2260
F 09
HOMEWORK #3 probs 4 and 5 solution
E
X
:
v
i
+
–
+
–
v
o
L
=
25
μ
H
C
=
250 nF
R
1
=
2.5
Ω
R
2
=
5
Ω
For the bandreject filter shown above, determine the transfer function V
o
/V
i
.
Hint:
Move R
1
to the right of L and C, place R
1
vertically, and suppose the output were
tapped from the point between C and R
1
.
Then use a vdivider.
For the bandreject filter above, calculate the following quantities:
a)
ω
o
b)
ω
C1
and
ω
C2
c)
β
d)
Q
S
OL
'
N
:
a) Although we could calculate
ω
o
without the transfer function, we derive
the transfer function first in order to understand the nature of the circuit.
As advised in the hint, we exchange the positions of the
R
1
and the parallel
LC
so that the
R
's are next to each other.
+
V
1
R
2
j
ω
L
+
–
V
i
–
V
o
+
–
R
1
1
j
ω
C
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Putting the
R
's together leaves the transfer function unaltered and allows
us to consider an output signal taken across both
R
's.
If we consider the
transfer function from
V
i
to
V
1
, we have a simple
RLC
filter.
We use a
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 Spring '12
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