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In this lab, we investigate the frequency response of the circuit shown in Figure 1. The circuit is energized by a sinusoidal voltage v(t). The output voltage is Vo, the voltage across the capacitor. The circuit forms a low-pass filter. Low frequency signals propagate through it. High frequencies are attenuated. This is caused by the frequency sensitivity of the capacitor.
The current through a capacitor is proportional to the time derivative of the voltage.
The phasor version of Equation 1 is,
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(1)
Summing the phasor voltages around the loop in Figure 1 yields,
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(2)
Solving for the current,
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(3)
Using the current in Equation 4, we can find the voltage across the capacitor.
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(4)
The magnitude of the voltage across the capacitor is,
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(5)
The phase of Vo relative the voltage source, V  is,
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(6)
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(7)
Equipment
Measure
Plot on the attached semi log paper,
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(8)
Use the logarithmic axis for frequency.
FIVE | [Reflect] |
Reflect upon your observations.Q: Does the circuit pass low frequencies and attenuate high frequencies?
Q: Is the output inversely proportional to frequency at high frequencies as predicted by Equation 5?