Lab 4: AC Circuits (II)
Transcript of Lab 4: AC Circuits (II)
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Lab 4: AC Circuits (II)
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REVIEW
AC analysis of circuits using complex numbers
Assumptions:
i) Steady-state
ii) Sinusoidal waveforms:
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C
L
90o phase-shift in polar form:
Ohm's Law for L and C:Impedance (Z) Measured in ohms
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R
C
Vin Vout
AC circuit: High-pass
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R
C
Vin
Vout
AC circuit: High-pass
R = 1 kΩ, C = 10 nF
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HW Bode1905—1982
Bell Labs
The Bode Plot for |Vout/Vin|
10 100 1k 10k 100k 1M
Plot frequency on a log10 scale
Plot amplitude on a dB scale
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In honor ofAlexander Graham Bell
The Decibel: A Ratio
POWER FIELD
RATIO
1
10
100
2
0.01
0 dB
10 dB
20 dB
3 dB
−20 dB
0 dB
20 dB
40 dB
6 dB
−40 dB
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R
C
Vin
Vout
AC circuit: High-pass
R = 1 kΩ, C = 10 nF
Bode Plot: AMPLITUDE RESPONSE
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Inductor-capacitor in AC circuit: Resonance
C
R
L
Parallel LC circuit
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Inductor-capacitor in AC circuit: Resonance
C
R
L
Parallel LC circuit
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Inductor-capacitor in AC circuit: Resonance
C
Resonance at:
R
L
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Inductor-capacitor in AC circuit: Resonance
C
R
L
C = 100 nFL = 100 uHfres = 50.3 kHz
R = 100Ω, 1 kΩ, 5kΩ
AMPLITUDE RESPONSE
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Inductor-capacitor in AC circuit: Resonance
C
R
L
C = 100 nFL = 100 uHfres = 50.3 kHz
R = 100Ω, 1 kΩ, 5kΩ
PHASE RESPONSE
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Q-factor: Sharpness of Resonance
Sharper resonance → Higher Q
∆ f = frequency range between the – 3 dB points
– 3 db ≈ 0.707 of the peak
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Q-factor: Sharpness of Resonance
Example RLC circuit:
R = 100 Ω, 1 kΩ, 5 kΩ
Q = 3.1, 31, 158
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Resonance in series LC circuit
C
R
L
Series LC circuit
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Resonance in series LC circuit
C
R
L
Series LC circuit
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Resonance in series LC circuit
C = 10 nFL = 10 uHfres = 503 kHz
R = 5 Ω, 10 Ω, 20 ΩQ = 6.3, 3.1, 1.6
AMPLITUDE RESPONSEC
R
L
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Resonance in series LC circuit
C = 10 nFL = 10 uHfres = 503 kHz
PHASE RESPONSEC
R
L