17.3 Efficiency and figure of merit definitions

Efficiency metrics are crucial for evaluating piezoelectric energy harvesting systems. From conversion and transfer efficiencies to system-level performance, these indicators help assess how well a harvester transforms mechanical energy into usable electricity.

Performance indicators like the electromechanical coupling coefficient and figure of merit provide deeper insights into material capabilities and overall system effectiveness. These metrics guide engineers in optimizing harvester designs for maximum power output and efficiency.

Energy Efficiency Metrics

Conversion and Transfer Efficiencies

• Energy conversion efficiency measures the ratio of useful electrical energy output to total mechanical energy input in piezoelectric systems
• Power transfer efficiency evaluates how effectively energy moves from the piezoelectric material to the electrical load
• Conversion efficiency typically ranges from 30-50% for most piezoelectric materials (PZT, PVDF)
• Transfer efficiency depends on impedance matching between the piezoelectric element and the electrical circuit
• Proper impedance matching can improve power transfer efficiency up to 80-90%

System-Level Efficiency and Harvesting Effectiveness

• System-level efficiency encompasses the entire energy harvesting process, from mechanical input to usable electrical output
• Factors affecting system-level efficiency include mechanical coupling, material properties, and circuit design
• Harvesting effectiveness compares the energy extracted to the maximum theoretically available energy in the environment
• Environmental factors like vibration frequency and amplitude impact harvesting effectiveness
• Typical system-level efficiencies for piezoelectric energy harvesters range from 10-30%
• Harvesting effectiveness varies widely depending on application, from less than 1% for ambient vibrations to over 50% for direct force applications

Performance Indicators

Electromechanical Coupling Coefficient

• Electromechanical coupling coefficient (k) quantifies a material's ability to convert between mechanical and electrical energy
• k^2 represents the fraction of mechanical energy converted to electrical energy (or vice versa)
• Calculated using the equation: $k^2 = \frac{\text{Converted Energy}}{\text{Input Energy}}$
• Values range from 0 to 1, with higher values indicating better energy conversion
• Typical values for piezoelectric materials: PZT (0.5-0.7), PVDF (0.1-0.2)
• Depends on material properties, geometry, and mode of operation (33 mode, 31 mode)
• Influences both energy conversion efficiency and power output of the harvester

Figure of Merit and Normalized Power Density

• Figure of merit (FOM) combines multiple material properties to assess overall performance
• Common FOM for piezoelectric energy harvesting: $FOM = \frac{d_{ij}^2}{\varepsilon_{33}^T s_{jj}^E}$
• d_ij represents the piezoelectric charge coefficient
• ε_33^T denotes the permittivity at constant stress
• s_jj^E signifies the elastic compliance at constant electric field
• Higher FOM values indicate better energy harvesting potential
• Normalized power density allows comparison between different harvester designs and sizes
• Calculated by dividing output power by device volume or area and input acceleration
• Expressed in units like μW/cm³/g² or mW/cm²/g²
• Enables fair comparison of harvester performance across various scales and applications
• Typical values range from 10 to 500 μW/cm³/g² depending on design and materials used