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Variable Description Value
Crab-leg suspension beam of driving plate
E Material Young modulus 169 GPa
w b Beam width 10 µm
t b Beam thickness 10 μm
L b Beam length 600 μm
L a Beam length (thigh) 50 μm
d p distance between plate and substrate 400 μm
A Area of driving plate 2.5E-07
M Mass of driving plate (kg) 1.0715e-8
Driving capacitors Cd 1 Cd 2
w Comb finger width 5 μm
t Comb finger thickness 10 μm
L d Comb finger length 70 μm
h d Overlapping height of electrodes 40 μm
n d Number of finger pairs 50
d RSd Rotor to stator finger spacing gap 3 μm
β Correction factor for the fringe effect 1.2 – 1.8
ε r Dielectric constant of air 1
ε 0 Permittivity of vacuum (F/m) 8.85e-12
V d Applied voltage at the electrodes 5 V
Pump charge capacitors C 1 , C 2
w Comb finger width 5 μm
t Comb finger thickness 10 μm
L Comb finger length 80 μm
h Overlapping height of electrodes 70 μm
N Number of finger pairs 20
d SS Stator to stator finger spacing gap 25 μm
d RS1 C 1 rotor to stator finger spacing gap 8 μm
d RS2 C 2 rotor to stator finger spacing gap 5 μm
Table 2: MEMS device parameters.
At resonance, the movable fingers oscillate around their initial
positions with an amplitude of x peak . In the folowing we assume
x min and x max being respectively the minimum and the maximum
position of the fingers.
(10)
(11)
Where d RS is the initial rotor to stator distance.
For the present device – described in Figure 2 –, the left and
right capacitance, C l and C r respectively, at x min and the total
maximum capacitance C max (the sum of C l and C r ) can be
calculated as follows [6]:
.
_ .
(12)
_ .
.
(13)
11-13 May 2011, Aix-en-Provence, France
. .
(14)
In the same way the total minimum capacitance C min when the
comb-finger is at x max can be expressed as:
. .
(15)
The output voltage of the DC/DC converter can then be
calculated as [7]:
(16)
We then find output voltages of 5.8V and 8.2V for the pump
charge capacitors C 1 and C 2 respectively.
C l
Rotor
C r
d RS
Stator
a)
h
w
L
Figure 2: Interdigitated comb finger
before and after x displacement.
IV. MEMS+ Modelling
Rotor
Stator
Figure 3 is a schematic of the whole system in Virtuoso. The
output of the MEMS converter is connected to a 500 fF reservoir
capacitor via a low leakage current diode to provide rectification
with minimal loss during the pumping cycles. The device is
driven at its resonant frequency.
This model is used to study the influence of the mechanical and
the electrical parameters of each block and their mutual
interdependence on the performance of the whole system. Figure
4 shows the influence of load resistance on the performance of
the converter. The better performance is obtained for a very high
resistive load (1TΩ) where an output voltage around 6.5V can
be obtained at the first output C 1 of the DC/DC converter.
However the output voltage drops to nil when the load resistivity
is under a few tens of giga-ohms. This MEMS-electronics
cosimulation allows us to understand that the system is suitable
for purely capacitive loads only. This is due to the
acknowledged inherent high impedance output of MEMS
converters [8]. The modeling prediction of the converter
behavior for low resistive loads is interesting and need some
more study.
x
d SS
b)
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