TF EIMLab3 Writeup

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).

[math]\omega_{break} = \frac{1}{RC}[/math]

[math]\Rightarrow R = \frac{1}{\omega_{break} C } = \frac{1}{25 \times 10^{3} \times 9.45 \times 10^{-9}} = 4,233 \Omega[/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[/math]	[math]V_{in}[/math]	[math]V_{out}[/math]	[math]\frac{V_{out}}{V_{in}}[/math]
Hz	Volts	Volts
50	0.6	0.3
100	0.5	0.18
250	0.5	0.075
500	0.45	0.04
1000	0.4	0.017
2500	0.28	0.005
5056	0.16	0.005

1. 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]

Questions

1.)compare the theoretical and experimentally measured break frequencies. (5 pnts)

\omega_{break} = \frac{1}{RC} = \frac{1}{400 \times 10^{3} \times 9.45 \times 10^{-9}} = = 2.6 \times 10^{2}

Theory	Exp	%diff

1. 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)
2. Compare the theoretical and experimental value for the phase shift [math]\theta[/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. what is the phase shift [math]\theta[/math] for a DC input and a very-high frequency input?(5 pnts)
5. 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