Nonlinear distortion compensation for capacitive MEMS microphones
Embodiments relate to systems and methods for compensating nonlinear distortions. The system receives a signal corresponding to an input sound pressure which is detected by a capacitive MEMS microphone. The capacitive MEMS microphone includes an active capacitance and a parasitic capacitance. The system determines a nonlinear relationship between the signal and the input sound pressure; and determines, based on the signal, an input parameter associated with the active capacitance and the parasitic capacitance. The system further determines an output signal based on the input parameter and the output signal and the input sound pressure have a linear relationship. The system compensates the signal based on the determined output signal and outputs the compensated signal as an output so that the output has the linear relationship with the input sound pressure.
1. A method comprising:
receiving a signal corresponding to an input sound pressure detected by a capacitive microelectromechanical system (MEMS) microphone, wherein the capacitive MEMS microphone includes an active capacitance and a parasitic capacitance;
determining that a nonlinear relationship exists between the signal and the input sound pressure;
determining, based on the signal, an input parameter associated with the active capacitance and the parasitic capacitance;
determining an output signal based on the input parameter, wherein the output signal and the input sound pressure have a linear relationship;
compensating the signal based on the determined output signal so that the compensated signal has the linear relationship with the input sound pressure; and
outputting the compensated signal as an output corresponding to the input sound pressure.
2. The method of claim 1 , wherein determining that the nonlinear relationship exists between the signal and the input sound pressure comprises:
determining a sound level of the signal; and
responsive to the determined sound level being higher than a threshold value, determining that the nonlinear relationship exists between the signal and the input sound pressure.
3. The method of claim 1 , wherein the input parameter is a normalized displacement (B) of a movable electrode in the active capacitance corresponding to the input sound pressure.
4. The method of claim 3 , wherein
β
=
-
v
(
1
+
α
)
v
α
-
V
b
,
and
α= C p /C e ,
C p is the parasitic capacitance,
C e is the active capacitance; and
V b is a bias voltage on C e .
5. The method of claim 4 , wherein determining the output signal based on the input parameter comprises:
estimating the input sound pressure (p) based on the normalized displacement (β); and
determining the output signal by multiplying p by a transfer function (TF).
6. The method of claim 5 , wherein
p
=
1
A
(
Z
(
s
)
β
d
e
-
F
(
β
)
)
,
and
A is an area of the movable electrode,
Z(s) is an impedance in the active capacitance,
d e is a distance between a backplate and the movable electrode in the active capacitance at equilibrium, and
F(β) is an electrostatic force in the active capacitance.
7. The method of claim 5 , wherein
TF
=
-
A
V
b
(
1
+
α
)
d
e
1
Z
(
s
)
,
and
A is an area of the movable electrode,
Z(s) is an impedance in the active capacitance,
d e is a distance between a backplate and the movable electrode in the active capacitance at equilibrium, and
F(β) is an electrostatic force in the active capacitance.
8. The method of claim 4 , wherein determining the output signal based on the input parameter comprises: multiplying β by a transfer function (TF′) to obtain the output signal, wherein
TF
′
=
V
b
1
+
α
.
9. A non-transitory computer-readable storage medium comprising stored instructions, the instructions when executed by a processor of a device, causing the device to:
receive a signal corresponding to an input sound pressure detected by a capacitive microelectromechanical system (MEMS) microphone, wherein the capacitive MEMS microphone includes an active capacitance and a parasitic capacitance;
determine that a nonlinear relationship exists between the signal and the input sound pressure;
determine, based on the signal, an input parameter associated with the active capacitance and the parasitic capacitance;
determine an output signal based on the input parameter, wherein the output signal and the input sound pressure have a linear relationship;
compensate the signal based on the determined output signal so that the compensated signal has the linear relationship with the input sound pressure; and
output the compensated signal as an output corresponding to the input sound pressure.
10. The non-transitory computer-readable storage medium of claim 9 , wherein the instruction to determine that the nonlinear relationship exists between the signal and the input sound pressure comprises:
determining a sound level of the signal; and
responsive to the determined sound level being higher than a threshold value, determining that the nonlinear relationship exists between the signal and the input sound pressure.
11. The non-transitory computer-readable storage medium of claim 9 , wherein the input parameter is a normalized displacement (β) of a movable electrode in the active capacitance corresponding to the input sound pressure,
β
=
-
V
(
1
+
α
)
v
α
-
V
b
,
and
α= C p /C e ,
C p is the parasitic capacitance,
C e is the active capacitance; and
V b is a bias voltage on C e .
12. The non-transitory computer-readable storage medium of claim 11 , wherein the instruction to determine the output signal based on the input parameter comprises:
estimating the input sound pressure (p) based on the normalized displacement (β); and
determining the output signal by multiplying p by a transfer function (TF).
13. The non-transitory computer-readable storage medium of claim 12 , wherein
p
=
1
A
(
Z
(
s
)
β
d
e
-
F
(
β
)
)
,
and
A is an area of the movable electrode,
Z(s) is an impedance in the active capacitance,
d e is a distance between a backplate and the movable electrode in the active capacitance at equilibrium, and
F(β) is an electrostatic force in the active capacitance.
14. The non-transitory computer-readable storage medium of claim 12 , wherein
TF
=
-
A
V
b
(
1
+
α
)
d
e
1
Z
(
s
)
,
and
A is an area of the movable electrode,
Z(s) is an impedance in the active capacitance,
d e is a distance between a backplate and the movable electrode in the active capacitance at equilibrium, and
F(β) is an electrostatic force in the active capacitance.
15. The non-transitory computer-readable storage medium of claim 11 , wherein the instruction to determine the output signal based on the input parameter comprises:
multiplying β by a transfer function (TF′) to obtain the output signal, wherein
TF
′
=
V
b
1
+
α
.
16. An audio system comprising:
a capacitive microelectromechanical system (MEMS) microphone configured to receive a signal corresponding to an input sound pressure, wherein the capacitive MEMS microphone includes an active capacitance and a parasitic capacitance;
a controller configured to:
determine that a nonlinear relationship exists between the signal and the input sound pressure;
determine, based on the signal, a normalized displacement (B) of a movable electrode in the active capacitance corresponding to the input sound pressure;
determine an output signal based on the normalized displacement, wherein the output signal and the input sound pressure have a linear relationship; and
compensate the signal based on the determined output signal so that the compensated signal has the linear relationship with the input sound pressure; and
a speaker configured to output the compensated signal as a sound output corresponding to the input sound pressure.
17. The system of claim 16 , wherein the controller is further configured to:
estimate the input sound pressure (p) based on the normalized displacement (β); and
determine the output signal by multiplying p by a transfer function (TF).
18. The system of claim 16 , wherein the controller is further configured to multiply β by a transfer function (TF′) to obtain the output signal.
19. The system of claim 16 , wherein the MEMS microphone includes a MEMS transducer.
20. The system of claim 16 , wherein the controller is configured to:
determine a sound level of the signal; and
responsive to the determined sound level being higher than a threshold value, determine that the nonlinear relationship exists between the signal and the input sound pressure.