PHYS-222 Worksheet 12 for Section 25 & 36

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PHYS-222 Worksheet 12 for Section 25 & 36
TA: Yang Li, [email protected], October 31, 2012
Problem: L-R-C circuit as signal filters
L-R-C series circuit (and its variations) has been very useful in modern electronical engineering. Today we’ll
explore their roles as signal filters. Here signal means some output voltage Vo .
• A low-pass filter passes low-frequency signals but attenuates high-frequency signals (Fig. a);
• A high-pass filter passes high-frequency signals but attenuates low-frequency signals (Fig. b);
• A band-pass filter passes signals within certain frequency band(s) but attenuates others (Fig. c);
(a) low-pass filter
(b) high-pass filter
(c) band-pass filter
(1) Determine the filter type when using VR as the output signal. To answer this question, first work out
an expression of VR as a function of ω. Then pick three frequencies and compute the corresponding
signal amplitude VR (ω). Compare the values with Fig. (a-c), you may be able to tell the filter type.
The below table may help you.
(2) Determine the filter type when using VL as the output signal.
(3) Determine the filter type when using VC as the output signal.
(4) The cutoff frequency ωc is defined as the one at which the signal amplitude drops to √12 ' 0.707 of the
original amplitude. In each case, compute OR read out ωc (The y-axeses start from 0.707 V).
Vo
VR
VL
VC
expression Vo (ω)
√ 2 VR
2
R +(ωL−1/ωC)
√ 2 V ωL
R +(ωL−1/ωC)2
V /ωC
√
R2 +(ωL−1/ωC)2
ω1 /rad · Hz
103
Vo (ω1 )/V
0.05
ω2 /rad · Hz
5 × 104
Vo (ω2 )/V
0.86
ω3 /rad · Hz
106
Vo (ω3 )/V
0.05
filter
band-pass
ωc /rad · Hz
15308, 65324
103
0.001
5 × 104
0.86
106
0.999
high-pass
35781
103
0.999
5 × 104
0.34
106
0.001
low-pass
27947
1
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