Post on 30-Jun-2020
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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.
6.002 Spring 2020 Lecture 11 2
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
6.002 Spring 2020 Lecture 11 4
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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6.002 Spring 2020 Lecture 11 5
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.
6.002 Spring 2020 Lecture 11 7
.
6.002 Spring 2020 Lecture 11 8
For positive feedback path:
For negative feedback path:
KCL in capacitor loop:
Also:
KCL here
.
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6.002 Spring 2020 Lecture 11 9
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.
6.002 Spring 2020 Lecture 11 10
If there is perturbation to output of this circuit, output evolves according to:
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6.002 Spring 2020 Lecture 11 11
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!
6.002 Spring 2020 Lecture 11 12
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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6.002 Spring 2020 Lecture 11 13
Problem with comparator around transition if there is noise on top of signal (“chattering”)
Here positive feedback can help
6.002 Spring 2020 Lecture 11 14
Consider following circuit:
How does this work?
vO can have two states:• vO=+VS
• vO=-VS
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6.002 Spring 2020 Lecture 11 15
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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6.002 Spring 2020 Lecture 11 17
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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6.002 Spring 2020 Lecture 11 19
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.