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 [math]\displaystyle{ L }[/math] = 10 - 100 [math]\displaystyle{ \mu H }[/math], R = 1k

[math]\displaystyle{ \Omega }[/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]

Let's estimate:

1. Construct the LC circuit using a non-polar capacitor
2. Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (25 pnts)
3. Compare the measured and theoretical values of the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) (10 pnts)

Questions

1. Is there a value of [math]\displaystyle{ R }[/math] in which [math]\displaystyle{ V_{out} \approx V_{in} }[/math] at resonance. What is the value?(5 pnts)

The RLC cicuit

1. Design and construct a series LRC circuit.
2. Measure and Graph the Gain as a function of the oscillating input voltage frequency. (25 pnts)
3. Measure and Graph the Phase Shift as a function of the oscillating input voltage frequency. (25 pnts)

Questions

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

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]

Let's estimate:

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

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

Forest_Electronic_Instrumentation_and_Measurement

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