The Ideal Op-amp (Operational amplifier) + – v+v+ v–v– V OUT + – + – V IN V OUT V IN [μV] V OUT [V] +15V –15V V OUT =A(v + –v – ) A~10 5 saturation

Op-amp Feedback V OUT + – v+v+ v–v– + – v+v+ v–v– V IN R1R1 R2R2 Non-Inverting Amplifier Circuit

Op-amp Feedback + – v+v+ v–v– Assumptions: Gain is very large (A) Inputs draw no current (Z IN =) Output attempts to make input voltage difference zero (v + =v – ) V OUT + – v+v+ v–v– V IN R1R1 R2R2 Non-Inverting Amplifier Circuit

+ V OUT V IN R1R1 Inverting Amplifier Circuit R2R2 – v–v– v+v+ i i Summing amplifier R2R2 – + v–v– v+v+ V OUT i V1V1 R1R1 V2V2 R1R1 V3V3 R1R1

RFRF – + v–v– v+v+ i V1V1 R1R1 V2V2 R2R2 V3V3 R3R3

V1V1 R1R1 R2R2 – + v–v– v+v+ V2V2 R1R1 Difference amplifier R2R2

Integrator V OUT V IN Capacitor as integrator R C ViVi V int If RC>>t V C <<V i

+ V OUT V IN R C – v–v– v+v+ i i Op-amp Integrator

Differentiation R C ViVi V diff Small RC 

+ V OUT V IN R C – v–v– v+v+ i i Op-amp Differentiator V OUT V IN

+ V OUT R2R2 C – v–v– v+v+ i i Complex analysis R1R1 V0ejωtV0ejωt High pass filter

Exploiting op-amp saturation + – v+v+ v–v– V OUT V OUT = A(v + –v – ) AV OUT = +V Sat v + >v – V OUT = –V Sat v + <v – Saturation voltage

Bridge circuits Bridge balanced when V A V B =0 V0V0 Z1Z1 Z3Z3 Z2Z2 Z4Z4 VAVA VBVB + – V OUT

Analogue – digital conversion (ADC) + – + – + – + – V IN V0V0 R R R R

V OUT  + R1R1 R1R1 C R Oscillator

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