Difference between revisions of "TF EIMLab4 Writeup"

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(Created page with ';RC High-pass filter = 1-50 kHz filter (20 pnts)= 1.) Design a high-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter's a…')
 
 
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= 1-50 kHz filter (20 pnts)=
 
= 1-50 kHz filter (20 pnts)=
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1.) Design a high-pass RC filter with a break point between 1-50 kHz.  The break point is the frequency at which the filter's attenuation of the AC signal goes to 0(not passed).  For a High pass filter, AC signals with a frequency below the 1-50 kHz range will be attenuated .
 
1.) Design a high-pass RC filter with a break point between 1-50 kHz.  The break point is the frequency at which the filter's attenuation of the AC signal goes to 0(not passed).  For a High pass filter, AC signals with a frequency below the 1-50 kHz range will be attenuated .
  
 
[[File:TF_EIM_Lab4.png | 400 px]]
 
[[File:TF_EIM_Lab4.png | 400 px]]
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:<math>\omega_{break} = \frac{1}{RC}</math>
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: <math>\Rightarrow R = \frac{1}{\omega_{break} C } = \frac{1}{25 \times 10^{3} \times 9.45 \times 10^{-9}} =  4,233 \Omega</math>
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{| border="3"  cellpadding="20" cellspacing="0"
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|R ||C || <math>\omega_B</math> || <math>\nu_B</math>
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|-
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| Ohms || Farads || rad/s ||Hz
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|-
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|  <math>10.5 </math>|| <math>1.25 \times 10^{-6}</math>|| 76190||92
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|-
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|  <math>167600 \Omega </math>|| <math>10.3 \times 10^{-9}</math>|| 579||12,126
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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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#compare the theoretical and experimentally measured break frequencies. (5 pnts)
 
#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>.(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>.(5 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)
 
#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)
 
#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)

Latest revision as of 19:04, 25 February 2011

RC High-pass filter

1-50 kHz filter (20 pnts)

1.) Design a high-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter's attenuation of the AC signal goes to 0(not passed). For a High pass filter, AC signals with a frequency below the 1-50 kHz range will be attenuated .

TF EIM Lab4.png

[math]\omega_{break} = \frac{1}{RC}[/math]
[math]\Rightarrow R = \frac{1}{\omega_{break} C } = \frac{1}{25 \times 10^{3} \times 9.45 \times 10^{-9}} = 4,233 \Omega[/math]
R C [math]\omega_B[/math] [math]\nu_B[/math]
Ohms Farads rad/s Hz
[math]10.5 [/math] [math]1.25 \times 10^{-6}[/math] 76190 92
[math]167600 \Omega [/math] [math]10.3 \times 10^{-9}[/math] 579 12,126


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

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

4.)Measure the input and output voltages for at least 8 different frequencies 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]

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].(5 pnts)
  3. Compare the theoretical and experimental value for the phase shift [math]\theta[/math]. (5 pnts)
  4. 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)
  5. what is the phase shift [math]\theta[/math] for a DC input and a very-high frequency input?(5 pnts)
  6. 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

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