17.1 Key performance indicators for energy harvesters

Energy harvesters need ways to measure how well they work. Key performance indicators help us understand their electrical output, frequency response, and energy conversion efficiency. These metrics are crucial for optimizing harvester designs and comparing different devices.

We'll look at power output, voltage, impedance matching, and frequency response. We'll also explore the importance of resonant frequency, coupling coefficients, and quality factors. Understanding these metrics helps engineers create better energy harvesting systems.

Electrical Output Metrics

Power and Voltage Considerations

• Power output measures the amount of electrical energy generated by the harvester per unit time
• Typically expressed in microwatts (μW) or milliwatts (mW)
• Depends on factors such as device size, material properties, and excitation conditions
• Voltage output represents the electrical potential difference produced by the harvester
• Usually measured in millivolts (mV) or volts (V)
• Influenced by the piezoelectric material's properties and the device's geometry
• Higher voltage output generally desirable for easier integration with electronic circuits

Impedance Matching and Efficiency

• Impedance matching optimizes power transfer between the harvester and the load
• Occurs when the source impedance equals the load impedance
• Improves overall system efficiency by minimizing power losses
• Can be achieved through circuit design techniques (resistive matching, capacitive matching)
• Maximum power transfer theorem states that maximum power is delivered when source and load impedances are conjugates
• Efficiency of power transfer calculated as the ratio of power delivered to the load to the maximum available power

Frequency Domain Metrics

Frequency Response and Bandwidth

• Frequency response describes the harvester's output as a function of input frequency
• Typically represented as a graph showing amplitude vs. frequency
• Helps identify optimal operating frequencies for maximum power output
• Bandwidth refers to the range of frequencies over which the harvester operates effectively
• Wider bandwidth allows for operation across a broader spectrum of vibration sources
• Calculated as the difference between upper and lower cutoff frequencies
• Cutoff frequencies defined as points where output power drops to half its maximum value (-3dB points)

Resonant Frequency and Performance

• Resonant frequency is the natural frequency at which the harvester produces maximum output
• Determined by the harvester's physical properties (mass, stiffness, dimensions)
• Operating at resonance maximizes energy conversion efficiency
• Can be tuned by adjusting the harvester's design parameters (beam length, proof mass)
• Multiple resonant frequencies possible in more complex harvester designs
• Off-resonance operation results in reduced power output and efficiency

Electromechanical Coupling Metrics

Coupling Coefficient and Energy Conversion

• Coupling coefficient (k) quantifies the efficiency of energy conversion between mechanical and electrical domains
• Ranges from 0 to 1, with higher values indicating better conversion efficiency
• Calculated using the equation: $k^2 = \frac{\text{Converted Energy}}{\text{Input Energy}}$
• Influenced by material properties, device geometry, and operating conditions
• Different coupling coefficients exist for various modes of operation (k31, k33, k15)
• Higher coupling coefficients lead to improved harvester performance and power output

Quality Factor and System Performance

• Quality factor (Q) measures the energy storage capability of the harvester relative to energy dissipation
• Defined as the ratio of energy stored to energy dissipated per cycle
• Higher Q values indicate lower energy losses and sharper resonance peaks
• Calculated using the equation: $Q = \frac{f_r}{\Delta f}$, where fr is the resonant frequency and Δf is the bandwidth
• Affects the harvester's frequency response and power output characteristics
• Trade-off exists between high Q (narrow bandwidth, high peak power) and low Q (wide bandwidth, lower peak power)
• Optimal Q factor depends on the specific application and environmental conditions