Op Amp Circuit

6.002

CIRCUITS AND ELECTRONICS

Operational Amplifier Circuits

6.002 Fall 2000

Lecture 20

1

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 16.5 & 16.6 of A & L.

6.002 Fall 2000

Lecture 20

2

Consider this circuit: i i

R1

v2 + – v1 + –

R2 v = v1 R1 + R2 ≈ v− +

v2 − v − i= R1

R1

R2

v− – v+ +

+ vOUT –

R2

vOUT = v − − iR2 − v − v = v− − 2 ⋅ R2 R1

R  R  = v − 1 + 2  − v2 2 R1  R1  = v1

R2 R + R2 R ⋅ 1 − v2 2 R1 + R2 R1 R1

R2 = (v1 − v2 ) R1 6.002 Fall 2000

subtracts!

Lecture 20

3

Another way of solving — use superposition v1 → 0

v2 → 0 R1

R2 R1 v2 +

–

v1 +

–

–

v+ + R2

–

vOUT2

+

vOUT2

vOUT1

R1 + R2 =v ⋅ R1 +

v1 ⋅ R2 R1 + R2 = ⋅ R1 + R2 R1 = v1

vOUT = vOUT1 + vOUT2 R2 = (v1 − v2 ) R1 6.002 Fall 2000

R2

R1

R1 || R2

R2 = − v2 R1

vOUT1

Lecture 20

R2 R1

Still subtracts! 4

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. 6.002 Fall 2000

Lecture 20

5

First try… use resistor + vR –

vI + –

i

+

R C

vO

vI →i R

– But, vO must be very small compared to vR, or else v i≠ 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 RC ≈ vI ωRC >> 1 dt t 1 or vO ≈ vI dt ∫ RC −∞ Demo 6.002 Fall 2000

Lecture 20

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There’s a better way… i

Notice i

– +

v − ≈ 0V under negative feedback vI i = so, R – R vI + – +

vI R

+

vC

–

– vI

+ –

R

+

vO = −vC

+ t vO 1 vI – vO = − ∫ dt C −∞ R

We have our integrator. 6.002 Fall 2000

Lecture 20

7

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.

6.002 Fall 2000

Lecture 20

8

Differentiator… Recall

i i

– + R

i

– + vO –

+ 0V

i

C vI + –

+ vC –

Demo 6.002 Fall 2000

R – +

vO = −iR

current to voltage

vO vI = vC dvI i=C dt

dvI vO = − RC dt Lecture 20

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