Apparatus and method using capacitive detection with inherent self-calibration
View Patent ↗The illustrated embodiment of the invention includes a capacitive detection method in a MEMS resonator comprising the steps of: vibrating a resonator with a drive signal; sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector; and extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order.
1. A capacitive detection method in a MEMS resonator comprising:
vibrating a resonator with a drive signal;
sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector; and
extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order,
where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector comprises detecting amplitudes of first order sidebands at frequencies ω c ±ω d and detecting amplitudes of second order sidebands at frequencies ω c ±2ω d ; and
where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
calculating a ratio of amplitudes using
r
=
V
ω
-
2
+
V
ω
2
V
ω
-
1
+
V
ω
1
or estimate using a single side pair of sidebands using
r
≈
V
ω
-
2
V
ω
-
1
≈
V
ω
2
V
ω
1
and
calculating normalized amplitude of motion
x 0 =2 r/r 2 +1.
2. The method of claim 1 where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands.
3. The method of claim 2 where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector and simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands comprises sensing a first pair of sidebands V ω −(k+1) and V ω (k+1) and a second pair of sidebands V ω −k and V ω k ,
obtaining the ratio r(x o )
V
ω
-
(
k
+
1
)
+
V
ω
(
k
+
1
)
V
ω
-
k
+
V
ω
k
=
r
(
x
0
)
=
x
0
(
1
+
1
-
x
0
2
)
and deriving x o therefrom, where x o is normalized motional amplitude, where V ω i is the harmonic component of a i th sideband frequency ω i of the total output voltage.
4. The method of claim 2 where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector and simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands comprises sensing a first pair of sidebands V ω −(k+1) and V ω −(k+1) and a second pair of sidebands V ω −k and V ω k ,
obtaining the ratio r(x o )
r
(
x
0
)
≈
V
ω
c
±
(
k
+
1
)
ω
d
V
ω
c
±
k
ω
d
r
(
x
0
)
=
x
0
(
1
+
1
-
x
0
2
)
and deriving x o therefrom, where x o is normalized motional amplitude, where V ω i is the harmonic component of a i th sideband frequency ω i of the total output voltage.
5. The method of claim 4 where deriving x o comprises setting x o =2r(x o ).
6. The method of claim 1 , where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector comprises differentially detecting amplitudes of a first pair of sidebands at frequencies ω c ±kω d where k is an odd integer and detecting amplitudes of a second pair of sidebands at frequencies ω c ±(k+2)ω d ; and
where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
calculating a ratio of amplitudes using
r
(
x
0
)
=
V
ω
-
(
k
+
2
)
+
V
ω
(
k
+
2
)
V
ω
-
k
+
V
ω
k
and
calculating normalized amplitude of motion from r(x o ).
7. The method of claim 1 , where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector comprises differentially detecting amplitudes of a first pair of sidebands at frequencies ω c ±kω d where k is an odd integer and detecting amplitudes of a second pair of sidebands at frequencies ω c ±(k+2)ω d ; and
where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
calculating a ratio of amplitudes using
r
(
x
0
)
≈
V
ω
±
(
k
+
2
)
V
ω
±
k
and
calculating normalized amplitude of motion from r(x o ).
8. The method of claim 1 , where ω d a drive frequency applied to the resonator, where the electromechanical amplitude modulation signal is a DC signal, and
where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector comprises detecting amplitudes at frequencies ω d and 2ω d ; and
where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
calculating a ratio of amplitudes using
r
(
x
0
)
=
V
2
ω
d
2
V
ω
d
and
calculating normalized amplitude of motion from r(x o ).
9. The method of claim 1 , where ω d a drive frequency applied to the resonator, and where the electromechanical amplitude modulation signal is a DC signal, and
where sensing vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a capacitive detector comprises differentially detecting amplitudes at frequencies odd harmonic drive frequencies kω d and (k+2)ω d where k is an odd integer, and
where extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
calculating a ratio of amplitudes using
r
(
x
0
)
=
k
V
(
k
+
2
)
ω
d
(
k
+
2
)
V
k
ω
d
=
V
3
ω
d
3
V
ω
d
.
and
calculating normalized amplitude of motion from r(x o ).
10. A capacitive detection system for use with a MEMS resonator comprising:
a sensor of the vibration of the resonator for detecting a plurality of sidebands of an electromechanical amplitude modulation signal; and
means for extracting an amplitude of motion from a ratio of two simultaneously sensed sidebands of different order,
where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal and comprises means for detecting amplitudes of first order sidebands at frequencies ω c ±ω d and means for detecting amplitudes of second order sidebands at frequencies ω c ±2ω d ; and
where the means for extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
means for calculating a ratio of amplitudes using
r
=
V
ω
-
2
+
V
ω
2
V
ω
-
1
+
V
ω
1
or an estimate using a single side pair of sidebands using
r
≈
V
ω
-
2
V
ω
-
1
≈
V
ω
2
V
ω
1
and
means for calculating normalized amplitude of motion
x
0
=
2
r
r
2
+
1
.
11. The detection system of claim 10 where the means for extracting the amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises means for simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands.
12. The detection system of claim 11 where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal and the means for simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands comprises means for sensing a first pair of sidebands V ω −(k+1) and V ω (k+1) and a second pair of sidebands V ω −k and V ω k ,
means for obtaining the ratio r(x o )
V
ω
-
(
k
+
1
)
+
V
ω
(
k
+
1
)
V
ω
-
k
+
V
ω
k
=
r
(
x
0
)
=
x
0
(
1
+
1
-
x
0
2
)
and means for deriving x o therefrom, where x o is normalized motional amplitude, where V ω i is the harmonic component of a i th sideband frequency ω i of the total output voltage.
13. The detection system of claim 11 where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal and the means for simultaneously processing multiple sidebands and producing a measurement of x o by using a ratio r of two different order sidebands comprises means for sensing a first pair of sidebands V ω −(k+1) and V ω (k+1) and a second pair of sidebands V ω −k and V ω k ,
means for obtaining the ratio r(x o )
r
(
x
0
)
≈
V
ω
c
±
(
k
+
1
)
ω
d
V
ω
c
±
k
ω
d
r
(
x
0
)
=
x
0
(
1
+
1
-
x
0
2
)
and means for deriving x o therefrom, where x o is normalized motional amplitude, where V ω i is the harmonic component of a i th sideband frequency ω i of the total output voltage.
14. The detection system of claim 13 where the means for deriving x o comprises means for setting x o =2r(x o ).
15. The detection system of claim 10 , where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal and comprises means for differentially detecting amplitudes of a first pair of sidebands at frequencies ω c ±kω d where k is an odd integer and detecting amplitudes of a second pair of sidebands at frequencies ω c ±(k+2)ω d ; and
where the means for extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
means for calculating a ratio of amplitudes using
r
(
x
0
)
=
V
ω
-
(
k
+
2
)
+
V
ω
(
k
+
2
)
V
ω
-
k
+
V
ω
k
and
means for calculating normalized amplitude of motion from r(x o ).
16. The detection system of claim 10 , where ω c is a carrier frequency and ω d a drive frequency applied to the resonator,
where sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a detector and comprises means for differentially detecting amplitudes of a first pair of sidebands at frequencies ω c ±kω d where k is an odd integer and detecting amplitudes of a second pair of sidebands at frequencies ω c ±(k+2)ω d ; and
where the means for extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
means for calculating a ratio of amplitudes using
r
(
x
0
)
≈
V
ω
±
(
k
+
2
)
V
ω
±
k
and
means for calculating normalized amplitude of motion from r(x o ).
17. The detection system of claim 10 , where ω d a drive frequency applied to the resonator, where the electromechanical amplitude modulation signal is a DC signal, and
where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal in a detector and comprises means for detecting amplitudes at frequencies ω d and 2ω d ; and
where the means for extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
means for calculating a ratio of amplitudes using
r
(
x
0
)
=
V
2
ω
d
2
V
ω
d
and
means for calculating normalized amplitude of motion from r(x o ).
18. The detection system of claim 10 , where ω d a drive frequency applied to the resonator, and where the electromechanical amplitude modulation signal is a DC signal, and
where the sensor capacitively senses vibration of the resonator by detecting a plurality of sidebands of an electromechanical amplitude modulation signal and comprises means for differentially detecting amplitudes at frequencies odd harmonic drive frequencies kω d and (k+2)ω d where k is an odd integer, and
where the means for extracting amplitude of motion from a ratio of two simultaneously sensed sidebands of different order comprises
means for calculating a ratio of amplitudes using
r
(
x
0
)
=
k
V
(
k
+
2
)
ω
d
(
k
+
2
)
V
k
ω
d
=
V
3
ω
d
3
V
ω
d
.
and
means for calculating normalized amplitude of motion from r(x o ).