# A Vibrational Energy Harvesting Sensor Based on Linear and Rotational Electromechanical Effects
## 6 Empirical and Model Analysis of the VEH Sensor
### Harvesting from Low-Level Non-Stationary Signals  
Long-term storage and monitoring application require successful harvesting of potentially low-level and infrequent sources of vibrational energy. In this second analysis, the energy harvesting capability of the VEH sensor is investigated utilizing a random acceleration spectrum generated from the white noise feature of the Keysight 3352B arbitrary waveform generator, Santa Rosa, CA, USA (AWG). For these tests, the AWG drives the shaker directly and the accelerometer is used to set the input acceleration magnitude of \(\dot{y}_{\text{RMS}}\sim 10^{-2}\) g, as determined from the reference accelerometer. The targeted noise spectrum is assumed white, centered at 130 Hz, with a 75 Hz bandwidth. Transient accelerometer data and the voltage output from the VEH harvester are recorded over a 7 min time window using a digital oscilloscope. The sampling rate for the oscilloscope is set at 0.2 ms, which resulted in a data record of approximately 20 k samples. The frequency spectra are calculated from the transient data using Fourier methods [28]. Figure 7 shows the acceleration input at the base of the harvesting sensor and the output spectra of the VEH harvester measured with a 50 \(\Omega\) load termination. The black line is the input acceleration spectrum measured by the reference accelerometer and converted to g m s\({}^{-2}\). The red line is the VEH sensor voltage output spectrum corresponding to an input random acceleration of \(\dot{y}_{\text{RMS}}\sim 10^{-2}\) g for comparison. Initially, it was thought that the random acceleration input spectrum would be flat across the bandwidth and the VEH sensor would be driven by a stochastically uniform acceleration  
Figure 7: VEH sensor response to stochastic, non-stationary vibration input. Black line: Input acceleration spectrum in g (m s\({}^{-2}\)) of the noise source. Red line: VEH sensor voltage power output spectrum. The output voltage is measured with a 50 \(\Omega\) load termination. The highlighted region of the graph is the useful sensor harvesting bandwidth, 130\(-\)150 Hz. The red dashed horizontal line is the lowest harvestable power attainable by the EH300 circuit, which is estimated to be 0.04 uW (see text). input. The calculated input acceleration spectrum is found to be biased towards a peak rms amplitude around 75 Hz, with an approximate \(-2\) dB/decade on either side. Unfortunately, a large portion of the energy in this spectrum falls outside the targeted range of the VEH; however, it still provides a test of the sensor's off nominal harvesting capability. The highlighted region of the graph is the useful harvesting bandwidth (130 Hz \(<\) VEH frequency \(<\) 150 Hz) of the sensor with the EH300 harvesting circuit. Essentially, this region represents an estimate based on the EH300 circuit's power harvesting capabilities defined as 4 V at 200 nA or 0.8 uW [27]. Across the 50 \(\Omega\) load resistance, this translates into a minimum power of 0.04 uW across the 20 Hz operational bandwidth of the highlighted region and is marked by the red dashed line relative to the voltage axis. A smaller region exists for the second peak; however, this is not considered for this analysis. An estimate of the harvesting efficiency of the VEH sensor based on the random acceleration is shown in Figure 8. The harvesting efficiency is defined as \(\eta=P/P_{\text{in}}\), where \(P\) is the average output power from the harvesting circuit, calculated as \(P=\left|V_{\text{out}}\right|^{2}/(R_{l}\Delta f)\), and \(P_{\text{in}}\) is the mechanical input power, calculated as \(P_{\text{in}}=\left|\hat{Y}\right|^{2}m\Delta f\). Here, \(m\) are the magnet masses and \(\Delta f\) is the frequency band [29]. The ratio between the output voltage and the input acceleration spectrum are plotted as a function of frequency across the harvesting bandwidth, essentially normalizing the VEH sensor output sensitivity by dividing out the noise signal response.