Revision as of 04:32, 2 February 2011

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], R = 1k [math]\displaystyle{ \Omega }[/math] (Note [math]\displaystyle{ R_L }[/math] is the inherent resistance of the inductor).
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 when r=0. (20 pnts)
Measure the Gain when an external resistance (r) approximately equals to the inherent resistance of the rf choke [math]\displaystyle{ r \approx R_{L} }[/math]. (20 pnts)
Compare the measured and theoretical values of the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) (10 pnts)

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)

Design and construct a series LRC circuit.
Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 pnts)

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

@@ Line 2: / Line 2: @@
 =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>, R = 1k <math>\Omega</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>, R = 1k <math>\Omega</math> (Note <math>R_L</math> is the inherent resistance of the inductor).
 #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 when r=0. (20 pnts)