Lab 5 TF EIM

LC Resonance circuits

The LC cicuit

1. 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].
2. Construct the LC circuit using a non-polar capacitor
3. Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (10 pnts)
4. Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke [math]\displaystyle{ R_{L} }[/math]. (10 pnts)
5. 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

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

The LRC cicuit

Forest_Electronic_Instrumentation_and_Measurement