The Joule-Thief™ has been designed to deliver electrical power at relatively high density (power per unit volume) compared to competing piezoelectric energy harvesting products. A simple schematic of the piezoelectric composite beam energy harvester is shown in Figure 1. In the figure, a0 is the input acceleration, fext is the excitation frequency of the base vibration and V is the resulting voltage from the PZT.

**Figure 1: Schematic of a Piezoelectric Composite Beam Energy Harvester**

The cantilever beam and proof mass is analogous to a simple single-degree-of-freedom oscillator subject to a base excitation as shown in Figure 2.

**Figure 2: Single-Degree-of-Freedom Representation of the Energy harvesting Beam**

AdaptivEnergy has developed a comprehensive analytical toolset that accurately models the behavior of a piezoelectric composite beam energy harvester as depicted in Figure 1. This electromechanical lumped-element model is valid for a cantilever beam until its first mode of vibration and is modeled using Euler-Bernoulli beam theory. This modeling technique employs circuit analogues using a two-port network transducer theory to effectively represent the complete energy harvesting beam in an equivalent circuit form. This model captures the interaction between various energy domains that are present in the energy harvester, namely, mechanical and electrical.

The energy conversion between various modules of the energy harvester is explained next. The ambient mechanical energy is first converted to its electrical equivalent using the piezoelectric transduction mechanism discussed earlier. This transfer results in an AC voltage generated by the RLP® that is then converted into a DC voltage using the energy harvesting circuit and later stored in the battery for subsequent use. Figure 3 represents the power transfer diagram for the Joule-Thief™. The objective of the power converter is to match the impedance of the RLP® energy harvesting beam to the load to maximize the power transfer.

**Figure 3: Energy Flow in a Vibration-Based Energy Harvester**

AdaptivEnergy uses both internally developed and commercial Finite Element Analysis software tools to analyze the projected performance of varying energy harvesting beam configurations. Design features such as dimensions, end mass and resonant frequencies are determined prior to developing any physical prototypes. A bimorph (two layers of piezoceramic) design would be considerably stiffer than a unimorph (single layer of piezoceramic) design.

As indicated in the above figure, the RLP® is comprised of a stainless steel shim to which is bonded a PZT ceramic using AdaptivEnergy’s proprietary polyamide adhesive layer with a capping layer at the top to further stress bias the ceramic layer. The unimorph design results in a deflected modeshape due to the stress bias, while the bimorph results in a straight beam due to its symmetry.

**III. ENERGY COLLECTION AND STORAGE ELECTRONICS**

The AdaptivEnergy EHD energy harvesting circuit is designed to function as an interface between the RLP® energy beam and any battery. Alternate version of the circuit that uses a capacitor as the storage mechanism is also available. The circuit is fully equipped to address issues such as avoiding over-charging and discharging beyond the allowable limits and preventing leakage when the module is not in use. Figure 5 shows a functional block diagram of the energy harvesting circuit. The EHD circuit consists of two functional sub-circuits that are designed to protect the battery from the above mentioned failure modes.

**Figure 5: Functional Block Diagram of the EHD Energy Harvesting Circuit**

Shown below is a picture of the evolution of the RLP® beams developed at AdaptivEnergy to harvest energy from a range of vibration sources. The sizes of the beams vary from 1.5” to 3.5” and 5 gm to 20 gm in mass. The beams are tuned to different frequencies to fit well with specific applications.

**Figure 6: Joule-ThiefTM RLP® beams**

Plots showing the performance curves for various Joule-Thief™ beams developed at AdaptivEnergy are included below. The first plot shows the power density with respect to volume for all the beams operating at their resonance as a function of input acceleration levels. These plots indicate the rms power delivered into an optimal load for each beam. The actual real power that is reclaimed will depend on the efficiency of the energy collection electronics. Energy harvesting circuits when designed to the right beam have been measured to be 60-80 % efficient. However, knowing the input vibration spectra such as acceleration, frequency is critical to achieve this efficiency.

The next plot shows the performance curve for power density with respect to overall mass of the package for various beams excited at resonance as a function of input acceleration. These plots should indicate the performance specs that can be achieved with the current selection of beams. More redesigning can be carried out with the internal modeling tools developed for this purpose to achieve higher power outputs at alternate frequencies.