Sections 94 and 95: Passive Filters
Problem 9.20
The element values of a series RLC bandpass filter are
R
=
5
Ω
,
L
=
20 mH, and
C
=
0
.
5
μ
F.
(a)
Determine
ϖ
0
,
Q
,
B
,
ϖ
c
1
, and
ϖ
c
2
.
(b)
Is it possible to double the magnitude of
Q
by changing the values of
L
and/or
C
, while keeping
ϖ
0
and
R
unchanged? If yes, propose such values,
and if no, why not?
Solution:
(a)
ϖ
0
=
1
√
LC
=
1
√
20
×
10
−
3
×
0
.
5
×
10
−
6
=
10
4
rad/s
,
Q
=
ϖ
0
L
R
=
10
4
×
20
×
10
−
3
5
=
40
,
B
=
ϖ
0
Q
=
10
4
40
=
250 rad/s
,
ϖ
c
1
=
ϖ
0
−
B
2
=
10
4
−
250
2
=
9875 rad/s
,
ϖ
c
2
=
ϖ
0
+
B
2
=
10
4
+
250
2
=
10125 rad/s
.
(b)
Q
=
ϖ
0
L
R
=
⇒
ϖ
0
R
=
Q
L
.
Since
ϖ
0
and
R
are constants, doubling
Q
requires that
L
be doubled, but to keep
ϖ
0
constant would require
C
to be reduced to one half. Thus, the new set of element
values are:
R
=
5
Ω
,
L
=
40 mH
,
and
C
=
0
.
25
μ
F
.
The corresponding values of
ϖ
0
and
Q
are:
ϖ
0
=
10
4
rad/s (unchanged)
Q
=
ϖ
0
L
R
=
80
.
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Problem 9.24
Design a parallel RLC filter with
f
0
=
4 kHz,
Q
=
100, and an input
impedance of 25 k
Ω
at resonance.
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 Spring '10
 Bedford
 LC circuit, jω, C R Vo, Generate spectral plots

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