Lab 2 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).

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 $(V_{in})$ and output $(V_{out})$ voltages for at least 8 different frequencies$(\nu)$ which span the frequency range from 1 Hz to 1 MHz.

$\nu$	$V_{in}$	$V_{out}$	$\frac{V_{out}}{V_{in}}$
Hz	Volts	Volts

5. Graph the $\log \left(\frac{V_{out}}{V_{in}} \right)$ -vs- $\log (\nu)$

phase shift (10 pnts)

1. measure the phase shift between $V_{in}$ and $V_{out}$ as a function of frequency $\nu$. Hint: you could use $V_{in}$ as an external trigger and measure the time until $V_{out}$ reaches a max on the scope $(\sin(\omega t + \phi) = \sin\left ( \omega\left [t + \frac{\phi}{\omega}\right]\right )= \sin\left ( \omega\left [t + \delta t \right] \right ))$.

Questions

1. compare the theoretical and experimentally measured break frequencies. (5 pnts)
2. Calculate and expression for $\frac{V_{out}}{ V_{in}}$ as a function of $\nu$, $R$, and $C$. The Gain is defined as the ratio of $V_{out}$ to $V_{in}$.(5 pnts)
3. Sketch the phasor diagram for $V_{in}$,$V_{out}$, $V_{R}$, and $V_{C}$. Put the current $I$ along the real voltage axis. (30 pnts)
4. Compare the theoretical and experimental value for the phase shift $\theta$. (5 pnts)
5. what is the phase shift $\theta$ for a DC input and a very-high frequency input?(5 pnts)
6. calculate and expression for the phase shift $\theta$ as a function of $\nu$, $R$, $C$ and graph $\theta$ -vs $\nu$. (20 pnts)

Forest_Electronic_Instrumentation_and_Measurement

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