6.002 Fall 2000 Lecture 1 20 6.002 CIRCUITS AND ELECTRONICS Operational Amplifier Circuits 6.002 Fall 2000 Lecture 2 20  Operational amplifier abstraction  Building block for analog systems  We will see these examples: Digital-to-analog converters Filters Clock generators Amplifiers Adders Integrators & Differentiators Reading: Chapter 15.5 & 15.6 of A & L. + – Review  ∞ input resistance  0 output resistance  Gain “A” very large 6.002 Fall 2000 Lecture 3 20 Consider this circuit: − + ≈ + = v RR R vv 21 2 1 1 2 R vv i − − = 2 iRvv OUT −= − 2 1 2 R R vv v ⋅ − −= − − 1 2 2 1 2 1 R R v R R v − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ += − 1 2 2 1 21 21 2 1 R R v R RR RR R v − + ⋅ + = () 21 1 2 vv R R −= subtracts! + – 2 R + – 1 R + – 1 R 2 R + v − v i i OUT v + – 1 v 2 v 6.002 Fall 2000 Lecture 4 20 Another way of solving — use superposition 1 21 1 R RR vv OUT + ⋅= + 1 21 21 21 R RR RR Rv + ⋅ + ⋅ = 1 2 1 R R v= 2 1 2 2 v R R v OUT −= + – 21 || RR + – 1 R 2 R 2 OUT v 2 v + – + – 1 R 2 R 1 OUT v 1 v 2 R + v 1 R 21 OUTOUTOUT vvv += () 21 1 2 vv R R −= 0 1 → v 0 2 → v Still subtracts! 6.002 Fall 2000 Lecture 5 20 Let’s build an intergrator… dti C 1 v t O ∫ ∞− = Let’s start with the following insight: v O is related to dti ∫ I v + – O v + – ∫ dt i + – i + – O v C But we need to somehow convert voltage v I to current. 6.002 Fall 2000 Lecture 6 20 But, v O must be very small compared to v R , or else R v i I ≠ When is v O small compared to v R ? First try… use resistor i R v I → O O v d t dv RC >> when I O v d t dv RC ≈ dtv RC 1 v t IO ∫ ∞− ≈ or IO O vv d t dv RC =+ R v larger the RC, smaller the v O for good integrator ωRC >> 1 I v + – i + – O v C R v + – R Demo 6.002 Fall 2000 Lecture 7 20 There’s a better way… R v i I = so, + – + – R I v + – + – R R v I I v C v + – + – O v i i under negative feedback V0v ≈ − Notice CO vv −= dt R v C 1 v t I O ∫ ∞− −= We have our integrator. + – 6.002 Fall 2000 Lecture 8 20 Now, let’s build a differentiator… I v + – O v + – dt d But we need to somehow convert current to voltage. i is related to dt dv I Let’s start with the following insights: dt dv Ci I = + – I v i C 6.002 Fall 2000 Lecture 9 20 Demo CI vv = dt dv Ci I = dt dv RCv I O −= Recall + – i i current to voltage iRv O −= V0 + – + – R I v + – O v C C v i Differentiator… + – i + – R v O . dv RC >> when I O v d t dv RC ≈ dtv RC 1 v t IO ∫ ∞− ≈ or IO O vv d t dv RC =+ R v larger the RC, smaller the v O for good integrator ωRC >>. Clock generators Amplifiers Adders Integrators & Differentiators Reading: Chapter 15.5 & 15.6 of A & L. + – Review  ∞ input resistance  0 output