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6.002 Spring 2020 Lecture 5 1

6.002 CIRCUITS ANDELECTRONICS

Lecture 5 - Operational Amplifier

February 20, 2020

Contents:1. Operational amplifier: intro2. An op-amp-based amplifier3. Methodology to analyze op-amp circuits: non-inverting amplifier4. Another example: inverting amplifier

Reading Assignment:Agarwal and Lang, Ch. 15 (§§15.1-15.3)

Handouts:Lecture 5 notes

Announcements:Soldering training session in lab tomorrow

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Doppler Ultrasound System

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Lab 3 – Doppler Ultrasound System

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6.002 Spring 2020 Lecture 5 6

1. Operational amplifier: IntroIdeal op-amp is a voltage-controlled voltage source:

Equivalent circuit of ideal op-amp:

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Op-amp can be used to enable numerous circuits, with applications in fields such as:– Signal processing– Instrumentation– Control– Power – Etc.

Inverting amplifier

Current-to-Voltage converter

Integrator

Band-pass filter

Sample-and-hold circuit

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Properties of ideal op-amp:

– Differential input– Single-ended output– Very large and constant voltage gain– Infinite input resistance à zero input current– Zero output resistance à can deliver or sink infinite output current at any output voltage– No saturation– Infinite bandwidth

Outputvs

Input

Output

The op-amp we will use in the lab: LF356

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Real op-amp:– Gain is non linear– Output signal limited by power supply

voltages (saturation)– Offset in output voltage– Input and output resistances less than ideal– Bandwidth limited– Gain and offset are temperature dependent

A better model:

+-

v+Voffset

Rin

Routi+

i-

+

-

vin+-vin-

vin+

vin-v-

+-

+

f(v*)

iOR

C v*

+ -

-+-

v+Voffset

Rin

Routi+

i-

+

-

vin+-vin-

vin+

vin-v-

+-

+

f(v*)

iOR

C v*

+ -

-+-

v+Voffset

Rin

Routi+

i-

+

-

vin+-vin-

vin+

vin-v-

+-

+

f(v*)

iOR

C v*

+ -

-

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2. An op-amp-based amplifier

• Consider a simple amplifier configuration:

Very large gain, but…– Output offset results in output even if no input signal– Output can easily saturate– Temperature sensitivity corrupts output voltage

“Open loop” configuration has large gain but it is unstable.

Need to find a way to “pin” the output to ground when there is no signal at the input.

Demo

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• Consider the following circuit:

How does it work?– When vIN=0, ideally vO=0– Suppose with vIN=0 there is output offset vO>0

à R1/R2 voltage divider results in v->0à v+-v-<0 drives vO to zero

– Now assume no output offset. If vIN>0, then vO>0 such that vO causes v+= v-

à vO//vIN gain of this amplifier is less than A!

“Closed loop” configuration à feedback path mitigates problems

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Amplifier gain (assume ideal op-amp):

Small-signal equivalent circuit model:

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Then:

Solving for vo:

As expected!

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Op-amp itself has “open-loop gain”: AOp-amp amplifier has “closed loop gain”: G

Why would anybody do this?à Traded-off gain for robustness!

Amplifier gain is set by ratio of two resistance values:à gain largely independent of temperature à also corrected output offset problem

Demo

G=

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3. Methodology to analyze op-amp circuits

• Look again at non-inverting amplifier:

How much is v+-v-?

Since A is very large, then v+-v-<<vIN, vO

In the scale of vIN, vO,

As Aà ∞

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Method to analyze op-amp circuits:– assume that Aà∞– assume that v+=v-

– work in large-signal domain

•Example: non-inverting amplifier

Voltage divider at output:

At input:

Combine these two equations and solve:

à i+=i-=0

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• Interesting limit of non-inverting amplifier when R1=0 and R2=∞:

This is called “buffer” or voltage followerUsed to buffer stages in a system

Assembly of a complete system much easier with adequate buffering of individual stages

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4. Another example: inverting amplifier

Consider:

Then:

And:

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Summary

• Op-amp = device with:– Differential input– Single-ended output– Very large but unstable voltage gain– Very high input resistance– Very low output resistance

• “Open-loop” use of op-amp results in unstable operation• In op-amp use, close loop and trade gain against stability• Analysis of op-amp circuits:

– Assume negligible voltage difference between two inputs– Assume negligible input currents