Just as in the pre-charge phase, harvesting also incurs conduction and switching losses, but no dead time losses, since only one switch is involved (MP5A
). To mitigate the adverse effects of clock feed-through and charge injection onto CMEMS
when the battery and CMEMS
are short-circuited and decrease the reverse-biased leakage currents associated with large source/drain areas from discharging CMEMS
, transistors MP5A
are small geometry devices. As a result, the switching losses in this phase are negligible relative to the conduction losses lost across the composite switch, which is especially acute for small transistors (large switch-on resistance):
where IHarv is the harvesting current, Rds5 the cumulative switch-on resistance of MP5A-MP5B, and τMax-Min the harvesting time, which is the time it takes CMEMS to reach its minimum capacitance point. The voltage drop across Rds5 further increases the voltage across CMEMS, effectively increasing the harvesting current (and energy). The power lost in this resistance is actually supplied by CMEMS, 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 CMEMS voltages just after the pre-charge phase. A voltage difference (VMismatch) between these two devices forces an energy exchange through lossy switch-on resistance Rds5, not the lossless inductor. This power loss is proportional to the vibration frequency and approximately
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, CMEMS 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:
where TVib is the period of the vibration and Ε PLosses the aggregate sum of all power losses. Even when a supposedly lossless inductor is used to transfer energy, the fundamental conduction (Rds, ESRs, and diodes), switching (Cg,Par and Cd,Par), and systematic (quiescent power and battery-CMEMS mismatch voltages) losses of the circuit limit the net yield of the system. Optimizing these losses is often contradicting, as is the case with Rds and Cd,Par-Cg,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 Cg,Par and Cd,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 firstname.lastname@example.org. More information about our research can be found at http://www.rincon-mora.com/research.
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