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# Passive Electronic Filters

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Equipment List:

• Voltage Generator
• Oscilloscope
• Ohmmeter
• Resistors
• Capacitors
• Prototyping board
• Wires / connectors

Background:

This experiment was performed to investigate the basic passive electronic filter which is the common RC filter. It uses passive components, resistors and capacitors, to filter particular ranges of frequencies. RC filters can be modified to act as either a low pass or high pass filter depending on the placement of the resistor and the capacitor. The cut-off frequency fc for this type of filter is given by the equation:. At this frequency, the input signal power is attenuated by 3dB or half power of the input signal.

Figure 1. Low-pass and High-pass configuration of RC filter

For the low-pass circuit, voltage division can be used to calculate the transfer function of the circuit. The transfer function was calculated to be: . The gain of the circuit is given by: .

For the high-pass circuit, voltage division can again be used to calculate the transfer function of the circuit. The result would be: . The gain for this circuit is given by: .

Methodology:

1. Set-up the circuit for the low-pass circuit (see fig. 1, circuit on left).
2. Connect the oscilloscope probe on Vo.
3. Connect the voltage generator on Vin of the circuit with Vpp equal to 1V and frequency equal to: .
4. Measure and record the output voltage of the seen by the oscilloscope.
5. Lower the input frequency and observe the output signal.
6. Measure and record the observation.
7. Set the frequency back to the original. Then slowly increase the input frequency.
8. Measure and record the output voltage.
9. Plot the output voltage with respect to frequency.
10. Do steps 1 to 9 for the high-pass circuit.

Results:

Low-pass RC filter

Figure 2. RC low-pass circuit

 Frequency (Hz) Measured Output Voltage (V) 106 0.707 10 0.996 1 0.999 1000 0.105 10000 0.011

Figure 3. Frequency vs. Vo (Low-pass filter)

High-pass RC Filter

Figure 4. RC High-pass filter

 Frequency (Hz) Measured Output Voltage (V) 106 0.707 10 0.094 1 0.09 1000 0.994 10000 0.999

Figure 5. Frequency vs. Vo (High-pass)

Conclusion:

Simple series RC circuit can be configured to act as either a low-pass or a high-pass circuit. Using RC filter, noise can be filtered from a signal using RC low-pass filter while DC can be blocked using high-pass RC filter. For an RC filter, the cut-off frequency was found to be . At this frequency, only half the power of the input signal is transferred to the output. For low-pass filter, the signal is attenuated when the frequency is greater than the cut-off frequency. On the other hand, when the frequency is less than the cut-off frequency, the signal is attenuated when it passes on a high-pass filter.

Reference:

Wolfe, Joe. RC filters, integrators and differentiators. [Online]. Available: http://www.physclips.unsw.edu.au/jw/RCfilters.html [29 November 2007].

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