ABE425 Engineering Measurement

Systems

Operational Amplifiers(OpAmps)

Dr. Tony E. Grift

Dept. of Agricultural & Biological EngineeringUniversity of Illinois

Agenda

PackagingOpAmp as a near-ideal Voltage AmplifierNon-inverting OpAmp

Virtual ground derivation

Inverting OpAmpVirtual ground derivation

Differentiating OpAmpIntegrating OpAmpVoltage follower (buffer)

Dual-in-line (DIP) and Surface Mount Device (SMD) packaging

Typical OpAmp pin assignment (741)

OpAmp as a near-ideal Voltage amplifier

Open loop amplification A very large

Input impedance very highOutput impedance very lowOpAmp has a Voltage source output

VVAVO

Non-inverting OpAmp

Ofi

i

i

O

VRR

RV

VV

VVAV

i

fii

i

fiO

i

fi

i

O

i

fi

i

O

ifi

iO

Ofi

iiO

R

RVV

R

RRV

A

V

RR

R

A

V

V

RR

RA

AV

AVRR

RAV

VRR

RVAV

1lim

1

1

1

1

i

fiO R

RVV 1

Non-inverting OpAmp : Virtual ‘ground’ principle

i

fiO R

RVV 1

i

O

VV

VVVVAV

Since no current is flowing intothe OpAmp:

f

iO

i

i

R

VV

R

V

What is the input resistance for the source ?iV

Inverting OpAmp

if

iO

if

fi

O

RR

RV

RR

RVV

V

VVAV

0

ii

fO

fi

i

fi

fi

fi

i

fi

fi

O

fi

fi

fi

iO

fi

iO

fi

fiO

VR

RV

A

RR

R

A

RR

RV

RR

RA

RR

RAV

V

RR

RAV

RR

RAV

RR

RV

RR

RVAV

lim

11

1

0

ii

fO V

R

RV

Inverting OpAmp: Virtual ground principle

0

V

VVVVAVO

ii

fO V

R

RV

i

f

i

O

f

O

i

i

R

R

V

V

R

V

R

Vi

Since no current is flowing intothe OpAmp:

What is the input resistance for the source ?iV

Capacitor equation

Charge across Capacitor (Coulomb)Capacitance value (Farad)Voltage across Capacitor (Volt)Current through Capacitor (Ampere)

dt

dQti

tVCtQ

CC

cC

*

ti

tV

C

tQ

C

c

C

Integrating Inverting OpAmp : Virtual ground

dttVRC

tV iO

1

0

V

VVVVAVO

dttVRC

tVdt

tdVRCtV

R

tV

dt

tdVC

dt

tdQti

tVtVR

tVti

iOO

i

iOCC

OCi

C

1

,

Differentiating Inverting OpAmp: Virtual ground

0

V

VVVVAVO

dt

tdVRC

dt

tdVRCtV

R

tV

dt

tdVC

dt

tdQti

R

tVti

iCO

OCCC

OC

dt

tdVRCtV i

O

Integrating Inverting OpAmp : Virtual ground

dttVRC

tV iO

1

0

V

VVVVAVO

dttVRC

tVdt

tdVRCtV

R

tV

dt

tdVC

dt

tdQti

tVtVR

tVti

iOO

i

iOCC

OCi

C

1

,

Differentiating Inverting OpAmp: Virtual ground

0

V

VVVVAVO

dt

tdVRC

dt

tdVRCtV

R

tV

dt

tdVC

dt

tdQti

R

tVti

iCO

OCCC

OC

dt

tdVRCtV i

O

Unity gain OpAmp (Voltage follower, buffer)

O iV t V t

This circuit has no amplification, but provides a very high impedance input and low impedance outputUse it after any sensor configuration to prevent loading errorsYou will need a symmetric power supply

Comparator function

SATO

SATO

VVvvif

VVvvif

OpAmp as comparator I

What could this circuit be used for if Vref can be varied?

Slope is termed ‘slew rate’

Voltage range detector

When does the LED come on?Why do we need the diodes?

How would you limit the current through the LED?

When Vin > Vref_high OR Vin < Vref, low

Comparator with hysteresis (Schmitt Trigger)

TV

OVRR

Rv

21

2

SATSATOi

SATSATOi

VRR

RvVVvvVif

VRR

RvVVvvVif

21

2

21

2

Schmitt trigger as debouncer in noisy signals

Regular comparator Schmitt trigger with hysteresis

Subtracting OpAmp

Use superposition!!Use virtual ground principle!!

First consider

23

40

4

0

3

2

2

0

vR

Rv

R

v

R

v

v

v

2v

Subtracting OpAmp

Use superposition!!Use virtual ground principle!!

Next consider

121

2

3

430

121

2

043

3

vRR

R

R

RRv

vRR

Rv

vRR

Rv

1v

Subtracting OpAmp

Add influences of both sources

23

41

21

2

3

430 v

R

Rv

RR

R

R

RRv

Current to voltage converter

INO RiV

Application current to voltage converter

Active filters combine amplification and filtering in one circuit!

What is the input impedance the source ‘sees’?

Active Low-Pass filter analysis (1st order)

2

1 1

22

2 22

2

1*

1\ \

1 1

Z R

RRj C

Z Rj C j R CR

j C

20

1

O

i

V RG

V R 2

1

O

i

V ZG

V Z

2 2 20

1 1 2 1 2 2

1 1 1

1 1 1

Z R RG G

Z R j R j j

Without C In general with impedances

02

1

1dB dB

dB

G Gj

Active High-Pass filter with OpAmp and Capacitor / Resistor pair (1st order)

What is the input impedance the source ‘sees’?

Active High-Pass filter analysis

1 1

2 2

1Z R

j C

Z R

20

1

O

i

V RG

V R 2

1

O

i

V ZG

V Z

1

2 2 2 1 10

1 1 1 11

1 1 1

Z R R j R C jG G

Z R j R C jRj C

Without C

0 11

1

1dB dB dBdB

G G jj

In general with impedances

High-pass and low-pass section separated by OpAmp

ABE425 Engineering Measurement Systems

Operational Amplifiers(OpAmps)

The End

Dept. of Agricultural & Biological EngineeringUniversity of Illinois