Difference between revisions of "Lab 3 TF EIM"

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= 1-50 kHz filter (20 pnts)=
 
= 1-50 kHz filter (20 pnts)=
 
1.) Design a low-pass RC filter with a break point between 1-50 kHz.  The break point is the frequency at which the filter starts to attenuate the AC signal.  For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed).
 
1.) Design a low-pass RC filter with a break point between 1-50 kHz.  The break point is the frequency at which the filter starts to attenuate the AC signal.  For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed).
 +
 +
Enter your values for<math> R, C,</math> and <math>\omega</math>
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{| border="3"  cellpadding="20" cellspacing="0"
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|R||C || <math> \omega</math> || <math>\nu</math>
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|-
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|  || || ||
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|}
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2.)Now construct the circuit using a non-polar capacitor.
 
2.)Now construct the circuit using a non-polar capacitor.
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[[File:TF_EIM_Lab3.png | 400 px]]
 
[[File:TF_EIM_Lab3.png | 400 px]]
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3.)use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.
 
3.)use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.
 +
 
4.)Measure the input <math>(V_{in})</math> and output <math>(V_{out})</math> voltages for at least 8 different frequencies<math> (\nu)</math>  which span the frequency range from 1 Hz to 1 MHz.
 
4.)Measure the input <math>(V_{in})</math> and output <math>(V_{out})</math> voltages for at least 8 different frequencies<math> (\nu)</math>  which span the frequency range from 1 Hz to 1 MHz.
  
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=Questions=
 
=Questions=
  
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#compare the theoretical and experimentally measured break frequencies. (5 pnts)
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#Compare the theoretical and experimentally measured break frequencies. (5 pnts)
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#Calculate and expression for <math>\frac{V_{out}}{ V_{in}}</math> as a function of <math>\nu</math>, <math>R</math>, and <math>C</math>.  The Gain is defined as the ratio of <math>V_{out}</math> to <math>V_{in}</math>.(5 pnts)
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#Calculate an expression for <math>\frac{V_{out}}{ V_{in}}</math> as a function of <math>\nu</math>, <math>R</math>, and <math>C</math>.  The Gain is defined as the ratio of <math>V_{out}</math> to <math>V_{in}</math>.(5 pnts)
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#Sketch the phasor diagram for <math>V_{in}</math>,<math> V_{out}</math>, <math>V_{R}</math>, and <math>V_{C}</math>. Put the current <math>I</math> along the real voltage axis. (30 pnts)
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#Sketch the phasor diagram for <math>V_{in}</math>,<math> V_{out}</math>, <math>V_{R}</math>, and <math>V_{C}</math>.(30 pnts)
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#Calculate an expression for the phase shift <math>\theta</math> as a function of <math>\nu</math>, <math>R</math>, <math>C</math> and graph <math>\theta</math> -vs <math>\nu</math>. (20 pnts)
 
#Compare the theoretical and experimental value for the phase shift <math>\theta</math>. (5 pnts)
 
#Compare the theoretical and experimental value for the phase shift <math>\theta</math>. (5 pnts)
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# what is the phase shift <math>\theta</math> for a DC input and a very-high frequency input?(5 pnts)
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# what is the phase shift <math>\theta</math> for a DC input (the limit as frequency goes to zero)  and a very-high frequency input?(5 pnts)
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# calculate and expression for the phase shift <math>\theta</math> as a function of <math>\nu</math>, <math>R</math>, <math>C</math> and graph <math>\theta</math> -vs <math>\nu</math>. (20 pnts)
 
  
  
 
[[Forest_Electronic_Instrumentation_and_Measurement]]
 
[[Forest_Electronic_Instrumentation_and_Measurement]]

Latest revision as of 17:59, 2 February 2015

RC Low-pass filter

1-50 kHz filter (20 pnts)

1.) Design a low-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter starts to attenuate the AC signal. For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed).

Enter your values for[math] R, C,[/math] and [math]\omega[/math]

R C [math] \omega[/math] [math]\nu[/math]


2.)Now construct the circuit using a non-polar capacitor.

TF EIM Lab3.png

3.)use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.

4.)Measure the input [math](V_{in})[/math] and output [math](V_{out})[/math] voltages for at least 8 different frequencies[math] (\nu)[/math] which span the frequency range from 1 Hz to 1 MHz.


[math]\nu[/math] [math]V_{in}[/math] [math]V_{out}[/math] [math]\frac{V_{out}}{V_{in}}[/math]
Hz Volts Volts

5.) Graph the [math]\log \left(\frac{V_{out}}{V_{in}} \right)[/math] -vs- [math]\log (\nu)[/math]

phase shift (10 pnts)

  1. measure the phase shift between [math]V_{in}[/math] and [math]V_{out}[/math] as a function of frequency [math]\nu[/math]. Hint: you could use[math] V_{in}[/math] as an external trigger and measure the time until [math]V_{out}[/math] reaches a max on the scope [math](\sin(\omega t + \phi) = \sin\left ( \omega\left [t + \frac{\phi}{\omega}\right]\right )= \sin\left ( \omega\left [t + \delta t \right] \right ))[/math].

Questions

  1. Compare the theoretical and experimentally measured break frequencies. (5 pnts)
  2. Calculate an expression for [math]\frac{V_{out}}{ V_{in}}[/math] as a function of [math]\nu[/math], [math]R[/math], and [math]C[/math]. The Gain is defined as the ratio of [math]V_{out}[/math] to [math]V_{in}[/math].(5 pnts)
  3. Sketch the phasor diagram for [math]V_{in}[/math],[math] V_{out}[/math], [math]V_{R}[/math], and [math]V_{C}[/math].(30 pnts)
  4. Calculate an expression for the phase shift [math]\theta[/math] as a function of [math]\nu[/math], [math]R[/math], [math]C[/math] and graph [math]\theta[/math] -vs [math]\nu[/math]. (20 pnts)
  5. Compare the theoretical and experimental value for the phase shift [math]\theta[/math]. (5 pnts)
  6. what is the phase shift [math]\theta[/math] for a DC input (the limit as frequency goes to zero) and a very-high frequency input?(5 pnts)


Forest_Electronic_Instrumentation_and_Measurement

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