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v +. V OUT. v –. +15V. +. +. –15V. –. –. +. –. The Ideal Op-amp. (Operational amplifier). saturation. V IN. V OUT. V OUT [V]. V OUT =A(v + –v – ). V IN [ μ V]. A~10 5. v +. v –. v +. V IN. V OUT. v –. R 1. R 2. Non-Inverting Amplifier Circuit. +. +. –. –. V OUT.

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Presentation Transcript
The ideal op amp

v+

VOUT

v–

+15V

+

+

–15V

+

The Ideal Op-amp

(Operational amplifier)

saturation

VIN

VOUT

VOUT [V]

VOUT=A(v+–v–)

VIN [μV]

A~105


Op amp feedback

v+

v–

v+

VIN

VOUT

v–

R1

R2

Non-Inverting Amplifier Circuit

+

+

VOUT

Op-amp Feedback


Op amp feedback1

v+

v–

v+

VIN

VOUT

v–

R1

R2

Non-Inverting Amplifier Circuit

+

+

Op-amp Feedback

Assumptions:

Gain is very large (A)

Inputs draw no current (ZIN=)

Output attempts to make input voltage difference zero (v+=v–)


The ideal op amp

Inverting Amplifier Circuit

R2

i

R1

v–

VIN

i

VOUT

v+

+

R1

R1

R1

V1

V3

V2

R2

i

v–

VOUT

Summing amplifier

v+

+


The ideal op amp

R1

R2

R3

V1

V2

V3

RF

i

v–

VOUT

v+

+


The ideal op amp

Difference amplifier

R2

R1

v–

V1

VOUT

v+

R1

+

V2

R2


Integrator
Integrator

VOUT

VIN

Capacitor as integrator

R

Vi

Vint

C

If RC>>t

VC<<Vi


Op amp integrator

i

v–

i

v+

Op-amp Integrator

C

R

VIN

VOUT

+


Differentiation
Differentiation

C

Vi

Vdiff

R

Small RC 


Op amp differentiator

i

v–

i

v+

Op-amp Differentiator

VOUT

VIN

R

C

VIN

VOUT

+


Complex analysis
Complex analysis

R2

i

C

R1

v–

i

VOUT

v+

V0ejωt

+

High pass filter


Exploiting op amp saturation

v+

VOUT

v–

+

Exploiting op-amp saturation

Saturation voltage

VOUT = A(v+–v–)

A VOUT = +VSat v+>v–

VOUT = –VSat v+<v–


Bridge circuits

+

Bridge circuits

Z1

Z3

VA

VB

V0

VOUT

Z4

Z2

Bridge balanced when VAVB=0


Analogue digital conversion adc

+

+

+

+

Analogue – digital conversion (ADC)

V0

R

R

VIN

R

R


Oscillator

R

VOUT

+

C

R1

R1

Oscillator


Op amp applications
Op-amp applications

Building block of analogue electronics

Signal amplifiers

Audio amplifiers

Integrators / differentiators

Voltage / current sources

Active filters

Oscillators

Digital-analogue and analogue-digital convertors