Lab 5 RS: Difference between revisions
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:<math>R_L=2.5 \Omega</math> | :<math>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 | 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> | :<math>f=\frac{\omega_0}{2\pi} = 27.4\ \mbox{kHz}</math> | ||
| Line 24: | Line 24: | ||
And | And | ||
:<math> | :<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== | ==Construct the LC circuit using a non-polar capacitor== | ||
Revision as of 21:00, 3 February 2011
- 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{ L=33\ \mu H }[/math]
- [math]\displaystyle{ C=1.024\ \mu F }[/math]
- [math]\displaystyle{ R=0.989\ k \Omega }[/math]
- [math]\displaystyle{ 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]
Construct the LC circuit using a non-polar capacitor
Measure the Gain [math]\displaystyle{ \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]\displaystyle{ \omega_{L} }[/math]) (10 pnts)
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
