Energy harvesting: A battle against power losses

(8)

where I_Harv is the harvesting current, R_ds5 the cumulative switch-on resistance of MP_5A-MP_5B, and τ_Max-Min the harvesting time, which is the time it takes C_MEMS to reach its minimum capacitance point. The voltage drop across R_ds5 further increases the voltage across C_MEMS, effectively increasing the harvesting current (and energy). The power lost in this resistance is actually supplied by C_MEMS, not the battery, in the form of additional mechanical work when separating its parallel plates, which can be offset by adjusting the elasticity of the MEMS capacitor.

There is one more power loss in the harvesting phase, and it results because of mismatches in battery and pre-charged C_MEMS voltages just after the pre-charge phase. A voltage difference (V_Mismatch) between these two devices forces an energy exchange through lossy switch-on resistance R_ds5, not the lossless inductor. This power loss is proportional to the vibration frequency and approximately

(9)

2: Recovery:
After harvesting ends, the energy left in the capacitor is only about 1-4% of the total energy harvested. The circuit complexity and associated conduction and power losses with recovering this energy tend to negate the absolute benefit of the exercise. For this reason, this left-over energy is considered a negligible loss. As a result, after opening all the switches, C_MEMS is allowed to return to its minimum plate-separation state under charge-constrained conditions, thereby decreasing the capacitor voltage to approximately 0 V.

In all, energy harvesting in micro-scale applications is challenging because the process of transferring power is itself lossy. This transfer-induced loss reduces the net energy gain of the system from the maximum theoretical limit depicted in (2) to:

(10)

where T_Vib is the period of the vibration and Ε P_Losses the aggregate sum of all power losses. Even when a supposedly lossless inductor is used to transfer energy, the fundamental conduction (R_ds, ESRs, and diodes), switching (C_g,Par and C_d,Par), and systematic (quiescent power and battery-C_MEMS mismatch voltages) losses of the circuit limit the net yield of the system. Optimizing these losses is often contradicting, as is the case with R_ds and C_d,Par-C_g,Par, where smaller devices yield lower switching losses and larger devices smaller conduction losses. The battery voltage also has a convoluted role in that it not only sets the gate-drive that determines the various switch-on resistances (that is, conduction losses) but it also establishes the extent to which C_g,Par and C_d,Par are charged and discharged (that is, switching losses). The objective is to therefore balance these losses and design and build a practical circuit prototype that is able to produce a net energy gain, which is currently under development at the Georgia Tech Analog and Power IC Laboratory.

For additional details, questions, and/or comments on this article, please contact us, the Georgia Tech Analog and Power IC Laboratory, at gtap@ece.gatech.edu. More information about our research can be found at http://www.rincon-mora.com/research.

References
[1] E.O. Torres and G.A. Rincón-Mora, "Long-lasting, self-sustaining, and energy-harvesting system-in-package (SiP) wireless micro-sensor solution," International Conference on Energy, Environment, and Disasters (INCEED), Charlotte, NC, 2005.
[2] E.O. Torres and G.A. Rincón-Mora, "Electrostatic energy harvester and Li-Ion charger circuit for micro-scale applications," IEEE Midwest Symposium on Circuits and Systems (MWSCAS), San Juan, Puerto Rico, August 2006.
[3] L. Balogh, "Design and application guide for high speed MOSFET gate drive circuits," Texas Instruments Power Supply Design Seminar (SEM-1400), 2001.
[4] M. Gildersleeve, H.P. Forghani-zadeh, and G.A. Rincón-Mora, "A comprehensive power analysis and a highly efficient, mode-hopping dc-dc converter," IEEE Asia-Pacific Conference on ASICs, pp. 153-6, Taipei, Taiwan, 2002.