1. The Ideal Op-amp (Operational amplifier) v+ VOUT v– +15V VIN VOUT –15V
saturation
VOUT
VOUT [V]
VOUT=A(v+–v–)
A~105
VIN [μV]

2. Op-amp Feedback v+ VOUT v– v+ VIN VOUT v– R1 R2
Non-Inverting Amplifier Circuit

3. Op-amp Feedback v+ v– Assumptions: Gain is very large (A)
Inputs draw no current (ZIN=)
Output attempts to make input voltage difference zero (v+=v–)
VOUT + – v+ v–
VIN R1 R2
Non-Inverting Amplifier Circuit

4. R2 R1 v– VIN i VOUT v+ R2 i R1 v– V1 VOUT v+ V2 V3
Inverting Amplifier Circuit R2 – v– v+ i
Summing amplifier R2 – + v– v+
VOUT i V1 R1 V2 V3

5. RF i V1 R1 V2 R2 V3 R3 v– –
VOUT v+ +

6. Difference amplifier R2 R1 v– V1 –
VOUT v+ R1 + V2 R2

7. Integrator VIN VOUT Capacitor as integrator R Vi C Vint If RC>>t
VC<<Vi

8. Op-amp Integrator C – v– v+ i R
VIN
VOUT +

9. Differentiation C Vi
Vdiff R
Small RC 

10. Op-amp Differentiator
VIN
VOUT R – v– v+ i C
VIN
VOUT +

11. Complex analysis R2 i C R1 v– – i
VOUT v+
V0ejωt +
High pass filter

12. Exploiting op-amp saturation+ – v+ v–
VOUT
Saturation voltage
VOUT = A(v+–v–)
A VOUT = +VSat v+>v–
VOUT = –VSat v+<v–

13. Analogue – digital conversion (ADC)+ – R + – R + –
VIN R + – R

14. Oscillator
VOUT  + R1 C R

15. 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

16. Bridge circuits Z1 Z3 VA VB V0 VOUT Z4 Z2 Bridge balanced when VAVB=0+ – VB V0
VOUT Z2 Z4
Bridge balanced when VAVB=0

17. End of Op-Amps!