5.1 Summary
The design and analysis of a DC electrostatic micropower generator with and without external mass attachment were accomplished. The optimal design parameters were found from the theoretical analysis and calculation. With the 1 cm2 chip area constraint, the device with external mass attachment can generate an output power of 40.5 μW at the output voltage of 40 V by using an external voltage source of 3.6 V.
For the device without external mass attachment, the output power is 0.87 μW.
In the fabrication process, LPCVD nitride deposition was adopted to prevent the leakage issue of the device. An accurate shadow mask was used to pattern electrical contact pads in order to avoid the electrical shortage. Gold was used as contact switch material to prevent oxidation corrosion due to its extremely high stability.
The mechanical characteristics of the device were observed by using the MMA and the vibration of shakers. The resonant frequency with and without the 4-gm external mass attachment was measured as 122 Hz and 1680Hz respectively. The results agreed with the device design value. Parasitic resistance was improved to 156MΩ and verified by using discharge time constant measurement. Finally, mechanical switches on the device were tested. The voltage on the variable capacitor had been raised to 14.6V. The pull-in and release voltage of Switch 2 of 98V and 54V were also measured.
5.2 Future work
In DC operation, the variable capacitor is charged initially by an external DC voltage source such as a battery. But the lifetime of the battery limits the application of this converter. Therefore, an AC operation mode is preferred since no net charge is needed to power the load.
The operation of the AC converter is shown in Fig. 5.1. The circuit is composed of an auxiliary power supply Vin, a vibration-driven variable capacitor Cv and an external load RL. The energy converter vibrates with the frequency of the vibration source. This result in the change of the variable capacitance Cv; the charge Q on the capacitor is also changed. Therefore, an AC current flows through the circuit and produces the output voltage Vo and thus the output power to the external load RL.
There is no DC current through the auxiliary power supply Vin and therefore it does not provide the net output power. Its lifetime can thus be extended.
Fig. 5.1 AC mode operation of the electrostatic energy converter
Fig. 5.1 shows the mass-damper-spring model of the variable capacitor. The nonlinear equation of motion can be written as
mz + b z + kz = - mx + F m e (5.1)
Vin Cv
RL Vo
i + Q -
where x is the displacement of the device frame caused by the vibration, b z is the m mechanical damping force and Fe is the electrostatic force caused by electric charge.
The time derivative of Q corresponds to the electric current i flow through the external load RL as shown in Eq. 5.2.
The energy converter can be described by three variables: electric charge Q, displacement z and velocity z. The output power P of the energy converter is
Therefore, the average output power to the external load RL can be written as
This mathematical model can be used to optimize the design parameters for the maximum output power for different initial gap and external load .
Because there is no net charge flows out the source, the auxiliary battery can be replaced by a pre-charged electret. In this case, the potential application of capacitive energe converter is extended.
Theoretical analysis for energy scavenging technology is an essential objective in our effort. Energy from vibration can be converted into the electrical power through different methods such as electrostatic, electromagnetic, and piezoelectric. But difficulties emerge when comparing characteristics between these methods. Thus, a common theoretical description or comparison foundation is one of the next goals for our group.
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APPENDIX A
The M-files used in calculation are listed in Table A.1 Table A.1 M-file used in calculation
M-file Descriptions
Fun01.m Nonlinear equation sets
Initial01.m Parameter setting and result acquiring
Fun01.m
w2= sqrt((k0-(Qr^2*phi*vin^2/(d^2-x(7)^2)^2))/m);
wd2=sqrt((k0-(Qr^2*phi*vin^2/(d^2-x(7)^2)^2))/m-(b^2)/(4*m^2));
p1= atan2(b,sqrt(4*(m^2)*((w1)^2)-b^2));
initial01.m
format long;
options = optimset('LargeScale','off','TolFun', 1e-32, 'TolX', 1e-32,
'MaxIter',10000,'display','off','MaxFunEvals',100000,'NonlEqnAlgorithm','dogleg');
end end end end end end end