5225 lecture 33 circuits ii student - · pdf fileeel5225: principles of mems transducers (fall...

11/24/2003 1EEL5225: Principles of MEMS Transducers (Fall 2003)

Accelerometers

Capacitive Position SensingCircuits for Capacitive SensingADI Capacitive AccelerometersOther MEMS Accelerometers

Reading: Senturia, Chapter 19, p.497-530

Lecture 33 by H.K. Xie 11/24/2003

EEL5225: Principles of MEMS Transducers (Fall 2003)Instructor: Dr. Hui-Kai Xie

Note: Most of figures in this lecture are copied from Senturia, Microsystem Design, Chapter 19.


Capacitive Position Sensing

Capacitive Position Sensing

MEMS Capacitive Sensors:• High impedance• Small sensing capacitance• Very small signal• Parasitic capacitance• Noise


( )10

1 2

1 2

1 2

2s s

s

CV V V

C CC C

VC C

= − ++

−=

+

Differential Capacitive Sensing

Differential Capacitive SensingFirst order cancellation of many effects

Temperature variationsCommon mode rejection


Interface circuitsTransimpedance amplifierTransimpedance amplifier with feedback capacitorSwitched-capacitor circuitsVoltage follower

Demodulation MethodsPeak detectorsSynchronous demodulators

Offset cancellation circuitsChopper-Stabilized AmplifiersCorrelated Double Sampling

Circuits for Capacitive Sensing


( )

( )

s

sC s

Q C x VdV C dxi C x Vdt x dt

=

∂= +

∂

Transimpedance amplifier

o F CV R i= −

• Parasitic capacitance is negligible• Output voltage depends on both the position x and velocity dx/dt• DC Vs: Output voltage is directly proportional to the velocity.• AC Vs: High frequency of Vs is desired.

• Large DC offset• Sensitivity is proportional to RF. But large resistors are difficult to

implement on-chip for integrated sensors.• Vs also generates electrostatic force which disturbs the position

of the rotor. Small Vs or Short pulses


Transimpedance amplifier with a feedback capacitor

Transimpedance Amplifier

( )Co s

F F

C xiV V

sC C≈ − ≈ −

• Assume a high-frequency AC source. Then velocity-dependent term of iC can be ignored.

• Assume ωRFCF >> 1.

• RF provides DC feedback to clamp the DC value at the inverting input node to zero voltage.

• This circuit suppresses the effect of parasitic capacitance because the inverting input is set at virtual ground.

• Large RF is normally required, which may be difficult to implement on-chip.


• Two non-overlapping clock pulses• High switching frequency for the clocks• DC source for Vs

Fig.14.34

Switched-Capacitor Circuit


22

( ) ( ( ) ) o s o sC xV V C V C x VC

= =∵

• φ1 turns on T1 and T3Unity-gain bufferCharge C(x)Vs on capacitor C(x)

• φ1 is low and turns off T1 and T3Isolating C(x) and turning the op-amp into an integrator

• φ2 turns on T2Grounding left-terminal of C(x)Shifting the charge C(x)Vs of the right-terminal of C(x) to the left-terminal of C2The circuit settles at

• Repeat the clock cycles. Vo alternates between zero and [C(x)/C2]Vs. A followed low-pass filter will give the average output.

Switched-Capacitor Circuit

This circuit suppresses the parasitic capacitance effect because of the virtual ground of the inverting input.


Voltage follower for differential capacitor

1 2

1 2x s

P

C CV V

C C C−

=+ +

Voltage Follower

• Parasitic capacitance reduces the signalSolution: a guard electrode driven by Vo

- Increased fabrication complexity- Difficult to cancel all parasitics

• Symmetric positive and negative sinusoidal or pulse signals (+/-Vs)

Guard electrode

Substrate electrode


Transimpedance amplifier for differential capacitor

1 20 s

F

C CV V

C−

= −

Differential Capacitive Sensing


Demodulation of a capacitive signal using a peak detector

Demodulation: Peak Detector


Analog multiplier

Synchronous Demodulators

( ) ( ) ( ) ( )( ) cos cos cos cos 22

rc r c c

S t VS t t V t tω ω θ θ ω θ⋅ + = + +

( )cos2

rV S tθAfter low-pass filtering, the output is

which is phase-sensitive.

Analog Devices MLT04


Track-and-hold circuit

Synchronous Demodulators

• T4 and T2 are synchronized through φ2, • CT always holds previous C(x)Vs/C2 for one period and updates

C(x)Vs/C2 every clock cycle. • R3C3 forms a low-pass filter that smoothes out the sampling

steps.


System block diagram

A Capacitive Measurement System


Chopper-stabilized amplifiers

Offset Cancellation

( )1 20 2

1 1 2

( )os

A R RV v V

AR R R +

+= −

+ +

Vos1, Vos2: input offsets of op-amp

1 1 2 2 1

2 1 2 1 2

During the phase, During the phase,

os os os

s os s os os

v V V V Vv V V V V V V

φφ

+

+

= ⇒ = −

= + ⇒ = + −After LPF, only Vs remains

• This circuit can also cancel out low-frequency amplifier noise, 1/f noise in particular

• Still affected by parasitic capacitance at the input node


Correlated Double Sampling

Offset Cancellation

Vos1, Vos2: input offsets of op-amp

1 1 20,1 1 2

1 2 1 21 1os osA A A

V V VA A A A

= − −+ + • This circuit can also cancel out

low-frequency amplifier noise, 1/f noise in particular

• Vos1 is attenuated by a factor of A1A2, while Vos2 is attenuated by a factor of A1

• NOT affected by parasitic capacitance at the input node

( )

( )

1 1 20,2 0,1

1 2 1

1 2

1 2 1

11

wher 1

1 for large A

sF

F

F

A C CV V B V

C C ACC C C

BC C A C

BA

−= − − ⋅

+ ++ +

=+ + +

→

φ1 phase:

φ2 phase:


Accelerometer model

Capacitive Accelerometer

2r

xx

x

aa

kmx

kxma

ω==

=

Proof massSpring

Anchor a

Displacement is proportional to acceleration, and can be picked up

piezoresistivelyPiezoelectricallyCapacitivelyOpticallyThermally

, 4

4n rms B

B r

a k Tb f

k T fmQω

= ∆

∆=

Brownian noise:


NPN NMOS Sensor Area

Thox

Nwell EmitterBase NSD

BPSG

Sensor Poly

MetPassivations

Courtesy of Mr. John Geen of Analog Devices, Inc.

Analog Devices (ADI) Accelerometers

Form transistors on bare wafers firstThen deposit and anneal MEMS structural materialsNo CMP neededOnly one interconnect metal layerWet etch to release MEMS structuresNeed a dedicated production line


Accelerometer structure


Accelerometer system block diagram


Sensing mechanism

2s

out sV

V V aα β= ± +


spring

anchor

shuttle


Tunneling Accelerometer (T. Kenny, et al)

Other MEMS accelerometers

dt

( )expt B I tI V dα∝ − Φ

VB: Bias voltage

• Small dt is typically obtained by moving the tip closer to the counter electrode through an actuation force after the microstructure is released.

• Force feedback to maintain constant distance.

• High resolution: sub-µg/Hz1/2.


DRIE CMOS-MEMS z-axis accelerometer (Xie, et al)


Top viewanchor

Self-test actuator

sense combfingers

proof mass

self-test actuator

z-spring

Size: 0.5mm x 0.6mmResonance: 3.9 kHzSensitivity: 2.6 mV/g(calculated 4.0 mv/g)Range: > 10 gLinearity: 0.5% (F.S.) Noise floor: 1 mg/Hz1/2

(Brownian 2.5 µg/Hz1/2)

y

x

z


Thermal MEMS accelerometer (MEMSIC, Inc.)


www.memsic.com

• Consists of thermal resistor, thermocouples and air as the inertial mass.

• Thermal heating creates a warm air bubble over the heating element.

• Any change in the sensor’s motion and/or orientation causes the cooler air to force the heated bubble toward the end of the package cavity in the direction of acceleration.

• This movement creates a temperature differential in the vicinity of the two thermocouples. Amplifying this difference produces an output signal that characterizes both the nature (e.g., shock or tilt) and the direction of the applied force.

5225 lecture 33 circuits ii student - · pdf fileeel5225: principles of mems transducers (fall...

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