Lab 5 RS

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LC Resonance circuits

The LC circuit

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{L} }[/math] and [math]\displaystyle{ \mbox{C} }[/math]:

[math]\displaystyle{ \mbox{L}=33\ \mu H }[/math]

[math]\displaystyle{ \mbox{C}=1.024\ \mu F }[/math]

[math]\displaystyle{ \mbox{R}=0.989\ k \Omega }[/math]

[math]\displaystyle{ \mbox{R}_L=2.5\ \Omega }[/math]

So the resonance frequency is [math]\displaystyle{ \omega_0=\frac{1}{\sqrt{33\ \mu H \cdot 1.024\ \mu F}} = 172 \cdot 10^3\ \frac{\mbox{rad}}{\mbox{sec}} }[/math]

[math]\displaystyle{ f=\frac{\omega_0}{2\pi} = 27.4\ \mbox{kHz} }[/math]

And

[math]\displaystyle{ \mbox{Q} = \frac{1}{\mbox{R}} \sqrt{\frac{\mbox{L}}{\mbox{C}}} = 2.27 }[/math]

Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (25 pnts)

Compare the measured and theoretical values of the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) (10 pnts)

Let's the plot the data from table above:

And let's zoom the graph above at resonance frequency:

So the experimentally measured resonance frequency is

[math]\displaystyle{ f = 27.7\ \mbox{kHz} }[/math]

And the predicted value of resonance frequency is

[math]\displaystyle{ f = 27.4\ \mbox{kHz} }[/math]

The error is:

[math]\displaystyle{ Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{27.7 - 27.4}{27.4} \right|= 1.09\ % }[/math]

The error is small so I was lucky

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

Questions

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

Forest_Electronic_Instrumentation_and_Measurement

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