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Escuti/Brickley
Fall 2008
ECE200 – Fall 2008 – Homework 9
Operational Amplifiers, Filters
Page 1 of 10
PROBLEM 1
The circuit shown below is used to divide an input signal between the left and right channels of a
stereo system.
a)
Derive equations for the signals applied to the left and right channel audio speakers as a
function of x.
The two resistors,
( )
Ω
k
x
10
and
( )( )
Ω
−
k
x
10
1
represent a
potentiometer with 0 < x < 1. (10 pts)
b)
If
() ( ) ( )
t
mV
t
v
in
1000
2
cos
100
π
=
is applied as the test signal and x = 0.2, find the power
delivered to the left and right channels. (5 pts)
Solution:
We note that the voltage at Node A is identical to the input voltage since the first stage is a unity
gain amplifier (voltage follower).
It serves as a buffer between the input source and the rest of the
circuit.
Inspecting the circuit carefully, we note that the signal at node A is passed through a voltage divider
(on each channel) before it is applied to the noninverting input of either opamp.
Therefore, by voltage division,
A
B
v
K
x
K
K
x
v
×
Ω
+
Ω
Ω
=
)
10
(
1
)
10
(
Since
)
(
t
v
v
in
A
=
,
()
)
(
10
1
10
)
(
10
1
10
t
v
x
x
t
v
x
K
K
x
K
v
in
in
B
⎥
⎦
⎤
⎢
⎣
⎡
+
=
⎥
⎦
⎤
⎢
⎣
⎡
+
=
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Fall 2008
ECE200 – Fall 2008 – Homework 9
Operational Amplifiers, Filters
Page 2 of 10
Similarly,
()
(
)
(
)
A
C
v
K
x
K
K
x
v
×
Ω
−
+
Ω
Ω
−
=
10
1
1
10
1
)
(
1
10
1
1
10
)
(
1
10
1
1
10
t
v
x
x
t
v
x
K
K
x
K
v
in
in
C
⎥
⎦
⎤
⎢
⎣
⎡
−
+
−
=
⎥
⎦
⎤
⎢
⎣
⎡
−
+
−
=
The two opamps form two independent noninverting amplifier stages with the same voltage gain,
11
1
10
1
1
=
+
=
+
=
K
K
R
R
A
n
f
v
This yields the following output voltages:
)
(
11
10
1
10
t
v
x
x
v
in
LEFT
×
×
⎥
⎦
⎤
⎢
⎣
⎡
+
=
)
(
11
)
1
(
10
1
)
1
(
10
t
v
x
x
v
in
RIGHT
×
×
⎥
⎦
⎤
⎢
⎣
⎡
−
+
−
=
b)
(
)
(
)
t
V
t
mV
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This note was uploaded on 03/10/2009 for the course ECE 200 taught by Professor Escuti during the Fall '07 term at N.C. State.
 Fall '07
 Escuti
 Amplifier, Operational Amplifier

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