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;LC Resonance circuits
=The LC cicuit=
[[File:TF_EIM_Lab5_LC.png| 200 px]]
==Design a '''parallel''' LC resonant circuit with a resonant frequency between 50-200 kHz.  use <math>L</math> = 10 - 100 <math>\mu H</math>.==

:<math>\omega_0=\frac{1}{\sqrt{\mbox{LC}}}</math>

I choose the following values for <math>\mbox{R}</math> and <math>\mbox{C}</math>:

:<math>R=aaa\ \Omega</math>
:<math>C=bbb\ \mu F</math>

So the resonance frequency is <math>\omega_0=\frac{1}{\sqrt{aaa\ \Omega\ bbb\ \mu F }} = ccc\ \frac{\mbox{rad}}{\mbox{sec}}</math>

Or <math>f=\frac{\omega_0}{2\pi} = ddd\ \mbox{kHz}</math>


Let's estimate:

[[File:L4 LC.png | 400 px]]

==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. (20 pnts)==
==Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke <math>R_{L}</math>. (20 pnts)==
==Compare the measured and theoretical values from the resonance frequency (<math>\omega_{L}</math>) and the Quality factor <math>Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}}</math> value for each case; <math>W = \frac{1}{2}LI^2</math>. (10 pnts)==

==Questions==

#If r=0, show that <math>Q = \frac{1}{\omega_0 R_L C}</math>. (10 pnts)
#Show that at resonance<math> Z_{AB} \approx Q \omega_0 L</math>. (10 pnts)

=The LRC cicuit=
[[File:TF_EIM_Lab5_RLC.png| 200 px]]
#Design and construct a '''series''' LRC circuit.
#Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 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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