6.002 Fall 2000 Lecture 1 19 6.002 CIRCUITS AND ELECTRONICS The Operational Amplifier Abstraction 6.002 Fall 2000 Lecture 2 19  MOSFET amplifier — 3 ports power port input port output port + – I v + – O v + – S V  Amplifier abstraction + – I v + – S V + – O v I v O v Function of v I Review 6.002 Fall 2000 Lecture 3 19  Can use as an abstract building block for more complex circuits (of course, need to be careful about input and output).  Today Introduce a more powerful amplifier abstraction and use it to build more complex circuits. Reading: Chapter 15 from A & L. I v O v Function of v I Review 6.002 Fall 2000 Lecture 4 19 Operational Amplifier Op Amp OUT v + – + – IN v More abstract representation: input port S V output port power port S V− + – + – + – 6.002 Fall 2000 Lecture 5 19 Circuit model (ideal): i.e.  ∞ input resistance  0 output resistance  “A” virtually ∞  No saturation O v Av ∞→ A + – + – v v + v – 0= i + 0= i – 6.002 Fall 2000 Lecture 6 19 (Note: possible confusion with MOSFET saturation!) Using it… + – VV S 12−=− L R O v + – 12V + – 12V VV S 12= Demo IN v μV10μV10− O v V12 V12− 6 10~ A but unreliable, temp. dependent saturation active region IN v 6.002 Fall 2000 Lecture 7 19 Let us build a circuit… Circuit: noninverting amplifier Equivalent circuit model 1 R O v + – 2 R IN v + v − v ( ) −+ − vvA + – 0 =i + 0 =i – o p a m p 1 R O v + – 2 R IN v + – + v − v 6.002 Fall 2000 Lecture 8 19 Let us analyze the circuit: Find v O in terms of v IN , etc. What happens when “ A ” is very large? ( ) −+ −= vvAv O ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + −= 21 2 RR R vvA OIN IN 21 2 O Av RR AR 1v = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + 21 2 IN O RR AR 1 Av v + + = 6.002 Fall 2000 Lecture 9 19 Let’s see… When A is large Gain:  determined by resistor ratio  insensitive to A, temperature, fab variations 21 2 IN O RR AR 1 Av v + + = ( ) 2 21 IN R RR v + ≈ gain Demo Suppose 6 10A = R9R 1 = RR = 2 RR9 R10 1 v10 v 6 IN 6 O + + ⋅ = 10vv INO ⋅≈ 10 1 101 v10 6 IN 6 ⋅+ ⋅ = 21 2 IN RR AR Av + ≈ 6.002 Fall 2000 Lecture 10 19 e.g. v IN = 5V Suppose I perturb the circuit… (e.g., force v O momentarily to 12V somehow). Stable point is when v + ≈ v - . Key: negative feedback Æ portion of output fed to – ve input. e.g. Car antilock brakes Æ small corrections. Why did this happen? Insight: + – R INO v2v = + – R IN v + v − v negative feedback 2 v O 5V 5V 10V 0i = – A 12V 6V 6V . 6.002 Fall 2000 Lecture 1 19 6.002 CIRCUITS AND ELECTRONICS The Operational Amplifier Abstraction 6.002 Fall 2000 Lecture. powerful amplifier abstraction and use it to build more complex circuits. Reading: Chapter 15 from A & L. I v O v Function of v I Review 6.002 Fall 2000