TF EIMLab4 Writeup

RC High-pass filter

1-50 kHz filter (20 pnts)

1.) 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 .

[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]

R	C	[math]\omega_B[/math]	[math]\nu_B[/math]
Ohms	Farads	rad/s	Hz
[math]10.5 [/math]	[math]1.25 \times 10^{-6}[/math]	76190	92
[math]167600 \Omega [/math]	[math]10.3 \times 10^{-9}[/math]	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.

[math]\nu[/math]	[math]V_{in}[/math]	[math]V_{out}[/math]	[math]\frac{V_{out}}{V_{in}}[/math]
Hz	Volts	Volts

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]

Questions

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