Lab 3 RS

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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).

To design low-pass RC filter I had:

[math]R=10.5\ \Omega[/math]  
[math]R=1.250\ \mu F[/math]
[math]\omega_b = \frac{1}{RC} = 76.2\ \mbox{kHz}[/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](V_{in})[/math] and output [math](V_{out})[/math] voltages for at least 8 different frequencies[math] (\nu)[/math] which span the frequency range from 1 Hz to 1 MHz.

[math]\nu\ [\mbox{kHz}][/math]	[math]V_{in}\ [V][/math]	[math]V_{out}\ [V][/math]	[math]\frac{V_{out}}{V_{in}}[/math]	[math]\delta t[/math]	[math]\phi = \omega \times \delta t[/math]
0.1	5.0	5.0	1.0
1.0	4.2	4.2	1.0
2.0	3.2	3.1	0.97
5.0	1.8	1.6	0.89
10.0	1.14	0.88	0.77
16.7	0.90	0.54	0.60
20.0	0.88	0.48	0.54
25.0	0.82	0.38	0.46
33.3	0.78	0.28	0.36
50.0	0.76	0.18	0.24
100.0	0.75	0.09	0.12
125.0	0.74	0.07	0.095
200.0	0.75	0.04	0.053
333.3	0.76	0.03	0.039
200.0	0.76	0.03	0.039
1000.0	0.78	0.06	0.077

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] as a function of frequency [math]\nu[/math]. Hint: you could use [math] V_{in}[/math] as an external trigger and measure the time until [math]V_{out}[/math] reaches a max on the scope [math](\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 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)
3. 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)
4. Compare the theoretical and experimental value for the phase shift [math]\theta[/math]. (5 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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