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# Review - Op-amp circuit analysis Notes | EduRev

## : Review - Op-amp circuit analysis Notes | EduRev

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Lecture 11, Slide 1 EECS40, Fall 2003 Prof. King
Lecture #11
ANNOUNCEMENTS
• Homework Assignment #4 will be posted today
• Midterm #1: Monday Sept. 29
th
(11:10AM-12:00PM)
– closed book; one page (8.5”x11”) of notes & calculator allowed
– covers Chapters 1-5 in textbook (HW#1-4)
• Midterm Review Session: Friday 9/26 7-9PM, 277 Cory
• Extra office hours:
– Steve: 9/26 from 12-2PM
– Farhana: 9/27 from 1-3PM, 9/28 from 9-11AM
• Practice problems and old exam are posted online
OUTLINE
– Review: op amp circuit analysis
– The capacitor (Chapter 6.2 in text)
Lecture 11, Slide 2 EECS40, Fall 2003 Prof. King
Review: Op Amp Circuit Analysis
Procedure:
1. Assume that the op amp is ideal
a) Apply KCL at (+) and (–) terminals, noting i
p
= 0 & i
n
= 0
b) Note that v
n
= v
p
c) Write an expression for v
o
2. Calculate v
o
3. Check: Is the op-amp operating in its linear region?
If V
–
= v
o
= V
+
,
,
then the assumption is valid.
If calculated v
o
> V
+
, then v
o
is saturated at V
+
If calculated v
o
< V
–
, then v
o
is saturated at V
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
Page 2

1
Lecture 11, Slide 1 EECS40, Fall 2003 Prof. King
Lecture #11
ANNOUNCEMENTS
• Homework Assignment #4 will be posted today
• Midterm #1: Monday Sept. 29
th
(11:10AM-12:00PM)
– closed book; one page (8.5”x11”) of notes & calculator allowed
– covers Chapters 1-5 in textbook (HW#1-4)
• Midterm Review Session: Friday 9/26 7-9PM, 277 Cory
• Extra office hours:
– Steve: 9/26 from 12-2PM
– Farhana: 9/27 from 1-3PM, 9/28 from 9-11AM
• Practice problems and old exam are posted online
OUTLINE
– Review: op amp circuit analysis
– The capacitor (Chapter 6.2 in text)
Lecture 11, Slide 2 EECS40, Fall 2003 Prof. King
Review: Op Amp Circuit Analysis
Procedure:
1. Assume that the op amp is ideal
a) Apply KCL at (+) and (–) terminals, noting i
p
= 0 & i
n
= 0
b) Note that v
n
= v
p
c) Write an expression for v
o
2. Calculate v
o
3. Check: Is the op-amp operating in its linear region?
If V
–
= v
o
= V
+
,
,
then the assumption is valid.
If calculated v
o
> V
+
, then v
o
is saturated at V
+
If calculated v
o
< V
–
, then v
o
is saturated at V
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
2
Lecture 11, Slide 3 EECS40, Fall 2003 Prof. King
Op Amp Circuit Analysis Example
Consider the following circuit:
Assume the op amp is ideal.
a) Calculate v
o
if v
s
= 100 mV
b) What is the voltage gain v
o
/v
s
of this amplifier?
c) Specify the range of values of v
s
for which the
op amp operates in a linear mode
+
–
+
v
o
–
–
+
v
s
i
n
+
v
p
–
+
v
n
–
10 k? 1 k? 10 V
–10 V
Lecture 11, Slide 4 EECS40, Fall 2003 Prof. King
Op Amp Circuit Analysis Example cont’d.
What if the op amp is not ideal?
R
i
= 10 k? R
o
= 1 k? A = 10
3
–
+
v
s
10 k? 1 k? +
v
o
–
+
–
R
o
A(v
p
–v
n
)
R
i
+
v
p
–
+
v
n
–
Page 3

1
Lecture 11, Slide 1 EECS40, Fall 2003 Prof. King
Lecture #11
ANNOUNCEMENTS
• Homework Assignment #4 will be posted today
• Midterm #1: Monday Sept. 29
th
(11:10AM-12:00PM)
– closed book; one page (8.5”x11”) of notes & calculator allowed
– covers Chapters 1-5 in textbook (HW#1-4)
• Midterm Review Session: Friday 9/26 7-9PM, 277 Cory
• Extra office hours:
– Steve: 9/26 from 12-2PM
– Farhana: 9/27 from 1-3PM, 9/28 from 9-11AM
• Practice problems and old exam are posted online
OUTLINE
– Review: op amp circuit analysis
– The capacitor (Chapter 6.2 in text)
Lecture 11, Slide 2 EECS40, Fall 2003 Prof. King
Review: Op Amp Circuit Analysis
Procedure:
1. Assume that the op amp is ideal
a) Apply KCL at (+) and (–) terminals, noting i
p
= 0 & i
n
= 0
b) Note that v
n
= v
p
c) Write an expression for v
o
2. Calculate v
o
3. Check: Is the op-amp operating in its linear region?
If V
–
= v
o
= V
+
,
,
then the assumption is valid.
If calculated v
o
> V
+
, then v
o
is saturated at V
+
If calculated v
o
< V
–
, then v
o
is saturated at V
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
+
–
+
v
n
–
+
v
p
–
i
p
i
n
i
o
+
v
o
–
2
Lecture 11, Slide 3 EECS40, Fall 2003 Prof. King
Op Amp Circuit Analysis Example
Consider the following circuit:
Assume the op amp is ideal.
a) Calculate v
o
if v
s
= 100 mV
b) What is the voltage gain v
o
/v
s
of this amplifier?
c) Specify the range of values of v
s
for which the
op amp operates in a linear mode
+
–
+
v
o
–
–
+
v
s
i
n
+
v
p
–
+
v
n
–
10 k? 1 k? 10 V
–10 V
Lecture 11, Slide 4 EECS40, Fall 2003 Prof. King
Op Amp Circuit Analysis Example cont’d.
What if the op amp is not ideal?
R
i
= 10 k? R
o
= 1 k? A = 10
3
–
+
v
s
10 k? 1 k? +
v
o
–
+
–
R
o
A(v
p
–v
n
)
R
i
+
v
p
–
+
v
n
–
3
Lecture 11, Slide 5 EECS40, Fall 2003 Prof. King
Re-draw the circuit
& analyze:
KCL @ node a:
KCL @ node b:
–
+
v
s
1 k? +
v
n
–
+
–
10
3
(–v
n
)
1 k? 10 k? 10 k? +
v
o
–
10 87 . 9 < ? -
s
o
v
v
ab
Lecture 11, Slide 6 EECS40, Fall 2003 Prof. King
L
KCL @ node b:
• For an ideal op amp (R
o
= 0 ? ), v
o
does not depend on
the “load”. However, for a realistic op amp, it does.
–
+
v
s
1 k? +
v
n
–
+
–
10
3
(–v
n
)
1 k? 10 k? 10 k? +
v
o
–
87 . 9 75 . 9 < ? -
s
o
v
v
ab
R
L
=1 k?
```
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