6.002 CIRCUITS AND ELECTRONICS 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 Review Operational amplifier abstraction + ∞ input resistance – Gain “A” very large 0 output resistance 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 Consider this circuit: R2 i i R1 v2 + – v1 + – R2 + v = v1 R1 + R2 ≈ v− v2 − v − i= R1 R1 v− – v+ + R2 + vOUT – vOUT = v − − iR2 v2 − v − =v − ⋅ R2 R1 − R2 ⎡ R2 ⎤ = v ⎢1 + ⎥ − v2 R1 ⎣ R1 ⎦ − R2 R1 + R2 R2 = v1 ⋅ − v2 R1 + R2 R1 R1 = R2 (v1 − v2 ) R1 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 Another way of solving — use superposition v1 → 0 v2 → 0 R1 R2 R1 v1 + – – v2 + – v+ + R2 – vOUT2 + vOUT2 R2 R1 R1 || R2 R2 = − v2 R1 vOUT1 vOUT1 R1 + R2 =v ⋅ R1 + v1 ⋅ R2 R1 + R2 = ⋅ R1 + R2 R1 = v1 vOUT = vOUT1 + vOUT2 R2 = (v1 − v2 ) R1 R2 R1 Still 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 Let’s build an intergrator… vI + – + vO – ∫ dt Let’s start with the following insight: i + i + – C vO – t 1 vO = ∫ i dt C −∞ vO is related to ∫ i dt But we need to somehow convert voltage vI to 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 First try… use resistor + vR – vI + – i + R C vO vI →i R – But, vO must be very small compared to vR, or else vI i≠ R When is vO small compared to vR ? dv larger the RC, RC O + vO = vI dt smaller the vO vR dvO when RC >> vO for good dt integrator dvO ≈ vI RC ωRC >> 1 dt t 1 or vO ≈ vI dt ∫ Demo 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 There’s a better way… i Notice i – + v − ≈ 0V under negative feedback vI i= so, R – R vI + – + vC vI + – R – vO = −vC R + vI – + t + vO 1 vI – vO = − ∫ dt 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 Now, let’s build a differentiator… + vO – d dt vI + – Let’s start with the following insights: i vI + – C dvI 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 Differentiator… Recall i i – + R i – + vO – + 0V i C vI + – + vC – Demo R – + vO = −iR current to voltage vO vI = vC dvI i=C dt vO = − RC dvI 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