Revision as of 19:33, 24 October 2010

1-50 kHz filter (20 pnts)

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).
Now construct the circuit using a non-polar capacitor.
use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.
Measure the input and output voltages for at least 8 different frequencies which span the frequency range from 1 Hz to 1 MHz.
Graph the [math]\displaystyle{ \log \left(\frac{V_{out}}{V_{in}} \right) }[/math] -vs- [math]\displaystyle{ \log (\nu) }[/math]

measure the phase shift between [math]\displaystyle{ V_{in} }[/math] and [math]\displaystyle{ V_{out} }[/math]

compare the theoretical and experimentally measured break frequencies. (5 pnts)
Calculate and 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]. The Gain is defined as the ratio of [math]\displaystyle{ V_{out} }[/math] to [math]\displaystyle{ V_{in} }[/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)

@@ Line 14: / Line 14: @@
 #compare the theoretical and experimentally measured break frequencies. (5 pnts)
-#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)
+#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)
 #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)