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| | ==Construct the LC circuit using a non-polar capacitor== | | ==Construct the LC circuit using a non-polar capacitor== |
| | ==Measure the Gain <math>\equiv \frac{V_{out}}{V_{in}}</math> as a function of frequency. (25 pnts)== | | ==Measure the Gain <math>\equiv \frac{V_{out}}{V_{in}}</math> as a function of frequency. (25 pnts)== |
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| − | {| border="1" cellspacing="0" style="text-align: center; width: 500px; height: 500px;"
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| − | |+ '''Table1. Voltage gain vs. frequency for parallel LC circut'''
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| − | |-
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| − | ! scope="col" width="50" | <math>\nu\ [\mbox{kHz}]</math>
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| − | ! scope="col" width="50" | <math>V_{in}\ [V]</math>
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| − | ! scope="col" width="50" | <math>V_{out}\ [V]</math>
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| − | |}
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| − | |0.867 22.3 0.096
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| − | |2.460 22.2 0.098
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| − | |3.385 22.2 0.101
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| − | |5.197 22.2 0.106
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| − | |6.645 22.1 0.112
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| − | |7.674 22.1 0.115
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| − | |8.387 22.1 0.117
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| − | |10.14 22.0 0.125
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| − | |11.15 22.0 0.133
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| − | |12.99 22.0 0.145
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| − | |15.17 22.0 0.161
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| − | |16.55 21.9 0.173
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| − | |17.52 22.0 0.185
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| − | |18.90 22.0 0.201
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| − | |20.30 21.9 0.219
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| − | |21.61 22.0 0.238
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| − | |22.10 22.0 0.244
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| − | |22.56 22.0 0.251
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| − | |23.19 21.9 0.259
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| − | |24.07 21.9 0.271
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| − | |24.59 21.9 0.278
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| − | |25.14 21.9 0.284
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| − | |25.86 21.9 0.292
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| − | |26.18 21.9 0.295
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| − | |26.83 21.9 0.299
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| − | |27.02 22.0 0.301
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| − | |27.18 21.9 0.300
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| − | |27.36 21.9 0.302
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| − | |27.43 21.9 0.300
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| − | |27.54 21.9 0.301
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| − | |27.62 21.9 0.301
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| − | |27.80 21.9 0.300
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| − | |27.94 21.9 0.302
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| − | |28.08 21.9 0.301
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| − | |28.25 21.9 0.301
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| − | |28.52 21.9 0.299
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| − | |28.77 21.9 0.299
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| − | |29.00 21.9 0.297
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| − | |29.65 21.9 0.292
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| − | |30.00 21.9 0.288
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| − | |30.62 21.9 0.282
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| − | |31.11 21.9 0.277
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| − | |32.24 21.9 0.263
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| − | |33.05 21.9 0.255
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| − | |34.14 21.9 0.243
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| − | |35.32 21.9 0.230
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| − | |36.43 21.9 0.220
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| − | |37.77 21.9 0.208
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| − | |39.50 21.9 0.194
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| − | |41.63 21.9 0.180
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| − | |43.33 21.9 0.171
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| − | |44.11 21.9 0.170
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| − | |45.12 21.9 0.164
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| − | |46.28 21.9 0.161
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| − | |48.11 21.9 0.153
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| − | |49.66 21.9 0.148
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| − | |50.93 21.9 0.146
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| − | |53.16 21.9 0.140
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| − | |56.67 21.8 0.131
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| − | |59.40 21.8 0.129
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| − | |63.17 21.9 0.123
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| − | |67.96 21.8 0.117
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| − | |72.95 21.8 0.113
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| − | |77.85 21.8 0.109
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| − | |83.20 21.8 0.104
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| − | |88.55 21.8 0.100
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| − | |95.07 21.8 0.096
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| − | |116.49 21.9 0.090
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| − | |}
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| | ==Compare the measured and theoretical values of the resonance frequency (<math>\omega_{L}</math>) (10 pnts)== | | ==Compare the measured and theoretical values of the resonance frequency (<math>\omega_{L}</math>) (10 pnts)== |
Revision as of 21:18, 3 February 2011
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- LC Resonance circuits
The LC circuit
Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]L[/math] = 10 - 100 [math]\mu H[/math], R = 1k [math]\Omega[/math]
- [math]\omega_0=\frac{1}{\sqrt{\mbox{LC}}}[/math]
I choose the following values for [math]\mbox{L}[/math] and [math]\mbox{C}[/math]:
- [math]\mbox{L}=33\ \mu H[/math]
- [math]\mbox{C}=1.024\ \mu F[/math]
- [math]\mbox{R}=0.989\ k \Omega[/math]
- [math]\mbox{R}_L=2.5\ \Omega[/math]
So the resonance frequency is [math]\omega_0=\frac{1}{\sqrt{33\ \mu H \cdot 1.024\ \mu F}} = 172 \cdot 10^3\ \frac{\mbox{rad}}{\mbox{sec}}[/math]
- [math]f=\frac{\omega_0}{2\pi} = 27.4\ \mbox{kHz}[/math]
And
- [math]\mbox{Q} = \frac{1}{\mbox{R}} \sqrt{\frac{\mbox{L}}{\mbox{C}}} = 2.27[/math]
Construct the LC circuit using a non-polar capacitor
Measure the Gain [math]\equiv \frac{V_{out}}{V_{in}}[/math] as a function of frequency. (25 pnts)
Compare the measured and theoretical values of the resonance frequency ([math]\omega_{L}[/math]) (10 pnts)
Questions
1.Is there a value of [math]R[/math] in which [math]V_{out} \approx V_{in}[/math] at resonance. What is the value?(5 pnts)
The RLC cicuit
Design and construct a series LRC circuit
Measure and Graph the Gain as a function of the oscillating input voltage frequency. (25 pnts)
Measure and Graph the Phase Shift as a function of the oscillating input voltage frequency. (25 pnts)
Questions
What is the current [math]I[/math] at resonance? (5 pnts)
What is the current as [math]\nu \rightarrow \infty[/math]? (5 pnts)
Forest_Electronic_Instrumentation_and_Measurement
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