Measuring and testing – Speed – velocity – or acceleration – Acceleration determination utilizing inertial element
Reexamination Certificate
2001-12-27
2004-02-17
Kwok, Helen (Department: 2856)
Measuring and testing
Speed, velocity, or acceleration
Acceleration determination utilizing inertial element
C073S862610
Reexamination Certificate
active
06691572
ABSTRACT:
BACKGROUND
1. Field of the Invention
The present invention relates to accelerometers of the type that include a micromechanical pendulum. More particularly, the invention pertains to such an accelerometer with control loop resetting.
2. Description of the Prior Art
Accelerometers that include a micromechanical pendulum in a differential capacitor arrangement with a resetting control loop are incorporated into, and proposed for, various basic devices. The operation of such an arrangement will be described with reference to the embodiments illustrated in
FIGS. 2 and 3
.
The first solution, shown in
FIG. 2
, employs a digital computer coupled to an analog charge amplifier. A computer
2
directs voltage pulses U
1
, U
2
(see
FIG. 4
) alternately to an upper electrode E
1
and to a lower electrode E
2
arranged relative to a pendulum P. If the arrangement is mistuned, a charge difference flows via the pendulum P, which is amplified at U
3
and is digitized at the A/D converter
4
. The computer
2
linearizes the pendulum characteristics and compensates (as can be seen from the central and right-hand diagrams of
FIG. 4
) for accelerations acting on the pendulum P by the pulse-width ratios of the time-sequential voltage pulses U
1
and U
2
, on the upper and lower electrodes E
1
, E
2
, respectively. At the same time, the computer
2
adjusts the offset of the pendulum P, and compensates for bias and scale factor, particularly as a function of temperature.
The second solution, illustrated in FIG.
3
and the three timing diagrams of
FIG. 5
, uses analog charge control with a digital section
1
for pulse-width resetting when the pendulum P is deflected. The individual charges on the two capacitors C
1
, C
2
are defined by a precision current source
5
over a constant, short time interval (e.g. 25 &mgr;s). In this case, only the current flowing via the pendulum P is controlled. Although the current is applied via the electrodes E
1
, E
2
, it is not governed by the control system
6
,
7
. The charge control means that the effective resetting force per electrode is independent of pendulum position and need not be linearized. The voltages on the electrodes E
1
, E
2
will differ, however, when the pendulum P is deflected. The charge difference represents the pick off voltage located at the input of an operational amplifier
6
. Acceleration is indicated by the charge difference, and is compensated by the pulse-width ratio. This is accomplished with a digital test within a separate time slot of, for example, 75 &mgr;s.
The two known solutions explained briefly with reference to
FIGS. 2 and 4
, as well as
3
and
5
, for the resetting control can be analyzed as follows. The first solution (
FIGS. 2 and 4
) is largely digital with bias and scale factor internally compensated. The voltage control on the electrodes E
1
, E
2
and linearization are matched to the stability of the pick off offset. In this situation, the requirements for relative pick off accuracy result from the potential and required bias accuracies. A range (e.g. 500 &mgr;g to 10 g) results in a required bias accuracy of 5×10
−5
.
Corresponding considerations with regard to the second known solution (
FIGS. 3 and 5
) lead to a relative pick off or bias accuracy of 1.7×10
−3
with respect to required acceleration for full-scale deflection of the pendulum of, for example, 500 &mgr;g to 0.3 g. Tests verify that the control electronics for the second approach are considerably less sensitive to bias errors. However, this solution has the disadvantage that circuit complexity is considerably greater and the overall measurement range is reduced by about 25% for corresponding voltages. Furthermore, it is impossible to compensate internally for scale factor.
The theory of switched electrostatic resetting for micromechanical pendulum systems yields the following expression for mean resetting force F:
F=Q
1
E
1
((&Dgr;
t+dt
)/&Dgr;
t
)−
Q
2
E
2
((&Dgr;
t−dt
)/&Dgr;
t
) (1)
For small angles, assuming linear deflection, the normal approximation sin&agr;≈&agr; can be assumed and the switching times for both voltages are the same. In such case:
F
mean force acting
Q
1,2
Charge on the upper and lower capacitances C
1
and C
2
, respectively
E
1,2
Field strength between the pendulum P and the
upper and lower electrodes E
1
and E
2
,
respectively
&Dgr;t
Time duration of switching pulses
dt
Difference between the two switching pulses on
the upper and lower capacitances C
1
and C
2
,
respectively
Due to resetting forces, any asymmetry can produce an additional bias error, (referred to as the reset bias or bias B). Setting dt=0 and F=m·a (m=mass of the pendulum P, a=acceleration), bias B is obtained from (1) as:
B
=(
Q
1
E
1
−Q
2
E
2
)(1
/M
) (2)
Scale factor S for the acceleration is obtained from the component where dt≠0:
S
=
(
Q
1
E
1
+
Q
2
E
2
)
dt
Δ
t
1
m
(
3
)
The range of reset acceleration for positive and negative acceleration R
+
or R
−
is given by:
R
+
=
[
Q
1
E
1
(
Δ
t
+
dt
ma
x
Δ
t
)
-
Q
2
E
2
(
Δ
t
-
dt
ma
x
Δ
t
)
]
1
m
R
-
=
[
Q
1
E
1
(
Δ
t
-
dt
ma
x
Δ
t
)
-
Q
2
E
2
(
Δ
t
+
dt
ma
x
Δ
t
)
]
1
m
(
4
)
For simplicity, assuming that dt
max
=&Dgr;t:
R
+
=
2
Q
1
E
1
m
and
R
-
=
2
Q
2
E
2
m
(
5
)
In the method described above as the first recommended solution (FIGS.
2
and
4
), the voltages U
1
and U
2
are applied to the capacitors C
1
, C
2
:
Q
1
=
C
1
U
1
=
ϵ
0
A
d
1
U
1
Q
2
=
C
2
U
2
=
ϵ
0
A
d
2
U
2
E
1
=
U
1
d
1
E
2
=
U
2
d
2
(
6
)
In this case:
A Areas of the capacitors C
1
, C
2
; assumed equal
∈
0
Dielectric constant
d
1,2
Distances between the pendulum P and the respective electrodes E
1
and E
2
.
If the following substitutions are made
d
1
=d
0
+d, d
2
=d
0
−d, U
1
=U
0
+U
and
U
2
=U
0
−U
, where
U
0
=mean switching voltage, then the following formulas are obtained from equations (2), (3), (5) and equation (6) if d<<d
0
and U<<U
0
:
B
≈
4
ϵ
AU
0
2
md
0
2
(
U
U
0
-
d
d
0
)
(7a)
S
≈
2
ϵ
AU
0
2
md
0
2
dt
Δ
t
(7b)
R
≈
2
ϵ
0
AU
0
2
md
0
2
(7c)
In this approximation is R
=
=R
+
=R, as is immediately evident for dt=&Dgr;t from equation 7b.
The major variables influencing resetting bias B, scale factor S and reset acceleration R are voltages U
0
and U, and distances D
0
and D. As can be seen from equation 7b, the scale factor S depends on (U
0
/d
0
)
2
. The first-described solution is based on the method and thus has the disadvantages, that the scale factor S depends critically on the stability of the mean switching voltage U
0
and all the possible contact resistances to the electrodes, while the scale factor S similarly varies critically with changes to the mean distances D
0
between the capacitors C
1
, C
2
(due, for example, to temperature or pressure changes).
Since the resetting bias B is measured via the scale factor S as a time change dt, the dependency on (U
0
/d
0
)
2
stands out—as can be seen from equation 7a. The resetting bias B also depends linearly on U/U
0
and d/d
0
. The stability requirements for this increase with the reset acceleration range since it follows from equations 7a and 7c that:
B
≈2
R
(
U/U
0
&minus
Kramsky Elliott N.
Kwok Helen
Litef GmbH
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