TF EIMLab4 Writeup: Difference between revisions
Jump to navigation
Jump to search
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…' |
|||
| (6 intermediate revisions by the same user not shown) | |||
| Line 2: | Line 2: | ||
= 1-50 kHz filter (20 pnts)= | = 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 . | 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]] | ||
:<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> | |||
{| border="3" cellpadding="20" cellspacing="0" | |||
|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. | 2.) Now construct the circuit using a non-polar capacitor. | ||
| Line 52: | Line 68: | ||
#compare the theoretical and experimentally measured break frequencies. (5 pnts) | #compare the theoretical and experimentally measured break frequencies. (5 pnts) | ||
#Calculate | #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 .
- [math]\displaystyle{ \omega_{break} = \frac{1}{RC} }[/math]
- [math]\displaystyle{ \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]\displaystyle{ \omega_B }[/math] | [math]\displaystyle{ \nu_B }[/math] |
| Ohms | Farads | rad/s | Hz |
| [math]\displaystyle{ 10.5 }[/math] | [math]\displaystyle{ 1.25 \times 10^{-6} }[/math] | 76190 | 92 |
| [math]\displaystyle{ 167600 \Omega }[/math] | [math]\displaystyle{ 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]\displaystyle{ \nu }[/math] | [math]\displaystyle{ V_{in} }[/math] | [math]\displaystyle{ V_{out} }[/math] | [math]\displaystyle{ \frac{V_{out}}{V_{in}} }[/math] |
| Hz | Volts | Volts | |
5.)Graph the [math]\displaystyle{ \log \left(\frac{V_{out}}{V_{in}} \right) }[/math] -vs- [math]\displaystyle{ \log (\nu) }[/math]
phase shift (10 pnts)
- measure the phase shift between [math]\displaystyle{ V_{in} }[/math] and [math]\displaystyle{ V_{out} }[/math]
Questions
- compare the theoretical and experimentally measured break frequencies. (5 pnts)
- Calculate an expression for [math]\displaystyle{ \frac{V_{out}}{ V_{in}} }[/math] as a function of [math]\displaystyle{ \nu }[/math], [math]\displaystyle{ R }[/math], and [math]\displaystyle{ C }[/math].(5 pnts)
- Compare the theoretical and experimental value for the phase shift [math]\displaystyle{ \theta }[/math]. (5 pnts)
- Sketch the phasor diagram for [math]\displaystyle{ V_{in} }[/math],[math]\displaystyle{ V_{out} }[/math], [math]\displaystyle{ V_{R} }[/math], and [math]\displaystyle{ V_{C} }[/math]. Put the current [math]\displaystyle{ i }[/math] along the real voltage axis. (30 pnts)
- what is the phase shift [math]\displaystyle{ \theta }[/math] for a DC input and a very-high frequency input?(5 pnts)
- calculate and expression for the phase shift [math]\displaystyle{ \theta }[/math] as a function of [math]\displaystyle{ \nu }[/math], [math]\displaystyle{ R }[/math], [math]\displaystyle{ C }[/math] and graph [math]\displaystyle{ \theta }[/math] -vs [math]\displaystyle{ \nu }[/math]. (20 pnts)