Physics 3330 Prelab 5 solutions
1 (A & B).
The circuit of interest is shown in Figure
1
Figure 1: Active band pass filter.
The design goals for the circuit are a resonant frequency of 16 kHz, a closed loop gain of

1,
and a
Q
of 10.
Note that the resonant frequency is
f
0
,
not
ω
0
which is the resonant angular
frequency which is measured in rad/s rather than Hz. Also, the closed loop gain is
G
which is
the gain of the circuit as a whole, namely
V
out
/V
in
. From the theory section we therefore know:
f
0
=
1
2
π
√
LC
= 16 kHz
(1)
Q
=
1
r
L
C
=
Z
0
r
= 10
(2)
G
(
ω
peak
)
=

Q
Z
0
R
=

1
(3)
(4)
We will use the 10 mH inductor so
L
= 10 mH and so we can solve for the other values:
C
=
1
L
(2
πf
0
)
2
=
1
0
.
01 H(2
π
(16
×
10
3
Hz))
2
= 9
.
9 nF = 0
.
01
μ
F
(5)
Z
0
=
r
L
C
=
r
0
.
01 H
1
×
10

8
F
= 1000 Ω
(6)
r
=
Z
0
Q
=
1000 Ω
10
= 100 Ω
(7)
R
=
QZ
0

G
(
ω
peak
)

=
10
·
1000 Ω
1
= 10
k
Ω
(8)
(9)
The final part of part B also asks for the two 3 dB frequencies. While it is possible to solve the
full gain equation for these frequencies, it is simpler to use
Q
=
f/
Δ
f
which gives Δ
f
=
f/Q
=
16 kHz
/
10 = 1
.
6 kHz. Since Δ
f
=
f
+

f

,
f
±
=
f
±
Δ
f
so
f

=
f

Δ
f/
2 = 16 kHz

0
.
8 kHz =
15
.
2 kHz and
f
+
=
f
+ Δ
f/
2 = 16 kHz

0
.
8 kHz = 16
.
8 kHz.
1
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2.
We now add positive feedback (output connected to the
non
inverting input) as shown in
Fig.
2
Figure 2: Active band pass filter plus positive feedback to make an LC oscillator.
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 '09
 Physics, Frequency, Positive feedback, Vout, Schmitt trigger

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