Instrumentation & Measurement Magazine 26-3 - 19

Fig. 8. Electrical behavior of the operating cycle #228 when the beam is excited by Zo = 2 μm and Ω = 5.1 kHz. (a) Evolution of the currents i1
of the capacitances C1 and C2; (c) Evolution of the voltages V1
, V2C, and VS; (d) Zoom on the evolution of the voltage VS
the extracted energy is about 0.32 nJ that corresponds to a
harvested power of 7.1 nW. As VS
V2C, and VS
continues to increase, the
harvested energy increases until the electrostatic force induces
the collapse of the comb-drive due to the pull-in instability.
The corresponding charge-voltage (Q-V) cycles are shown
in Fig. 7b, Fig. 7c and Fig. 7d for a few operational cycles of the
voltages VS
, V1 and V2C
(vibration cycle 200 to 230 of the beam).
As depicted, the Q-V cycle can be subdivided into four phases
(AB, BC, CD and DE), described for each case in its corresponding
figure. The electrical behavior of the device with the Bennet
doubler as a conditioning circuit is investigated in details for
the different phases (AB, BC, CD and DE) of one single operational
cycle.
As shown in Fig. 8 the results illustrate the electrical behavior
of the conditioning circuit, while a steady-state cycle
is considered (from t = 44.44 to 44.67 ms). During this period,
C1
( 1 11
Max min Max
C CC
varies between its maximum and minimum values
 ), while C2
and maximum values ( 22 2
min Max
varies between its minimum
min
CC C ). The state of the
diodes D1, D2 and D3 are represented by the evolution of the
currents i1, i2, and i3
itive, the diode is close, otherwise it is open). The voltage V1
May 2023
, respectively (when current is strictly pos,
.
across
C1, C2, and CS
, respectively, are plotted. In the
following, we detail the electrical behavior of the conditioning
circuit for each phase of one operational cycle:
◗ Phase AB: From A to B, the capacitance C1
decreases and
C2 increases. All diodes are OFF, and according to the
charge conservation law (Q1, Q2, and QS
The voltage V1 increases and V2C
are not varied):
decreases, while VS
remains constant.
◗ Phase BC: The charging phase starts at B, where V1
becomes higher than VS
+V2C, here D3
to C2, and CS
configuration of capacitances is established). V1
. V2C, C2 and VS
increase until reaching C.
◗ Phase CD: The circuit is isolated again, all diodes are
OFF, C1
starts increasing and C2 decreases and following
the charge conservation law V1 should decrease and V2C
increases while VS
remains constant.
◗ Phase DE: The diodes D1 and D2
are closed, letting the
occurrence of a parallel configuration. The capacitor C1
receives a charge of 2ΔQ from C2
and CS
IEEE Instrumentation & Measurement Magazine
(each capacitance
loses ΔQ, as a result VS observes a small decrease).
19
as a source for V2C, VS, and a charge ΔQ is transferred at
each cycle from C1
turns ON (a series
behaves
continue to
, i2
and i3
; (b) Evolution

Instrumentation & Measurement Magazine 26-3

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