Difference between revisions of "Lab 5 RS"

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:<math>C=1.024\ \mu F</math>
 
:<math>C=1.024\ \mu F</math>
 
:<math>R=0.989\ k \Omega</math>
 
:<math>R=0.989\ k \Omega</math>
:<math>R_L=2.5 \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>
 
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>

Revision as of 21:01, 3 February 2011

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LC Resonance circuits

The LC circuit

TF EIM Lab5 LC.png

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]L=33\ \mu H[/math]
[math]C=1.024\ \mu F[/math]
[math]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

TF EIM Lab5 RLC.png

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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