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Opam2

Electronics

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Opam2

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  1. CIRCUITS AND ELECTRONICS 6.002 Operational Amplifier Circuits Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  2. Review ? Operational amplifier abstraction ? ∞ input resistance ? 0 output resistance ? Gain “A” very large + – ? 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. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  3. Consider this circuit: R i 2 1 R i − v – +– 2v + + v + OUT v – 1 R +– 1v R 2 − = − vOUT v iR v R 2 + = v v 2 − 1 − + v R R − = − ⋅ v R 2 1 2 2 − ≈ R v 1 − − v v ⎤ ⎡+ R R = − i 2 = − v v 1 2 2 ⎢⎣ ⎥⎦ 2 R R R 1 1 1 + R + R R R = ⋅ − v v 2 1 2 2 1 2 R R R R 1 2 1 1 R ( ) = − v v 2 1 2 R 1 subtracts! Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  4. Another way of solving — use superposition 1→ v 2→ 0 v 0 1 R R + v 2 + v OUT 1 1 R +– R 1v 2 – – R +– 2 2v v + R OUT 2 1 R 1|| R 2 + R R + = ⋅ vOUT v 1 2 R R = − 1 vOUT v 2 1 2 R 2 ⋅ + 1 v R R R = ⋅ 1 2 1 2 + R R R 1 2 1 R = v 2 1R = + OUT v OUT v R OUT v 1 1 2 ( ) = − v v 2 1 2 R Still subtracts! 1 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  5. Let’s build an intergrator… + O v ∫dt +– Iv – Let’s start with the following insight: i + +– i O v C – t 1 ∫ ∞ − = v i dt O C vOis related to i∫ dt But we need to somehow convert voltage vIto current. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  6. First try… use resistor R v + – i + R +– vI→ Iv O v i C R – But, vOmust be very small compared to vR, or else i ≠ v I R When is vOsmall compared to vR? dv RC = + larger the RC, smaller the vO v v O O I dt R v dv when >> v RC O for good integrator ωRC >> 1 O dt dv ≈ v RC O I 1 dt v t ∫ ∞ − or ≈ v dt Demo O I RC Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  7. There’s a better way… i Notice i – + under negative feedback − v ≈ 0 V v = so, i I R – R +– Iv + C v + vI – R – = − v v R +– O C Iv + – + O v t 1 v ∫ ∞ − = − v dt I O C R We have our integrator. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  8. Now, let’s build a differentiator… + O v d +– Iv dt – Let’s start with the following insights: i dv +– = Iv i C I C dt dvI i is related to dt But we need to somehow convert current to voltage. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

  9. Differentiator… Recall i i – + R i – + – + = − vO iR vO current to voltage 0 V i R C – O v C v +– – + Iv + v = v I C dv = i C I dt Demo dv = − v RC I O dt Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 20

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