Lab 5 RS

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LC Resonance circuits

The LC cicuit

1. Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use $L$ = 10 - 100 $\mu H$.
2. Construct the LC circuit using a non-polar capacitor
3. Measure the Gain $\equiv \frac{V_{out}}{V_{in}}$ as a function of frequency. (20 pnts)
4. Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke $R_{L}$. (20 pnts)
5. Compare the measured and theoretical values from the resonance frequency ($\omega_{L}$) and the Quality factor $Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}}$ value for each case; $W = \frac{1}{2}LI^2$. (10 pnts)

Questions

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

The LRC cicuit

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

Questions

1. What is the current $I$ at resonance? (5 pnts)
2. What is the current as $\nu \rightarrow \infty$? (5 pnts)

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