on the high-voltage switch and the design of the control logic that operates on the harvested energy. Since the power harvested from a TENG is typically in the microwatt range, even small losses in the switching element can significantly degrade the overall efficiency of the PMU. In discrete implementations, the switch is typically implemented using a high-voltage discrete transistor or a silicon-controlled rectifier (SCR), both of which are prone to significant leakage current losses. The losses on the SCR-based switch can reach almost 50% of the transferred power [42]. In contrast, IC implementations require the use of a high-voltage transistor in combination with a level shifter to enable proper control of the switch and operation at cold start.

Dual-output rectifiers, as shown in Section IV-A, offer increased efficiency in interfacing TENGs with high values of $\beta$ due to the asymmetric extracted charge in two half-cycles. Instead of using a buck converter with two inductors, dual-input buck converters with bidirectional inductor current are designed to combine the extracted charge into a single output voltage [55].

Due to the low voltage conversion ratio (much lower output voltage compared to the input voltage), the cascading of two stages of DC-DC conversion reduces energy loss. The first stage of this hybrid DC-DC converter is a buck converter followed by a switched-capacitor (SC) DC-DC converter [53].

C. Maximum Power Point Tracking for TENGs

Maximum Power Point Tracking (MPPT) adapts the input impedance of the harvesting circuit to optimize the energy extracted from a harvesting source. For PEH devices with a time-invariant internal capacitance $C_{\mathrm{T}}$, with FWR connected to the PEH, the voltage at the PEH terminals is half of the open-circuit voltage [90]. Since PEH open-circuit voltages typically range from 2–10V, the optimal rectifier voltage is easily accommodated in conventional IC technologies. At the interface with PEHs, MPPT techniques have proven highly effective, with reported tracking efficiencies between 81% and 98.66% for various implementations [91]. The success of MPPT in PEH systems is due to their moderate voltage levels and time-invariant internal capacitance, which allow the optimal operating point to be maintained consistently within the technology limit.

Alternatively, in TENG devices, the time-varying nature of the internal capacitance of TENG $C_{\mathrm{T}}\left(t\right)$ requires that the optimal load resistance vary according to (10). Assuming that the load resistance is time-variant, the optimal load resistance is obtained from the maximum harvested power in (11). The optimal load resistance and the output voltage for that load resistance depend on the parameters of TENG, as well as the time-waveform of the electrode displacement. When an FWR interfaces with TENG, the optimal voltage, defined by (17), depends on the mechanical parameters of TENG (ignoring the voltage drop across the diode, which is much smaller than the open circuit voltage of TENG). For example, the optimal voltage for two different TENGs is empirically obtained to be between 0.3 and 0.4 times the open-circuit voltage [55]. The fractional open-circuit voltage (FOCV) technique monitors the open-circuit voltage and regulates the system to maintain the rectifier voltage around the optimal value [55], [92]. For a TENG with the maximum open-circuit voltage in the range of a few thousand volts or more (see Table I of the following Section), the optimal rectifier voltage ranges from a few hundred volts to several thousand volts. These voltages are higher than the typical voltage limits of IC technology. For P-SSHI, from (22), the optimal rectifier voltage is defined by the maximum rectifier voltage. Therefore, tracking of the open-circuit voltage is not needed, as optimal voltage is determined by the voltage limit of the technology [89].

TABLE I:

Comparison of Different TENG Power Management Systems

Parameter	2015 [54]	2020 [42]*	2020 [55]	2021 [53]*	2022 [40]	2024 [41]	2024 [93]	2024 [89]	2024 [96]	2025 [95]
$V_{\mathrm{o}\mathrm{c},\text{max}}$	7000	65000	NA	15800	500	2500	430	100	300	145
$C_{\mathrm{T}}$	NA	4–180	NA	15–825	20–245	105–1150	2300	30–230	NA	70–140
$V_{\mathrm{rec},\text{max}}$	250	494	3.5–70	70	48	509	70	70	300	70
Technology	Discrete	Discrete	Integrated	Integrated	Integrated	Discrete	Integrated	Integrated	Integrated	Integrated
$V_{\mathrm{oc},\text{max}}/V_{\mathrm{rec},\text{max}}$	28	131.57	NA	226	10.48	4.91	6.14	1.43	1	2.07
Rectification	FWR	FWR	DOR	P-SSHI	FWR	DOR	P-SSHI	ECB	SECE	ECB
Frequency (Hz)	4	3.3	20–50	1	5	2	45.6	150	1	70
MPPT	FOCV	-	FOCV	-	P&O	-	P&O	Auto-MPPT	-	DCB
Output Power (μW)	202.3	298.6	10.95	2.89†	8.3	110.3	153	127.6	44.6	85.4
Reported efficiency (%)	59.8	-	52.9	32.7	52.9	-	81.2	-	51.2	-
$P_{\mathit{out}}/P_{\mathit{FWR},\mathit{\text{max}}}$	-	0.84	-	-	-	2.75	-	14	-	5.98
${\eta }_{\mathit{\text{system}}}$	2.04	0.87	-	0.068	15.96	9.87	-	24.44	-	10.27

Note*: The values of $V_{\mathrm{oc},\text{max}}$ and $C_{\mathrm{T}}$ for these references were calculated based on the reported TENG characteristics and were not directly provided in the papers.

Note^†: The reported 2.89 μW represents the average output power, assuming the reported instantaneous power of 722 μW is available for 4 ms within each 1-second cycle.

In the perturb and observe (P&O) technique, the input and output energies of the rectifier are monitored using voltage and current sensors [93]. The harvested charge is then optimized by partially adjusting the discharge energy and comparing the corresponding power levels. Although this method handles varying mechanical excitations and achieves MPPT efficiencies exceeding 99% [94], it exhibits a slow convergence rate, often requiring tens or even hundreds of cycles to locate the maximum power point. This limitation is critical when the excitation force changes rapidly. Moreover, the control circuits necessary for this method tend to be power-intensive and complex to design.

The Digital Charge Balancing (DCB) MPPT method is a closed-loop digital tracking scheme that optimizes energy extraction from TENG [95]. The DCB method regulates the rectifier output voltage based on the real-time charge dynamics rather than relying on periodic voltage or power measurements. In this approach, the control circuit continuously monitors the charge transfer process and digitally adjusts the reference voltage or switching instant to maintain the optimal charge balance between the internal capacitance of the TENG and the rectifier capacitor. Compared to conventional MPPT techniques, for a TENG operating with variable force, this method achieves faster and more accurate tracking by maintaining continuous operation and adjusting the rectifier output voltage directly through charge-balance feedback. However, this method requires more complex and power consuming circuitry to operate efficiently.

V. The Impact of the Introduced FOM on the assessment of the current TENG PMUs

Table I summarizes the performance of recent state-of-the-art TENG systems. These works adopt varying definitions of efficiency, which makes a fair comparison challenging. For example, in [54], [55], [53], [40], [93], and [96], an end-to-end efficiency metric is employed, where the power delivered to the final load is compared with the power extracted from the rectifier. In [42], [41], [89], and [95] efficiency is defined as the ratio of power delivered to the load to the maximum power achievable when the TENG is connected to a FWR with an optimal load. However, both of these definitions overlook the impedance mismatch between the TENG and the rectifier, which is typically the most significant source of energy loss. However, the efficiency definition ${\eta }_{\mathit{\text{system}}}$ introduced in Section III, as given by (14), accounts for this mismatch, providing a fair and consistent basis for comparing different systems. We provide details of a few implementations for which the proposed FoM (and therefore the system efficiency ${\eta }_{\mathit{\text{system}}}$ given by (14)) can be computed with the information provided on the TENG device. Note that some of these studies do not report all of the parameters needed to compute the proposed FoM. Thus, for those papers, the corresponding entry in the last row (calculated system efficiency) is left blank. We analyze the relationship between the maximum open-circuit voltage and the maximum voltage allowed in the implementation technology, the ratio $V_{oc,max}/V_{rec,max}$, the ratio $\beta$, the reported efficiency, and the proposed FoM.

TENG PMU utilizing a transformer in conjunction with a FWR was demonstrated to harvest biomechanical energy in [54]. The prototype connected ten TENG units in series, each producing 700 V. Due to its discrete architecture, the maximum rectifier voltage was capped at 250 V, resulting in a $V_{oc,max}/V_{\text{rec},max}$ ratio of 28 and consequently reducing impedance-mismatch losses. Although an efficiency of 59.8% was reported, the FOM indicates that only 2.04% of the available power was ultimately delivered. In addition, microcontroller-based control circuitry consumed additional power that was not included in the reported results, further lowering the effective efficiency.

A discrete TENG PMU that combines an FWR and a DC–DC buck converter driven by an SCR is presented in [42]. The rectifier achieved a discharge voltage of 494 V, while a mechanically large TENG produced an open-circuit voltage of 65,000 V. This resulted in an extremely high $V_{oc,\mathit{\text{max}}}/V_{\mathit{\text{rec}},\mathit{\text{max}}}$ ratio of 131.57, leading to a substantial loss due to impedance mismatch. The system did not implement MPPT; instead, the discharge timing was experimentally adjusted for specific operating points. Although the design delivered 0.84 times the power of a baseline FWR, the FoM-based system efficiency is only 0.87%.

A fully integrated TENG PMU, fabricated in a 180 nm high-voltage CMOS process, was introduced, featuring a P-SSHI rectifier and a buck converter [53]. Integration reduced parasitic losses, but the maximum acceptable rectifier voltage was restricted to 70 V, while the TENG generated up to 15,800 V. This large difference produced a very large $V_{oc,\mathit{\text{max}}}/V_{\mathit{\text{rec}},\mathit{\text{max}}}$ ratio of 226, causing most of the generated power to dissipate due to impedance mismatch. Although P-SSHI was used to enhance energy extraction and the discharge profile was tuned empirically (without MPPT), the stringent voltage limit severely limited performance. A peak power of 722 μW was reported; however, it was maintained for only 4 ms, corresponding to an average of 2.89 μW. According to the FoM, the resulting system efficiency is only 0.068%.

Integrated PMU that utilized a perturb-and-observe MPPT scheme was presented in [40]. The TENG delivered $V_{oc,max}=500\mathrm{V}$, while the rectifier voltage tolerance was limited to 48 V, resulting in a $V_{oc,max}/V_{\mathit{\text{rec}}}$ ratio of 10.48. This relatively modest ratio, paired with MPPT-controlled operation, enabled a system efficiency of 15.96%. However, the TENG exhibited high capacitance variability ($\beta =12.25$), which fundamentally restricted the harvesting efficiency and limited further improvements in the power extraction efficiency of the system.

A discrete PMU architecture using a dual-output rectifier (DOR) and a flyback converter with a discrete high-voltage switch was reported [41]. TENG delivered 2500 V and the rectifier discharged at 509 V, corresponding to a $V_{oc,max}/V_{\mathit{\text{rec}},max}$ ratio of 4.91. The low ratio significantly reduced the impedance mismatch compared to earlier implementations. Although no MPPT or adaptive discharge technique was applied, the design achieved a 2.75× higher efficiency than a conventional FWR. According to the FoM, the efficiency of the system is 9.87%, highlighting the benefit of maintaining a relatively low voltage ratio.

A fully integrated TENG PMU was introduced in [89] where the TENG produces an open-circuit voltage of only 100 V. Energy extraction was performed using an ECB rectifier, and the system applied an auto-MPPT strategy that fixed $V_{\mathit{\text{rec}}}$ at the maximum allowable voltage (70 V). Consequently, the $V_{oc,max}/V_{\mathit{\text{rec}}}$ ratio was only 1.43, which enabled highly efficient power extraction. Operating at 150 Hz and combined with low source voltage, this design achieved the highest system efficiency among the surveyed works, reaching 24.44% and extracting 127.6 μW from a compact TENG source.

A closer examination of existing TENG PMUs—including their design, characteristics, and a comparison using the proposed ${\eta }_{\mathit{\text{system}}}$—reveals that TENG-based energy harvesting systems generally exhibit lower efficiency than PEHs. This is primarily due to the intrinsic nature of TENG devices, which feature high output voltage, low current, and a time-varying internal capacitance.

We have shown that the primary source of power loss in TENG PMUs arises from impedance mismatch at the rectifier stage. In general, TENG devices with greater $V_{oc,max}$ and higher values of $\beta$ experience greater power loss due to mismatch, resulting in reduced efficiency. A high $V_{oc,\mathit{\text{max}}}$ decreases efficiency because, under ideal matching conditions, the rectifier load voltage must reach up to one-quarter of $V_{oc,\mathit{\text{max}}}$, which is often impractical due to the voltage limitations of standard electronic components. Similarly, a high $\beta$ value reduces efficiency since the rectifier's input impedance is typically fixed, whereas ideal matching would require it to be variable.

VI. Conclusions and Future Prospects

This paper has examined power transfer in TENGs from a system viewpoint, emphasizing the implications of two device-level attributes that fundamentally shape interface-circuit design: a time-varying internal capacitance that induces dynamic source impedance, and a significantly high effective source impedance that yields very high open-circuit voltages at low currents. We argued that conventional evaluation practices that are tailored to the average power measured at the rectifier input obscure losses that arise prior to the PMU due to impedance mismatch. To address this gap, we introduced a theoretical benchmark for the ideal maximum power of the device (under instantaneous impedance tracking) and a FoM that quantifies the fraction of this maximum that reaches the rectifier input. These metrics provide not only a better and more complete understanding of the effectiveness of the TENG-PMU interface, but also a reference for a fair comparison of existing TENG-based energy harvesting systems.

We critically evaluated the applicability of existing power transfer techniques developed primarily for piezoelectric energy harvesters (PEHs) to TENGs. We derived device-aware upper bounds on extractable power for various rectification methods and analyzed the impact of technology-imposed voltage limits.

A survey of recent TENG demonstrations and their PMU interfaces was then interpreted through the proposed FoM, illustrating how the metric helps identify dominant loss mechanisms and reveals when improving intrinsic PMU efficiency yields diminishing system-level returns relative to impedance-tracking limitations.

Future research on TENG-based energy harvesting systems can explore the feasibility of cycle-synchronous, real-time impedance tracking rather than cycle-average MPPT, particularly for TENGs with large variation in internal capacitance (high $\beta$). Such an effort would require effective circuitry to estimate instantaneous capacitance/charge and predictive control strategies to configure rectifier accordingly. However, the power budget for such control logic must be carefully considered. This power can represent a significant fraction of the harvested power in low-power TENG systems [53], [97]. The feasibility of real-time tracking depends on whether the improvement in FoM justifies the additional control overhead, favoring efficient implementations such as event-driven control and analog-based sensing.

Existing research has studied charge-shaping methods such as synchronized switched harvesting or synchronized charge extraction to transfer greater power. The efficacy of these methods is greatly increased at higher technology voltage limits. Thus, future research can also explore the applicability of wide bandgap semiconductor based power electronics for TENG interface circuits. For example, technologies that rely on SiC or GaN devices enable not only higher voltages but also opportunities for low leakage and fast switches. These advantages can significantly improve the efficiency of dynamic impedance tracking and rectification.

Another important opportunity lies in developing co-design methodologies (including frameworks for co-simulations/analysis) for jointly optimizing TENG geometry/materials and PMU architecture/control under practical process limits. This co-design methodology is expected to achieve greater power transfer because it jointly shapes the TENG’s electro-mechanical waveform and the PMU’s time-varying load to minimize impedance mismatch over the entire cycle and synchronizes switching actions with the device’s charge dynamics, and embeds technology voltage constraints into the optimization, thereby reducing rectification and conversion losses that decoupled designs leave unaddressed.

Furthermore, some applications can benefit from the aggregation of multiple TENG transducers, arranged in parallel and/or series, where the series connection is helpful specifically for sensing applications. Since individual elements may experience identical or different mechanical motions, array-level architectures with per-channel impedance adaptation and distributed MPPT are needed to maximize aggregate energy capture. Future work should develop source-aware methods to combine multiple TENG devices while considering the technology voltage limits. Collectively, these research directions are expected to substantially increase the extractable power from triboelectric harvesters and enable robust self-powered electronics across a broad range of applications.