EECS 314
Winter 2008
Homework set 6
Student’s name ___________________________
Discussion section # _______
(Last, First, write legibly, use ink)
(use ink)
Instructor is
not responsible
for grading and entering scores for HW papers lacking clear
information in the required fields above
© 2008 Alexander Ganago
Page 1 of 2
Scores for the HW set:
Problem
1
2
3
4
5
6
7
Total
Score
Problem 1
Op Amp Integrator circuit
The Big Picture
The circuit shown on this diagram is an integrator: its output voltage is
V
OUT
(
t
)
=
K
"
V
IN
(
t
)
"
dt
#
Here the constant
K
does not
depend on time and voltage, but it depends on
R
and
C
in the circuit.
Note that, in order to match the units on the both
sides of the above equation, the constant
K
must
have units of
(sec)
1
.
Also note that there is a typo on page 27 of Chapter 13 in
Making sense of EE.
One problem with the integrator is that its output signals saturates if it reaches the supply
voltage (on this diagram, –10 V or +10 V). To avoid saturation, the capacitor must be
discharged (shortcircuited with a closed switch, which is usually a MOSFET).
The Assignment
Part 1 (10 points)
For the circuit shown on the diagram, derive the equation for the coefficient
K
(be
careful with its sign!).
Your answer:
K
= _________________
For the circuit shown on the diagram, assume
R
= 25 k
Ω
,
C
= 4 nF,
and calculate
the numerical value of
K
(be careful with its sign!).
Your answer:
K
= _________________
Part
1
2
3
Total
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View Full DocumentEECS 314
Winter 2008
Homework set 6
Student’s name ___________________________
Discussion section # _______
(Last, First, write legibly, use ink)
(use ink)
Instructor is
not responsible
for grading and entering scores for HW papers lacking clear
information in the required fields above
© 2008 Alexander Ganago
Page 2 of 2
Problem 1, continued
Part 2 (15 points)
Suppose that the input
signal is a constant equal to
+20 mV,
and that the
output voltage in the circuit
above (with component
values as in
Part 1
) was set
to zero at time
t
= 0
.
Obtain the equation for the
output voltage as function
of time.
Sketch the output voltage
as function of time on the
grid.
Carefully label the axes and
indicate the slope of the
linear function.
Since the integral of a
constant is a linear function, the output voltage would eventually outgrow the source
voltage and saturate (clip). Determine at what time
t
s
the output voltage saturates, and
whether it saturates at
+10 V
or at
–10 V.
Your answer:
t
s
= _________________; saturation occurs at ______________
Part 3 (15 points)
Suppose you need to change the circuit so that the saturation occurs at the later time
10
⋅
t
s
[assume that the input is still equal to
+20 mV
, and
V
OUT
( t = 0 )
= 0
].
There are 2 ways of changing the circuit to achieve this goal:
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 Winter '07
 Ganago
 Operational Amplifier, Alexander Ganago, hw papers, clear information, ___________________________ Discussion section

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