Lab 3 TF EIM

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).
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 [math]\displaystyle{ (V_{in}) }[/math] and output [math]\displaystyle{ (V_{out}) }[/math] voltages for at least 8 different frequencies[math]\displaystyle{ (\nu) }[/math] 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

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

phase shift (10 pnts)

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

Questions

1. compare the theoretical and experimentally measured break frequencies. (5 pnts)
2. 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)
3. Compare the theoretical and experimental value for the phase shift [math]\displaystyle{ \theta }[/math]. (5 pnts)
4. 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)
5. what is the phase shift [math]\displaystyle{ \theta }[/math] for a DC input and a very-high frequency input?(5 pnts)
6. 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)

Forest_Electronic_Instrumentation_and_Measurement