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Piezoresistive MEMS Accelerometer Consider the following MEMS Piezoresistive accelerometer: Piezoresistors Vibration Cantilever Substratę Base Proof mass The density, modulus and dimensions of the beam and the proof mass are known. The equivalent mechanical damping. , of the beam has been determined experimentally as a function of the velocity of the proof mass. A piezoresistive material mounted to the beam changes resistance as the beam bends. The resistance of the piezoresistor is proportionally related to the position of the proof mass by the piezoresistive constant, p, such that: R = py The change in resistance is measured as an output voltage, Vo, using a simplified circuit with a constant current supply. Simplified Circuit: The behavior of the system during operation can be modeled with the supply current as a constant system parameter. The input to the system is the displacement of the base, and the output is the voltage, vo. Using the mechanical description of the accelerometer, you will develop a Dynamic Equation for the output voltage as a function of the displacement of the base an compare the behavior of the system for two different beam heights. a) Derive the mechanical model of the accelerometer using the equivalent mass and stiffness. b) Use the electrical model of the current source circuit and the piezoresistive constant relationship to develop the transfer function and dynamic equation. c) For the system parameters, and the two different beam heights provided, observe the transfer functions. What characteristics of the behavior can be identified?

Piezoresistive MEMS Accelerometer Consider the following MEMS Piezoresistive accelerometer: Piezoresistors Vibration Cantilever Substratę Base Proof mass The density, modulus and dimensions of the beam and the proof mass are known. The equivalent mechanical damping. , of the beam has been determined experimentally as a function of the velocity of the proof mass. A piezoresistive material mounted to the beam changes resistance as the beam bends. The resistance of the piezoresistor is proportionally related to the position of the proof mass by the piezoresistive constant, p, such that: R = py The change in resistance is measured as an output voltage, Vo, using a simplified circuit with a constant current supply. Simplified Circuit: The behavior of the system during operation can be modeled with the supply current as a constant system parameter. The input to the system is the displacement of the base, and the output is the voltage, vo. Using the mechanical description of the accelerometer, you will develop a Dynamic Equation for the output voltage as a function of the displacement of the base an compare the behavior of the system for two different beam heights. a) Derive the mechanical model of the accelerometer using the equivalent mass and stiffness. b) Use the electrical model of the current source circuit and the piezoresistive constant relationship to develop the transfer function and dynamic equation. c) For the system parameters, and the two different beam heights provided, observe the transfer functions. What characteristics of the behavior can be identified?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Piezoresistive MEMS Accelerometer Consider the following MEMS Piezoresistive accelerometer: Piezoresistors Vibration Cantilever Substrate Base Proof mass The density, modulus and dimensions of the beam and the proof mass are known. The equivalent mechanical damping, , of the beam has been determined experimentally as a function of the velocity of the proof mass. A piezoresistive material mounted to the beam changes resistance as the beam bends. The resistance of the piezoresistor is proportionally related to the position of the proof mass by the piezoresistive constant, p, such that: R = py The change in resistance is measured as an output voltage, Vo, using a simplified circuit with a constant current supply. Simplified Circuit: i,(1 The behavior of the system during operation can be modeled with the supply current as a constant system parameter. The input to the system is the displacement of the base, and the output is the voltage, vo. Using the mechanical description of the accelerometer, you will develop a Dynamic Equation for the output voltage as a function of the displacement of the base an compare the behavior of the system for two different beam heights. a) Derive the mechanical model of the accelerometer using the equivalent mass and stiffness. b) Use the electrical model of the current source circuit and the piezoresistive constant relationship to develop the transfer function and dynamic equation. c) For the system parameters, and the two different beam heights provided, observe the transfer functions. What characteristics of the behavior can be identified?
Transcribed Image Text:Piezoresistive MEMS Accelerometer Consider the following MEMS Piezoresistive accelerometer: Piezoresistors Vibration Cantilever Substrate Base Proof mass The density, modulus and dimensions of the beam and the proof mass are known. The equivalent mechanical damping, , of the beam has been determined experimentally as a function of the velocity of the proof mass. A piezoresistive material mounted to the beam changes resistance as the beam bends. The resistance of the piezoresistor is proportionally related to the position of the proof mass by the piezoresistive constant, p, such that: R = py The change in resistance is measured as an output voltage, Vo, using a simplified circuit with a constant current supply. Simplified Circuit: i,(1 The behavior of the system during operation can be modeled with the supply current as a constant system parameter. The input to the system is the displacement of the base, and the output is the voltage, vo. Using the mechanical description of the accelerometer, you will develop a Dynamic Equation for the output voltage as a function of the displacement of the base an compare the behavior of the system for two different beam heights. a) Derive the mechanical model of the accelerometer using the equivalent mass and stiffness. b) Use the electrical model of the current source circuit and the piezoresistive constant relationship to develop the transfer function and dynamic equation. c) For the system parameters, and the two different beam heights provided, observe the transfer functions. What characteristics of the behavior can be identified?
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