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6.002 Spring 2020 Lecture 11 1

6.002 CIRCUITS ANDELECTRONICS

Lecture 11 – Op-amp Stability

March 12, 2020

Contents:1. Op-Amp stability: negative/positive feedback2. Comparator3. Oscillator

Reading Assignment:Agarwal and Lang, Ch. 15 (§§15.7, 15.8)

Handouts:Lecture 22 notes

Announcements:• This Friday’s lab is canceled• Starting after Spring break, we will have recitations instead of Friday lab.• From now on, all lectures/recitations will be online• Quiz 1 is postponed until ~week of March 30th. Logistics for this and other exams TBD• We have added a few extra questions to Pset 5. The due date for Pset 5 has been

moved to April 1st.

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1. Op-amp stability: Positive and negative feedback

What is the difference between these two op-amp configurations?

+

-

+- vOvIN

R1

R2

+

-

v-v+

+-

+- vOvIN

R1

R2

+

-

v-

v+

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Difference: response to perturbations.Consider vIN=0. Expect vO=0.What happens if there is some noise and momentarily vO>0?

Due to feedback path:

Momentarily, voltage difference at input:

Drives output:

Tends to correct perturbation.

+

-

+- vOvIN

R1

R2

+

-

v-v+

vIN=0

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Now look at second configuration:

Due to feedback path:

Momentarily, voltage difference at input:

Drives output:

Tends to enhance perturbation!Since perturbations are unavoidable, this configuration is unstable and op-amp easily saturates.

+-

+- vOvIN

R1

R2

+

-

v-

v+

vIN=0

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To analyze situations like this, need dynamic model for op-amp.

Most op-amps designed to have dynamics dominated by a single time constant.

Simple model:

Time constant of op-amp without feedback is:

+-

v+

v* Av*

R

C

+

-

+

-v+-v-v-

+-

Inside the ubiquitous 741 op amp…

6.002 Spring 2020 Lecture 11 6http://www.righto.com/2015/10/inside-ubiquitous-741-op-amp-circuits.html

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With this circuit, can now analyze stability issues. Consider following circuit with simultaneous positive and negative feedback

Equivalent circuit:

Derive differential equation that describes dynamics.

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.

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For positive feedback path:

For negative feedback path:

KCL in capacitor loop:

Also:

KCL here

.

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All together, differential equation that governs dynamics:

Since A is large, approximately:

Solution to this equation is of form:

tfb is time constant of system with feedback

This can be either positive or negative.

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If there is perturbation to output of this circuit, output evolves according to:

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If there is perturbation to output of this circuit, output evolves according to:

Two cases:– Net negative feedback:àdecaying exponential à system stable

– Net positive feedback:àrising exponential à system unstable

Is positive feedback always a problem?à Many uses for positive feedback!

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3. ComparatorCan use positive feedback to design a comparator circuit.Comparator is to decide if vIN is bigger or smaller than a certain reference voltage vREF.

Comparator characteristics:

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Problem with comparator around transition if there is noise on top of signal (“chattering”)

Here positive feedback can help

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Consider following circuit:

How does this work?

vO can have two states:• vO=+VS

• vO=-VS

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If vO=+VS circuit switches when

If vO=-VS circuit switches when

Hysteretic behavior:

Demo

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If noise not too high, chattering eliminated

d designed to accommodate expected noise level

DemoSchmitt trigger

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4. Charge relaxation oscillatorNow consider this circuit:

Note:

If vC initially zero, vO=+VS, C will charge towards +VS à vC↑

As vC crosses through:

Op-amp switches to vO=-VS

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With vO=-VS, C starts discharging à vC↓

v+ is now:

As vC crosses through v+, op-amp switches again to vO=+VS, and C starts charging again

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Summary

• Op-Amp offset can be important in some circuits.• Negative feedback stabilizes op-amp circuits in the

presence of noise.• Positive feedback leads to op-amp saturation.• Many useful circuits exploit positive feedback.