TF EIMLab4 Writeup

RC High-pass filter

1-50 kHz filter (20 pnts)

< font size = 24>Design </font size>

Design 

1.) < font size = 24>Design a high-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter's attenuation of the AC signal goes to 0(not passed). For a High pass filter, AC signals with a frequency below the 1-50 kHz range will be attenuated .

$\omega_{break} = \frac{1}{RC}$

$\Rightarrow R = \frac{1}{\omega_{break} C } = \frac{1}{25 \times 10^{3} \times 9.45 \times 10^{-9}} = 4,233 \Omega$

R	C	$\omega_B$	$\nu_B$
Ohms	Farads	rad/s	Hz
$10.5$	$1.25 \times 10^{-6}$	76190	92
$167600 \Omega$	$10.3 \times 10^{-9}$	579	12,126

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 and output voltages for at least 8 different frequencies 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 $V_{out}$

Questions

1. compare the theoretical and experimentally measured break frequencies. (5 pnts)
2. Calculate an expression for $\frac{V_{out}}{ V_{in}}$ as a function of $\nu$, $R$, and $C$.(5 pnts)
3. Compare the theoretical and experimental value for the phase shift $\theta$. (5 pnts)
4. 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)
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