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11/21/2003 1EEL5225: Principles of MEMS Transducers (Fall 2003)

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

Introduction to Interface Electronics

Lumped Circuit ElementsGeneral AmplifiersOperational Amplifiers

Reading: Senturia, Chapter 14, p.353-395

Lecture 32 by H.K. Xie 11/21/2003


Lumped Circuit Elements

Linear 1-port (2-terminal) passive devicesResistor: energy dissipationCapacitor: energy storageInductor: energy storage


Lumped Circuit Elements

Non-linear 1-port (2-terminal) passive devicesP/N junction diodeNonlinear I-V characteristic

d

1

Note: Diode voltage,

: 1

1: i

D

D

qvkT

D S

D D d

qVkT

D S

Dd d

d

i I e

v V v

DC I I e

qISmall signal v v

kT r

= −

= +

= −

− = =

Ref. Sedra and Smith, Microelectronic Circuits, p. 132.


P/N Diode

0.7 (silicon diode at room temp.)

V≈

Low-frequency large-signal equivalent circuit

High-frequency small-signal equivalent circuit



Zener Diode

Exploits very sharp current-voltage characteristic at reverse breakdown for voltage regulation



Diode Circuits

AC-to-DC converter

Ref. Sedra and Smith, Microelectronic Circuits, p. 176,184.


Active Devices

SourcesEnergy supplied into system from external source (sometimes not shown)

Independent voltage sourcewith series source resistance

Independent current sourcewith shunt source resistance

v

v

i

i


Active Devices

SourcesDependent sources

Dependent voltage source

Dependent current source

Ref. Van Valkenbur, Network Analysis, p. 38.


Active Devices -- BJT & MOSFET

Cross-sectionN/P/N Bipolar Junction Transistor (BJT)

n-channel Metal Oxide Semiconductor Field Effect Transistor (n-channel MOSFET)

Ref. Sedra and Smith, Microelectronic Circuits, p. 231, 355.



Common-emitter configurationiC vs. vCE DC characteristics with base-emitter voltage (or base current) as parameter

Other configurations are common-base and common-collector

Common-source configurationiD vs. vDS DC characteristics with gate-to-source voltage as parameter

Other configurations are common-gate and common-drain




BJT High-Frequency Small-signal Equivalent Circuit

MOSFET High-Frequency Small-signal Equivalent Circuit



General Amplifiers

Signal Amplification

( )

( )

( )

V

I

P

Voltage gain, A 20 log

Current gain, A 20 log

Power gain, A 10log

OV

I

OI

I

O OLP

I I I

vA dB

vi

A dBi

v iP A dBP v i

≡

≡

≡ =

Note: We will discuss the frequency response later.



General Amplifiers

Amplifier Saturationhard limit at power supply limitsJargon: “rail” = power supply

rail-to-rail

Amplifier Nonlinearity

( ) ( )O O ov t V v t= +

( ) ( )I I iv t V v t= +

At operating point (known also as Quiescent point)

OV

I

dvA

dv=



General Amplifiers

Voltage Amplifier Equivalent Circuit

Voltage amplifier with signal source and load connected

0

input resistanceoutput resistanceopen circuit voltage gain

i

O

V

RRA

≡≡≡

( )0

0

Overall gain:

LO V i

L O

ii S

i S

O i LV

S i S L O

Rv A v

R RR

v vR R

v R RA

v R R R R

=+

=+

=+ +



General Amplifiers

Frequency Response of Amplifiers

function of

function of

For a linear circuit, for a sinusoidal input,( ) sin , the output is sinusoidal

with the same frequency:( ) sin( )

Amplifier transfer function, T( ):

T( )

T( )=

i i

o o

o

i

v t V t

v t V t

VV

ω

ω

ω φω

ω

ω φ

=

= +

=

∠

Analyze amplifier circuit in the complexfrequency variable (s- or Laplace-domain).

ω



General Amplifiers

Frequency Response of Amplifiers

Capacitively coupled ac-amplifier Direct-coupled dc-amplifier

Tuned or bandpass amplifier Ref. Sedra and Smith, Microelectronic Circuits, p. 26..


Single Time-Constant Networks

Review of Single Time-Constant Networkscircuits that can be reduced to one reactive component (capacitance or inductance) and one resistive component

High Pass FilterLow Pass Filter




Low Pass Filter

0

0

2

0

1

0

Replacing the circuit elements with their impedances,1R R and C

sC( ) 1 1( )( ) 1 1

1 1where . Replacing s with ,

1( )

1

( ) tan

o

i

V sT s

sV s sRC

jRC

T j

T j

ω

ω ωτ

ωωω

ωωω

−

→ →

= = =+ +

= =

=

+

∠ = −

1sC

iV ( )s oV ( )s




Magnitude and Phase Response of Low Pass STC Network

01RC

ω ω= =




High Pass Filter

0

0

20

1 0

Replacing the circuit elements with their impedances,1R R and C

sC( )

( )( ) 1

1 1where . Replacing s with ,

1( )

1

( ) tan

o

i

V s sRC sT sV s sRC s

jRC

T j

T j

ω

ω ωτ

ωωω

ωω

ω−

→ →

= = =+ +

= =

= +

∠ =

iV ( )s oV ( )s

1sC




Magnitude and Phase Response of High Pass STC Network

01RC

ω ω= =




Amplifier Frequency Response

V0A iV

Find the amplifier voltage transfer function, DC gain, and high frequency roll-off.Ref. Sedra and Smith, Microelectronic Circuits, p. 33.



Direct-coupled amplifier with input capacitance


( )

0

0

1//( ) ( ) and ( ) ( )

1//

( ) 1 1 1( )( ) 1 //1 1

This voltage transfer function has the same form as the low pass STC network.

DC

iiL

o V i i sL o

i Si

oV

o si i S i

L i

RsCR

V s A V s V s V sR R R R

sC

V sT s A

R RV s sC R RR R

= =+ +

= = + + +

( )

00

0

1 1 gain: T(s)1 1

1 1High frequency rolloff: //

Vso s

L i

i S i

AR RR R

C R Rω

τ

→

= + +

= =

V0A iV



Direct-coupled Amplifier with Input Capacitance

( )

V0

V0

0

Example: 20 , 100 , 60

A 144 , 200 , 1

DC gain:

1 1A 1001 1

High frequency rolloff: 1 1 159

//

s i i

o L

o s

L i

i S i

R k R k C pFV R R kV

VKR R VR R

kHzC R R

ωτ

= Ω = Ω =

= = Ω = Ω

= = + +

= = =

V0A iV




Capacitively-coupled Voltage Amplifier

0

0

0

Example: Capacitively coupled ideal voltage amplifier( )

( )1( )

High frequency gain: 100

Low frequency rolloff: 1 1 15.9

oV

i

V

V s sT s AV s s

RC

K A

HzRC

ωτ

= =+

= =

= = =



Application: Piezoresistive Microphone

Capacitively coupled amplifier used to reject DC offset

Ref. Arnold, MEMS-based Directional Acoustic Array, M.S. Thesis 2001.

Amplifier

MicrophoneCapacitor

Resistor

Lid

PackageBody

SiliconSubstrate

C

C

R

R

R0 R0

R0R0

G

MicrophoneHybrid Package Vs+

Vs-

OUT

GND

Vb

Diff. Amp.


Operational AmplifiersOperational Amplifiers

Basic building block for analog signal processing circuits

First integrated circuit operational amplifier, µ709, made by Fairchild Semiconductor in 1960s followed by the µ741.Consists of active transistors, resistors, and limited number of capacitorsApproximated by single-pole frequency response

Three stagesDifferential amplifier stage

Amplifies difference between two inputs

High-gain amplifier stageOutput amplifier stage

Inverting input

Non-inverting input

Power supply

Power supply

Output

Ref. Senturia, Microsystem Design, p. 382.


Operational Amplifiers

u741 Opamp


Operational AmplifiersWide variety of operational amplifiers:•High power•Low power•Precision•Low noise


Operational AmplifiersGeneral input signals

Differential signal from transducerCommon mode signal

For example, 60 Hz electromagnetic interference appearing on both inputs

Differential gain

Common-mode gain

dv

2

2

dcm

dcm

vv v

vv v

+

−

= +

= − +

Common Mode Rejection Ratio (CMRR)

or 20log

Actual opamps, CMRR range from1000 to 100,000 (60dB to 100dB)

d d

cm cm

A ACMRR

A A=

( )o o

dd

v vA

v v v+ −

= =−

( ) / 2o o

cmcm

v vA

v v v+ −

= =+




Voltage FollowerOutput follows inputVo=Vi

Serves as bufferVery high input impedanceLow output impedance



Non-inverting AmplifierShort op-amp analysis method:Assume that the input current is zero (infinite input impedance) and =0 ( ).

Using this method, we can analyze the transfer function for the non-invertingamplifier:

o

v v

vv

ε + −≈

1

2

2

1

If R , 1

[Unity-gain buffer or voltage follower.]

s

o

s

RR

vv

= +

= ∞ =




Inverting Amplifier


1 2

2 2

1 12

1

Open-loop gain is .

Equating currents:

1Closed-loop gain: 11 1

0 when .

s

o

s

AV AR R

V R RV R RR

A R

A

ε ε ε

ε

− +=

= − → − + +

→ → ∞∵



Inverting Amplifier

0

0

What is the frequency response of this configuration?

Replace A with the STC single-pole response, ( ) .1

AA s

ss

=+


( )

0 02 2

1 120 0 0

1

20 0

10

2

1

Substituting the single-pole response for A gives:

R with a DC gain of

R1

1and 3dB frequency determined by the pole at .

1

Note t

o

s

V A sRV R R

A s s sR

RA s

Rs

RR

= −

+ + +

+ +

= −+

0 0hat the gain-bandwith product is preserved: .A s

0ω 0 0A ω



Transimpedance Amplifier

1

Since the input current is negligible,

The transimpedance amplifier (voltage at output proportionalto current at input) is used as a current-to-voltage converter.

o sv R I= −




Integrator

1

1

1

Since the input current is negligible and the voltage at is approximatelythe same as at ground,

0

1 ( )

Note that the output voltage, .Therefore,

1 ( ) [

s cc

c s

o c

o s

vv

v dvi C

R dt

v V t dtR C

v v

v V t dtR C

−

+

−= =

=

= −

= −

∫

∫ Output is integral of input!]

Note: The integrator circuit is extremely sensitive to parasitic DC leakage currents.




Differentiator

1

Similarly, we find that for the differentiator circuit,

[Output is derivative of input!]

Note: The output of the differentiator is limited by how fast the output of the

op-amp can change

so

dvv R C

dt= −

change in output voltage, defined by the slew rate= .time

Typical slew rates are on the order of 1V/ sec.µ


zlumped circuit elements...zvoltage amplifier equivalent circuit zvoltage amplifier with signal...

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