Lab 5 RS

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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]\displaystyle{ L }[/math] = 10 - 100 [math]\displaystyle{ \mu H }[/math], R = 1k [math]\displaystyle{ \Omega }[/math]

[math]\displaystyle{ \omega_0=\frac{1}{\sqrt{\mbox{LC}}} }[/math]

I choose the following values for [math]\displaystyle{ \mbox{L} }[/math] and [math]\displaystyle{ \mbox{C} }[/math]:

[math]\displaystyle{ \mbox{L}=33\ \mu H }[/math]

[math]\displaystyle{ \mbox{C}=1.024\ \mu F }[/math]

[math]\displaystyle{ \mbox{R}=0.989\ k \Omega }[/math]

[math]\displaystyle{ \mbox{R}_L=2.5\ \Omega }[/math]

So the resonance frequency is [math]\displaystyle{ \omega_0=\frac{1}{\sqrt{33\ \mu H \cdot 1.024\ \mu F}} = 172 \cdot 10^3\ \frac{\mbox{rad}}{\mbox{sec}} }[/math]

[math]\displaystyle{ f=\frac{\omega_0}{2\pi} = 27.4\ \mbox{kHz} }[/math]

And

[math]\displaystyle{ \mbox{Q} = \frac{1}{\mbox{R}} \sqrt{\frac{\mbox{L}}{\mbox{C}}} = 2.27 }[/math]

Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (25 pnts)

Table1. Voltage gain vs. frequency for parallel LC circut

[math]\displaystyle{ \nu\ [\mbox{kHz}] }[/math]	[math]\displaystyle{ V_{in}\ [V] }[/math]	[math]\displaystyle{ V_{out}\ [V] }[/math]

|0.867 22.3 0.096 |2.460 22.2 0.098 |3.385 22.2 0.101 |5.197 22.2 0.106 |6.645 22.1 0.112 |7.674 22.1 0.115 |8.387 22.1 0.117 |10.14 22.0 0.125 |11.15 22.0 0.133 |12.99 22.0 0.145 |15.17 22.0 0.161 |16.55 21.9 0.173 |17.52 22.0 0.185 |18.90 22.0 0.201 |20.30 21.9 0.219 |21.61 22.0 0.238 |22.10 22.0 0.244 |22.56 22.0 0.251 |23.19 21.9 0.259 |24.07 21.9 0.271 |24.59 21.9 0.278 |25.14 21.9 0.284 |25.86 21.9 0.292 |26.18 21.9 0.295 |26.83 21.9 0.299 |27.02 22.0 0.301 |27.18 21.9 0.300 |27.36 21.9 0.302 |27.43 21.9 0.300 |27.54 21.9 0.301 |27.62 21.9 0.301 |27.80 21.9 0.300 |27.94 21.9 0.302 |28.08 21.9 0.301 |28.25 21.9 0.301 |28.52 21.9 0.299 |28.77 21.9 0.299 |29.00 21.9 0.297 |29.65 21.9 0.292 |30.00 21.9 0.288 |30.62 21.9 0.282 |31.11 21.9 0.277 |32.24 21.9 0.263 |33.05 21.9 0.255 |34.14 21.9 0.243 |35.32 21.9 0.230 |36.43 21.9 0.220 |37.77 21.9 0.208 |39.50 21.9 0.194 |41.63 21.9 0.180 |43.33 21.9 0.171 |44.11 21.9 0.170 |45.12 21.9 0.164 |46.28 21.9 0.161 |48.11 21.9 0.153 |49.66 21.9 0.148 |50.93 21.9 0.146 |53.16 21.9 0.140 |56.67 21.8 0.131 |59.40 21.8 0.129 |63.17 21.9 0.123 |67.96 21.8 0.117 |72.95 21.8 0.113 |77.85 21.8 0.109 |83.20 21.8 0.104 |88.55 21.8 0.100 |95.07 21.8 0.096 |116.49 21.9 0.090 |}

Questions

1.Is there a value of [math]\displaystyle{ R }[/math] in which [math]\displaystyle{ V_{out} \approx V_{in} }[/math] at resonance. What is the value?(5 pnts)

The RLC cicuit

Questions

What is the current as [math]\displaystyle{ \nu \rightarrow \infty }[/math]? (5 pnts)

Forest_Electronic_Instrumentation_and_Measurement

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