Lab 5 RS
- 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].
- [math]\displaystyle{ \omega_0=\frac{1}{\sqrt{\mbox{LC}}} }[/math]
I choose the following values for [math]\displaystyle{ \mbox{R} }[/math] and [math]\displaystyle{ \mbox{C} }[/math]:
- [math]\displaystyle{ R=aaa\ \Omega }[/math]
- [math]\displaystyle{ C=bbb\ \mu F }[/math]
So the resonance frequency is [math]\displaystyle{ \omega_0=\frac{1}{\sqrt{aaa\ \Omega\ bbb\ \mu F }} = ccc\ \frac{\mbox{rad}}{\mbox{sec}} }[/math]
Or [math]\displaystyle{ f=\frac{\omega_0}{2\pi} = ddd\ \mbox{kHz} }[/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 a series 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? (5 pnts)
- What is the current as [math]\displaystyle{ \nu \rightarrow \infty }[/math]? (5 pnts)