Piezoelectric Energy Harvesters (PEHs)

Updated 24 November 2025

Piezoelectric Energy Harvesters (PEHs) are devices that convert mechanical energy into electrical energy via the direct piezoelectric effect, enabling autonomous power for sensing applications.
They utilize diverse material platforms like PZT, PMN-PT, and PVDF and common device architectures such as cantilevers and bimorph beams to optimize resonance and electromechanical coupling.
Advanced circuit techniques and structural innovations extend operational bandwidth and support simultaneous energy harvesting and sensing for IoT, wearables, and structural health monitoring.

Piezoelectric Energy Harvesters (PEHs) are devices that convert mechanical energy from ambient vibrations, deformations, or shocks into electrical energy using the direct piezoelectric effect. They are central to the development of energy-autonomous systems for distributed sensing, wearables, structural health monitoring, and the Internet of Things, due to their compact size, relatively high power density, and dual potential as both transducers and passive sensors.

1. Physical Principles and Material Platforms

PEHs operate based on the reversible coupling between mechanical stress/strain and electric polarization in non-centrosymmetric materials. The fundamental constitutive relations in linear piezoelectricity are

$D_i = d_{ij} T_j + \epsilon_{ij} E_j,\qquad S_i = s_{ij} T_j + d_{ij} E_j,$

where $D$ is electric displacement, $T$ is stress, $E$ is electric field, $S$ is strain, $d_{ij}$ are piezoelectric coefficients, $s_{ij}$ is compliance, and $\epsilon_{ij}$ is permittivity (Shirvanimoghaddam et al., 2017).

The most prevalent material systems for PEHs are lead-based ceramics such as PZT (lead zirconate titanate), single crystals (e.g., PMN-PT), and polymers (typically PVDF). Each presents distinct trade-offs in terms of piezoelectric coupling ( $d_{33}, k^2$ ), compliance, mechanical loss, and processability (Ghazanfarian et al., 2021, Shirvanimoghaddam et al., 2017).

Table 1. Representative material parameters for common PEH materials

Material	$d_{33}$ (pC/N)	$\epsilon_r$	$k_{33}$	Notes
PZT	300–600	1000–2000	0.60–0.75	High coupling, brittle
PMN-PT	1200–2000	3000–6000	0.85–0.95	Ultra-high coupling, fragile
PVDF	20–30	10–15	0.10–0.15	Flexible, wide bandwidth

The intrinsic electromechanical coupling coefficient fundamentally limits achievable power density. For device-level operation, the global coupling,

$k^2 = \frac{f_{oc}^2 - f_{sc}^2}{f_{oc}^2}$

can be directly extracted from open- and short-circuit resonant frequency measurements (Forges et al., 7 Jan 2025).

2. Device Architectures and Electromechanical Modeling

Most PEHs employ cantilever or plate geometries—unimorph or bimorph beams, often with a proof mass or specialized tip—configured for resonant response to ambient excitation (Shirvanimoghaddam et al., 2017). Stack structures and less common configurations (diaphragm, cymbal, shells) are also used (Ghazanfarian et al., 2021).

The standard modeling approaches span:

Lumped-parameter (SDoF) models: Mass–spring–damper systems coupled electrically via a transformer or voltage source. Electrical and mechanical circuits are coupled through:

$m \ddot{x} + c \dot{x} + k x - \theta v = F(t),\qquad C_p \dot{v} + G v + \theta \dot{x} = 0$

where $\theta$ is the electromechanical coupling and $C_p$ is the capacitance (Ghazanfarian et al., 2021).

Distributed-parameter (beam/plate) models (Kirchhoff–Love, Timoshenko), discretized via FEA or IsoGeometric Analysis (Peralta-Braz et al., 2022, Yao et al., 17 Nov 2025).
Nonlinear and broadband models: Incorporating geometric nonlinearity, elastic extensions, or auxiliary mass for bandwidth enhancement (Zhou et al., 2019).

Optimization of geometry—particularly length, thickness, and width, as well as piezo layer coverage and tip mass—enables tailoring of resonance and coupling to the target vibration spectrum (Peralta-Braz et al., 2022, Miyajima et al., 25 Jan 2024).

3. Circuit Interfaces and Bandwidth Control

Power electronics play a critical role in the energy extraction efficiency and operational bandwidth of PEHs. Linear systems with resistive loads reach maximum efficiency when the load is optimally matched, typically

$R_L^{\mathrm{opt}} = 1/(\omega_0 C_p)$

at resonance. However, in practical applications where vibrations are broadband or impulsive, advanced interfaces are essential.

Notable architectures include:

Full-Bridge Rectifiers (SEH): Simple but low bandwidth and low energy extraction under nonresonant conditions (Morel et al., 2018).
Synchronized Switch Harvesting on Inductor (SSHI) and Synchronous Electric Charge Extraction (SECE):
- SSHI utilizes switched inductors to invert the piezo voltage, increasing energy output particularly in periodic signals (Quelen et al., 2018).
- SECE extracts all available charge at each mechanical extremum and is especially effective for shock-based excitation, achieving up to 420% improvement in energy per shock over standard rectifiers (Quelen et al., 2018, Morel et al., 2018).
Bias-Flip (BF) and Phase-Variable Synchronized Switch Harvesting: These offer real and imaginary impedance tunability, drastically expanding the usable 3 dB bandwidth (from ~7% to >15%) when high electromechanical coupling $k^2$ is present (Zhao et al., 2019, Zhao et al., 2022).

Adaptive impedance control (via switched capacitor arrays or digital controllers) and hybrid/maximum power point tracking (MPPT) further enhance bandwidth and energy capture robustness under variable vibration environments (Karmakar et al., 16 Jul 2025).

4. Optimization, Topology, and Manufacturability

Recent advances target not just conventional beam optimization but also manufacturability-constrained topology design. Level-set-based topology optimization allows concurrent tuning of substrate and piezo domains, subject to constraints on cross-sectional uniformity (for etchability), output voltage, and target eigenfrequency (Miyajima et al., 25 Jan 2024).

Key metrics for design optimization:

Electromechanical Coupling ( $k^2$ or $k_{e,\text{piezo}}$ ): Directly relates to maximum achievable energy conversion. Auxetic or hollow substrates can increase the elastic energy fraction in the piezo, thus increasing global coupling, even if intrinsic material coupling is unchanged (Forges et al., 7 Jan 2025).
Energy conversion coefficient ( $\eta_n$ ): For the nth mode,

$\eta_n^{\max} = \frac{k_n^2}{k_n^2 + 2\zeta_n}$

at optimal load and modal damping $\zeta_n$ (Khazaee et al., 2022).

Voltage-per-strain and overall Figure of Merit: Metrics that capture both power output and material utilization for fatigue/failure analysis (Khazaee et al., 2022).

Manufacturability considerations mandate constraints such as feature size (lithography limits), cross-sectional regularity (for MEMS etching), and robust performance to fabrication deviations.

5. Simultaneous Energy Harvesting and Sensing (SEHS)

PEHs inherently function as vibration transducers, allowing them to serve as both power sources and sensing elements. This dual-use capacity underpins emerging Simultaneous Energy Harvesting and Sensing (SEHS) methodologies:

SHM and Fault Detection: PEH voltage features, when processed via conventional or unsupervised deep learning (e.g., variational autoencoders on time-frequency scalograms), can outperform accelerometer-based classifiers for bridge damage or bearing fault detection. PEHs tuned to the relevant modal frequency can yield 11–13 percentage points improvement in detection accuracy, with a 98% reduction in sensing energy (Yao et al., 17 Nov 2025, Zhang et al., 21 Feb 2024, Peralta-Braz et al., 10 Mar 2025).
Passive Feature Extraction: Using multiple PEHs as analog band-pass filters, system features (e.g., harvested energies in distinct frequency bands) are computed directly in hardware, massively reducing the data acquisition and transmission burden. Sampling rates can be reduced by four to five orders of magnitude while achieving ~89% bearing fault accuracy (Zhang et al., 21 Feb 2024).
Wearables and Gait Recognition: Integrated footwear insoles with multimodal PEHs achieve up to 127% more harvested energy and >98% recall in walking-pattern classification, while lowering sensor power by over one-third compared to state-of-the-art systems (Ma et al., 2020).
IoT Architectures: SEHS strategies eliminate the need for battery replacement, offering a path to fully self-powered "smart" nodes (Shirvanimoghaddam et al., 2017).

6. Bandwidth, Nonlinearity, and Structural Innovation

Standard piezoelectric cantilevers are inherently narrowband due to high-Q resonant operation. Techniques to extend bandwidth or enable multi-modal harvesting include:

Bias-Flip and Phase-Variable Circuits: Allow real-time electronic tuning of resonance and impedance for multi-frequency operation (Zhao et al., 2019, Zhao et al., 2022).
Structural Modifications: Elastic extensions, multi-modal or bistable elements, auxiliary masses, and auxetic or hollow substrates all enable either creation of additional resonances or transfer of more strain energy to the active piezo layers, increasing both bandwidth and global coupling—e.g., four-point-bending schemes achieving >3× energy conversion efficiency and improved fatigue life relative to cantilever designs (Zhou et al., 2019, Khazaee et al., 2022, Forges et al., 7 Jan 2025).
Switched Capacitor Arrays: Enable electrical tuning of the resonance to track input frequency drift, offering up to 63% more power off-resonance, and robustify operation against variability in environmental input (Karmakar et al., 16 Jul 2025).

7. Applications, Implementation Trade-offs, and Future Challenges

Prominent implementations include:

Structural Health Monitoring and Infrastructure: Distributed arrays of PEHs on bridges for power-autonomous sensors, with bi-objective design (Pareto front) selection for power/accuracy or energy per footprint (Peralta-Braz et al., 2022, Yao et al., 17 Nov 2025).
Wearables/Implantables: Sub-mW piezo harvesters for biomedical or IoT devices (Ma et al., 2020, Shirvanimoghaddam et al., 2017).
Low-Power Remote Sensing: Fully self-powered wireless nodes for industrial, environmental, or process monitoring (Quelen et al., 2018, Morel et al., 2018).

Challenges:

Narrow operational bandwidth and sensitivity to frequency mismatch remain a central bottleneck; advanced circuit topologies and structural co-design are the leading remedies.
Mechanical reliability—fatigue, depolarization, material fracture—places constraints on strain distribution and peak operational cycles (Khazaee et al., 2022, Shirvanimoghaddam et al., 2017).
Integration of nonlinear effects, parameter drift, and environmental uncertainties into design optimization remains underexplored but crucial for true real-world deployment.

Future research directions include hybrid multiphysics architectures (piezo-pyro-triboelectric), flexible/biocompatible/integrated MEMS harvesters, machine-learning-based real-time tuning, and establishment of standardized performance metrics and testing protocols (Ghazanfarian et al., 2021, Shirvanimoghaddam et al., 2017).

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