Berkeley ELENG C247B - Capacitive Position Sensing: Electronic and Mechanical Noise (11 pages)

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Capacitive Position Sensing: Electronic and Mechanical Noise



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Capacitive Position Sensing: Electronic and Mechanical Noise

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Pages:
11
School:
University of California, Berkeley
Course:
Eleng C247b - Introduction to MEMS Design

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EE C245 ME C218 Introduction to MEMS Design Fall 2003 Roger Howe and Thara Srinivasan Lecture 23 Capacitive Position Sensing Electronic and Mechanical Noise EE C245 ME C218 Fall 2003 Lecture 23 Today s Lecture Basic CMOS buffer amplifiers for position sensing Electronic noise sources transistors and resistors Brownian noise Signal to noise ratio Reading Gray P R and Meyer R G Analysis and Design of Analog Integrated Circuits 3rd Ed 1993 EE C245 ME C218 Fall 2003 Lecture 23 2 1 The Capacitive Half Bridge Revisited v t V cos t C x C x oA go x C x oA go x Cin 0 1X vout C x v t V cos t Z x Z x Vout V V Z Z x Z Z x x Vout Vin V go EE C245 ME C218 Fall 2003 Lecture 23 3 Precision Unity Gain via Feedback VDD v vout Ad v v vv vin vin Ad is large v vout vout Ad vin vout EE C245 ME C218 Fall 2003 Lecture 23 4 2 Basic CMOS Differential Amplifier VDD Simplified analysis B v v v v 2 ISS 2 vout M1 v M2 b v ro cs vout A ro2 ISS g m2vgs2 vgs2 v a EE C245 ME C218 Fall 2003 Lecture 23 5 Differential Gain Ad vout gm2vgs2 ro2 vout ro2 g m2vgs2 vgs2 v vout gm2 ro2 v Typical values gm2 ro2 200 Ad 100 EE C245 ME C218 Fall 2003 Lecture 23 6 3 Basic Unity Gain Buffer VDD ISS 2 Zin M1 M2 vout Input resistance Rin Input capacitance Cin vin ISS EE C245 ME C218 Fall 2003 Lecture 23 7 Input Capacitance Cin Cin Vin Vgs1 ro cs Cgd1 Cgs1 ro1 ro2 ro cs R g m1Vgs1 gate drain short on transistor M2 g m2Vgs2 gm2Vds2 Resistor R Therefore Vgs1 Input capacitance EE C245 ME C218 Fall 2003 Lecture 23 8 4 Improved Unity Gain Buffer VDD Weijie Yun Ph D EECS 1992 ISS 2 M3 M4 Zin vin M1 M2 vout ISS Result EE C245 ME C218 Fall 2003 Lecture 23 VDD 9 Setting the DC Bias ISS 2 v t V cos t M3 Node A has no path to ground so it s called a floating node M4 C x vout A M1 M2 Solutions C x ISS v t V cos t EE C245 ME C218 Fall 2003 Lecture 23 10 5 Electronic Noise Sources 1 Thermal noise in resistors generated by random motion of electrons or holes white spectral density up to 10 THz vn 2 4k BTR f spectral density Example



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