Lab 5 TF EIM: Difference between revisions
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#Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use <math>L</math> = 10 - 100 <math>\mu H</math>. | #Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use <math>L</math> = 10 - 100 <math>\mu H</math>. | ||
#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. ( | #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>. ( | #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) | #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) | ||
Revision as of 20:02, 24 October 2010
LC Resonance circuits
The LC cicuit
- 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].
- 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. (20 pnts)
- Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke [math]\displaystyle{ R_{L} }[/math]. (20 pnts)
- Compare the measured and theoretical values from the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) and the Quality factor [math]\displaystyle{ Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}} }[/math] value for each case; [math]\displaystyle{ W = \frac{1}{2}Li^2 }[/math]. (10 pnts)
Questions
- If r=0, show that [math]\displaystyle{ Q = \frac{1}{\omega_0 R_L C} }[/math]. (10 pnts)
- Show that at resonance[math]\displaystyle{ Z_{AB} \approx Q \omega_0 L }[/math]. (10 pnts)
The LRC cicuit
- Design and construct an LRC circuit.
- Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 pnts)
Questions
- What is the current [math]\displaystyle{ i }[/math] at resonance? (10 pnts)
- What is the current as [math]\displaystyle{ \nu \rightarrow \infty }[/math]? (10 pnts)