Lab 3 RS

Go Back to All Lab Reports

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\ [\mu s][/math]	[math]\phi = \omega \ \delta t\ [rad][/math]
0.1	5.0	5.0	1.0
1.0	4.2	4.2	1.0	15.0	15.0
2.0	3.2	3.1	0.97	15.0	30.0
5.0	1.8	1.6	0.89	15.0	75.0
10.0	1.14	0.88	0.77	10.0	100
16.7	0.90	0.54	0.60	10.0
20.0	0.88	0.48	0.54	8.0
25.0	0.82	0.38	0.46	7.0
33.3	0.78	0.28	0.36	6.0
50.0	0.76	0.18	0.24	4.5
100.0	0.75	0.09	0.12	2.0
125.0	0.74	0.07	0.095	1.8
200.0	0.75	0.04	0.053	0.8
333.3	0.76	0.03	0.039	0.25
200.0	0.76	0.03	0.039	-0.25
1000.0	0.78	0.06	0.077	-0.25

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

Go Back to All Lab Reports