Difference between revisions of "Lab 5 RS"
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− | Let's | + | Let's plot the data from table above: |
− | [[File:L5 LC circuit.png | | + | [[File:L5 LC circuit.png | 900 px]] |
And let's zoom the graph above at resonance frequency: | And let's zoom the graph above at resonance frequency: | ||
− | [[File:L5 LC zoom.png | | + | [[File:L5 LC zoom.png | 900 px]] |
− | So the experimentally measured resonance frequency is | + | So the experimentally measured resonance frequency is: |
<math>f = 27.7\ \mbox{kHz}</math> | <math>f = 27.7\ \mbox{kHz}</math> | ||
− | And the predicted value of resonance frequency is | + | And the predicted value of resonance frequency is: |
<math>f = 27.4\ \mbox{kHz}</math> | <math>f = 27.4\ \mbox{kHz}</math> | ||
Line 59: | Line 59: | ||
The error is small so I was lucky | 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 | ||
− | + | <math>\delta f = 37\ \mbox{kHz}</math> | |
=The RLC cicuit= | =The RLC cicuit= | ||
Line 67: | Line 81: | ||
==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. (25 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)== | ==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)=== | ||
+ | |||
+ | [[File:Question1.png | 800 px]] | ||
+ | |||
===What is the current as <math>\nu \rightarrow \infty</math>? (5 pnts)=== | ===What is the current as <math>\nu \rightarrow \infty</math>? (5 pnts)=== | ||
+ | |||
+ | [[File:Question2.png | 400 px]] | ||
+ | |||
Latest revision as of 15:23, 7 February 2011
- LC Resonance circuits
The LC circuit
Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use = 10 - 100 , R = 1k
I choose the following values for
and :So the resonance frequency is
And
Construct the LC circuit using a non-polar capacitor
Measure the Gain as a function of frequency. (25 pnts)
Compare the measured and theoretical values of the resonance frequency ( ) (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:
And the predicted value of resonance frequency is:
The error is:
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
The bandwidth defined as the width from
to where the amplitude of signal drop down to .At this point
. Let's plot this line and calculate the bandwidth.
So the bandwidth of the above circuit is
The RLC cicuit
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:
- 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 at resonance? (5 pnts)
What is the current as ? (5 pnts)