Lab 5 RS

Go Back to All Lab Reports

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 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

Question. What is the bandwidth of the above circuit? (5 pnts)

From the plot above we have [math]\displaystyle{ \left(\frac{V_{out}}{_{Vin}} \right)_{max} = 0.0138 }[/math]

The bandwidth defined as the width from [math]\displaystyle{ \omega_1 }[/math] to [math]\displaystyle{ \omega_2 }[/math] where the amplitude of signal drop down to [math]\displaystyle{ \frac{1}{\sqrt{2}} }[/math].

At this point [math]\displaystyle{ \left(\frac{V_{out}}{V_{in}} \right) = \frac{0.0138}{\sqrt{2}} = 0.00976 }[/math]. Let's plot this line and calculate the bandwidth.

So the bandwidth of the above circuit is

[math]\displaystyle{ \delta f = 37\ \mbox{kHz} }[/math]

The RLC cicuit

Measure and Graph the Gain as a function of the oscillating input voltage frequency. (25 pnts)

In the table below are my measurements for voltage gain and phase shift:

And let's graph the gain as a function of the input voltage frequency:

Measure and Graph the Phase Shift as a function of the oscillating input voltage frequency. (25 pnts)

My phase shift measurements presented in the table above. And let's graph the phase shift as a function of the input voltage frequency:

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)

Forest_Electronic_Instrumentation_and_Measurement

Go Back to All Lab Reports