Online proceedings - EDA Publishing Association

11-13 May 2011, Aix-en-Provence, France
TABLE II
ACCELEROMETER SPECIFICATIONS
Model’s total dimensions 370μm×414μm×3.5μm
Proof mass
1.2μg
Number of finger pairs 50
The range of Δd
-1.5μm~1.5μm
The range of acceleration -3g~3g (1g=9.8m/s 2 )
The range of capacitive change 132.81fF~929.67fF
C + = n⋅[ε 0 ε r A/(d 0 -Δd)] (4)
C - = n⋅[ε 0 ε r A/(d 0 +Δd)] (5)
where, n is the number of the finger pairs;
ε 0 = 8.854×10 −12 F m –1 is the electric constant;
ε r = 1 is the dielectric constant of the material
between the plates;
A is the area of the overlapping of the two plates;
d 0 = 2μm is the distance of two plates when there’s
no acceleration existing.
Fig.2. The simplified schematic of a differential capacitive model, (a)
acceleration is zero (a=0); (b) acceleration is non zero (a>0); (c) the
structures of four tethers.
tethers work like mechanical springs. When the substrate
undergoes any external acceleration (a) in its sense direction
(for this model is horizontal direction), the proof-mass exerts
a force (F) on the suspension, according to Newton second
law. At the same time, for frequencies below the mechanical
resonance of the spring-mass system, this force causes the
suspension to deflect a distance (Δd), according to Hooke’s
law. The relationship of these values can be showed using
following (1) and (2).
F = ma (1)
where, m is the total mass of the proof;
a is the external acceleration;
F is the force of the proof generated.
Δd = F/k = ma/k = a(1/ω 2 n ) (2)
where, Δd is the distance for proof-mass moving;
k is the overall spring constant;
ω n is the natural frequency of the sensor in the
direction of applied acceleration.
The overall spring constant is,
k = x⋅(12EI/L 3 ) = x⋅(Ewt 3 /L 3 ) (3)
where, x = 4 is the number of the tethers;
E is the Young’s modulus of UTM;
w = 3.5μm is the width of the tether;
t = 2μm is the thickness of the tether;
L = 170μm is the length of the tether.
The equivalent circuit of the differential capacitive sensor
for the MEMS model is shown in Fig.3. Table II describes
the specifications of this accelerometer. The values of these
two capacitors can be derived from the distance changing of
Δd, as (4) and (5) shown.
III.
DESIGN OF A SIGMA-DELTA ANALOG-TO-DIGITAL
CONVERTER (Σ-Δ ADC)
A. Overall Design
Fig.4 demonstrates the whole system block diagram. This
CMOS monolithic chip mainly contains two parts, sensor
and interface circuit. The sensor circuit converts the physical
parameter to an analog signal, which is sent to the ADC. The
CMOS monolithic chip provides a 1-bit digital output which
is fit for signal processing or transmission. In order to make
design simple, low cost, and high resolution, first-order
sigma-delta analog-to-digital converter was chosen as the
interface circuit.
The circuit level design is presenting in Fig.5. The MEMS
sensor part is represented as two sensor capacitances C + and
C - which are both in the range of pF or fF. The sensor circuit
converts the sensing capacitances to analog voltage, as
described in (6) below.
V a = V 1 [(C + -C - )/(C + +C - )] = V 1 (Δd/d 0 ) (6)
where, V 1 is the amplitude of the sinusoid.
Fig.4. Integrated micro system block diagram.
Fig.3. The equivalent circuit of differential capacitive sensor.
Fig.5. The whole chip circuit design.
19