Difference between revisions of "Lab 5 RS"

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;LC Resonance circuits
 
;LC Resonance circuits
=The LC cicuit=
+
=The LC circuit=
 +
 
 
[[File:TF_EIM_Lab5_LC.png| 200 px]]
 
[[File:TF_EIM_Lab5_LC.png| 200 px]]
#Design a '''parallel''' LC resonant circuit with a resonant frequency between 50-200 kHz.  use <math>L</math> = 10 - 100 <math>\mu H</math>.
 
#Construct the LC circuit using a non-polar capacitor
 
#Measure the Gain <math>\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>R_{L}</math>. (20 pnts)
 
#Compare the measured and theoretical values from the resonance frequency (<math>\omega_{L}</math>) and the Quality factor <math>Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}}</math> value for each case; <math>W = \frac{1}{2}LI^2</math>. (10 pnts)
 
  
==Questions==
+
==Design a '''parallel''' LC resonant circuit with a resonant frequency between 50-200 kHz.  use <math>L</math> = 10 - 100 <math>\mu H</math>, R = 1k <math>\Omega</math>==
 +
 
 +
:<math>\omega_0=\frac{1}{\sqrt{\mbox{LC}}}</math>
 +
 
 +
I choose the following values for <math>\mbox{L}</math> and <math>\mbox{C}</math>:
 +
 
 +
:<math>\mbox{L}=33\ \mu H</math>
 +
:<math>\mbox{C}=1.024\ \mu F</math>
 +
:<math>\mbox{R}=0.989\ k \Omega</math>
 +
:<math>\mbox{R}_L=2.5\ \Omega</math>
 +
 
 +
So the resonance frequency is <math>\omega_0=\frac{1}{\sqrt{33\ \mu H \cdot 1.024\ \mu F}} = 172 \cdot 10^3\ \frac{\mbox{rad}}{\mbox{sec}}</math>
 +
 
 +
:<math>f=\frac{\omega_0}{2\pi} = 27.4\ \mbox{kHz}</math>
 +
 
 +
And
 +
 
 +
:<math>\mbox{Q} = \frac{1}{\mbox{R}} \sqrt{\frac{\mbox{L}}{\mbox{C}}} = 2.27</math>
 +
 
 +
==Construct the LC circuit using a non-polar capacitor==
 +
==Measure the Gain <math>\equiv \frac{V_{out}}{V_{in}}</math> as a function of frequency. (25 pnts)==
 +
 
 +
[[File:L5 LC table.png | 600 px]]
 +
 
 +
==Compare the measured and theoretical values of the resonance frequency (<math>\omega_{L}</math>) (10 pnts)==
 +
 
 +
 
 +
Let's plot the data from table above:
 +
 
 +
[[File:L5 LC circuit.png | 900 px]]
 +
 
 +
 
 +
And let's zoom the graph above at resonance frequency:
 +
 
 +
[[File:L5 LC zoom.png | 900 px]]
 +
 
 +
 
 +
So the experimentally measured resonance frequency is:
 +
 
 +
<math>f = 27.7\ \mbox{kHz}</math>
 +
 
 +
And the predicted value of resonance frequency is:
 +
 +
<math>f = 27.4\ \mbox{kHz}</math>
 +
 
 +
The error is:
 +
 
 +
<math>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>\left(\frac{V_{out}}{_{Vin}} \right)_{max} =  0.0138 </math>
 +
 
 +
The bandwidth defined as the width from <math>\omega_1</math> to <math>\omega_2</math> where the amplitude of signal drop down to <math>\frac{1}{\sqrt{2}}</math>.
 +
 
 +
At this point <math>\left(\frac{V_{out}}{V_{in}} \right) =  \frac{0.0138}{\sqrt{2}}  = 0.00976</math>. Let's plot this line and calculate the bandwidth.
 +
 
 +
 
 +
[[File:L5 LC bandwidth.png | 900 px]]
 +
 
 +
 
 +
So the bandwidth of the above circuit is
  
#If r=0, show that <math>Q = \frac{1}{\omega_0 R_L C}</math>. (10 pnts)
+
<math>\delta f = 37\ \mbox{kHz}</math>
#Show that at resonance<math> Z_{AB} \approx Q \omega_0 L</math>. (10 pnts)
 
  
=The LRC cicuit=
+
=The RLC cicuit=
 
[[File:TF_EIM_Lab5_RLC.png| 200 px]]
 
[[File:TF_EIM_Lab5_RLC.png| 200 px]]
#Design and construct a '''series''' LRC circuit.
+
==Design and construct a '''series''' LRC circuit==
#Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 pnts)
+
==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:
 +
 
 +
[[File:L5 RLC table.png | 400 px]]
 +
 
 +
:And let's graph the gain as a function of the input voltage frequency:
 +
 
 +
[[File:L5 RLC circuit.png | 800 px]]
 +
 
 +
==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:
 +
 
 +
[[File:L5 RLC circuit phase m1.png | 800 px]]
 +
 
 +
<br><br><br><br>
 +
 
 
==Questions==
 
==Questions==
#What is the current <math>I</math> at resonance? (5 pnts)
+
===What is the current <math>I</math> at resonance? (5 pnts)===
#What is the current as <math>\nu \rightarrow \infty</math>? (5 pnts)
+
 
 +
[[File:Question1.png | 800 px]]
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 +
===What is the current as <math>\nu \rightarrow \infty</math>? (5 pnts)===
 +
 
 +
[[File:Question2.png | 400 px]]
 +
 
  
  
  
 
[[Forest_Electronic_Instrumentation_and_Measurement]]
 
[[Forest_Electronic_Instrumentation_and_Measurement]]
 +
 
[https://wiki.iac.isu.edu/index.php/Electronics_RS Go Back to All Lab Reports]
 
[https://wiki.iac.isu.edu/index.php/Electronics_RS Go Back to All Lab Reports]

Latest revision as of 15:23, 7 February 2011

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LC Resonance circuits

The LC circuit

TF EIM Lab5 LC.png

Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]L[/math] = 10 - 100 [math]\mu H[/math], R = 1k [math]\Omega[/math]

[math]\omega_0=\frac{1}{\sqrt{\mbox{LC}}}[/math]

I choose the following values for [math]\mbox{L}[/math] and [math]\mbox{C}[/math]:

[math]\mbox{L}=33\ \mu H[/math]
[math]\mbox{C}=1.024\ \mu F[/math]
[math]\mbox{R}=0.989\ k \Omega[/math]
[math]\mbox{R}_L=2.5\ \Omega[/math]

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

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

And

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

Construct the LC circuit using a non-polar capacitor

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

L5 LC table.png

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

Let's plot the data from table above:

L5 LC circuit.png


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

L5 LC zoom.png


So the experimentally measured resonance frequency is:

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

And the predicted value of resonance frequency is:

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

The error is:

[math]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]\left(\frac{V_{out}}{_{Vin}} \right)_{max} = 0.0138 [/math]

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

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


L5 LC bandwidth.png


So the bandwidth of the above circuit is

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

The RLC cicuit

TF EIM Lab5 RLC.png

Design and construct a series LRC circuit

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:

L5 RLC table.png

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

L5 RLC circuit.png

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:

L5 RLC circuit phase m1.png





Questions

What is the current [math]I[/math] at resonance? (5 pnts)

Question1.png

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

Question2.png



Forest_Electronic_Instrumentation_and_Measurement

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