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RC filters

Curricula: Sek II, electronics courses

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Aim

Measure the frequency responses of RC low-pass and high-pass filters.

The bench

Source: sine, amplitude 5 V (RMS 3.54 V), 159.15 Hz — the cut-off frequency of the filters. At the bottom — the low-pass filter: a 1 kΩ resistor, then a 1 µF capacitor, output across the capacitor. At the top — the high-pass filter: a capacitor, then a resistor, output across the resistor. Voltmeters in AC mode at the outputs.

Procedure

  1. Record the output voltages of both filters.
  2. Set 20, 50, 100, 300, 500 and 1000 Hz in turn and record both outputs at each frequency.
  3. Plot graphs of the ratio \(U_{out} / U_{in}\) against frequency. Take \(U_{in}\) to be the RMS voltage of the source, 3.54 V.
Expected result

At the cut-off frequency \(f = 1 / (2\pi RC)\) ≈ 159 Hz both outputs are about 2.50 V — 0.71 of the input. At 20 Hz: low-pass — about 3.5 V, high-pass — about 0.44 V. At 1000 Hz: low-pass — about 0.56 V, high-pass — about 3.5 V.

Questions

  1. Which filter is suitable for removing high-frequency noise from a sensor signal?
  2. How will the cut-off frequency change if a 0.1 µF capacitor is used?
Answers
  1. The low-pass filter. It passes slow changes of the signal almost unchanged, about 3.5 V of 3.54 V at 20 Hz, and weakens fast ones: at 1000 Hz only about 0.56 V remains. Its cut-off frequency is chosen above the frequencies of the useful signal and below those of the noise.
  2. It rises tenfold: \(f = 1 / (2\pi RC)\) = 1 / (2π · 1 kΩ · 0.1 µF) ≈ 1.59 kHz.