RC low-pass filter on a noisy sensor line

Compare a noisy sensor signal with the output of an RC low-pass filter.

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Predict the reading, then compare it with the measurement.

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Compare a noisy sensor signal with the output of an RC low-pass filter.

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Version tested: Prepared circuit opened from the launch link on 2026-09-06; no version number exposed. Date: 2026-09-06.

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Steps

Screens captured against Falstad CircuitJS Prepared circuit opened from the launch link on 2026-09-06; no version number exposed on 2026-09-06; the tool may have moved on — the text steps are the contract.

  1. Step 1

    Do
    In the circuit canvas, inspect the source, 10 kΩ resistor, and 1 µF capacitor.
    You will see
    The source combines a 1.65 V offset with a 1 kHz ripple of 0.2 V peak amplitude.
    Why it matters
    The chapter chooses filtering from the wanted signal and unwanted changes. Identifying the ripple frequency gives this filter a specific job to test.

  2. Step 2

    Do
    In the scope panel beneath the circuit canvas, compare the input and output time traces.
    You will see
    The output scope shows a maximum near 1.656 V, while the input scope shows a maximum of 1.85 V.
    Why it matters
    Comparing both traces makes the reduction visible. The chapter warns that a smoother output can also erase a change you need to detect.

  3. Step 3

    Do
    In the circuit canvas, use the resistor and capacitor labels to calculate the time constant R × C.
    You will see
    The labels show 10 kΩ and 1 µF, giving a calculated time constant of 0.01 s, or 10 ms.
    Why it matters
    Filtering changes timing as well as amplitude. The chapter checks whether the resulting wait still fits the measurement decision.

  4. Step 4

    Do
    In the circuit canvas, use the resistor and capacitor labels to calculate the cutoff 1 / (2πRC).
    You will see
    The 10 kΩ resistor and 1 µF capacitor give a calculated cutoff of about 15.9 Hz.
    Why it matters
    The cutoff must follow the signal you need to retain. The chapter rejects filter choices based only on how smooth the result looks.

  5. Step 5

    Do
    In the scope panel beneath the canvas, compare the output maximum with the ripple estimate 0.2 / sqrt(1+(1000/15.9)²).
    You will see
    The displayed maximum is near 1.656 V. The ideal steady-state calculation predicts 3.18 mV ripple above the 1.65 V offset.
    Why it matters
    The captured maximum and steady-state estimate describe different evidence. The chapter requires timing and amplitude checks before accepting a filter result.

  6. Step 6

    Do
    In the source’s right-click menu, choose Edit and change Frequency from 1000 Hz to 1 Hz.
    You will see
    The source measurement panel shows 1 Hz, and the output follows the slow input change more closely.
    Why it matters
    Changing frequency tests which changes the filter preserves. The chapter distinguishes slow measurements from fast signals that need different filter choices.

Chapter checks

These questions refer to the chapter’s examples. Use the return links to review their answers.

  1. You have a noisy temperature sensor that occasionally produces spike values (e.g., 22C, 23C, 55C, 22C). Which filter is better for removing these spikes?

    Return to the chapter’s knowledge check

  2. Your temperature sensor reads 1.2C in an ice bath (should be 0C) and 98.8C in boiling water (should be 100C). What is the calibration slope?

    Return to the chapter’s knowledge check

Return to Sensor Processing: Filter Selection and Validation · Browse Labs