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).

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

R	C	[math]\displaystyle{ \omega }[/math]	[math]\displaystyle{ \nu }[/math]

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

5.) 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] as a function of frequency [math]\displaystyle{ \nu }[/math]. Hint: you could use[math]\displaystyle{ V_{in} }[/math] as an external trigger and measure the time until [math]\displaystyle{ V_{out} }[/math] reaches a max on the scope [math]\displaystyle{ (\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]\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. 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].(30 pnts)
4. Calculate an 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)
5. Compare the theoretical and experimental value for the phase shift [math]\displaystyle{ \theta }[/math]. (5 pnts)
6. what is the phase shift [math]\displaystyle{ \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