RC low-pass filter on a noisy sensor line

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

Physics Phoebe, your practice guide

Physics Phoebe
Predict the reading, then compare it with the measurement.

Falstad CircuitJS

Third party Tool

Tier 1 · Web · No account

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

Open the prepared circuit.

Open this circuit in Falstad (new tab)

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
    Source panel: "f = 1 kHz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 200.276 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.65 V"; "C = 1 μF". Output wire panel: "V = 1.65 V".
    Why it matters
    Expected: The source specification is 1.65 V offset plus 0.2 V peak at 1 kHz. Meaning: The RC network should pass the offset while attenuating the fast ripple.

  2. Step 2

    Do
    In the scope panel beneath the circuit canvas, compare the input and output time traces.
    You will see
    Source panel: "f = 1 kHz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 58.816 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.647 V"; "C = 1 μF". Output wire panel: "V = 1.647 V". Live scope labels: "Max=1.85 V" (input); "Max=1.656 V" (output).
    Why it matters
    Expected: The scope retains Max=1.85 V at the input and Max=1.656 V at the output. Meaning: These scope maxima include startup history; settled output samples are closer to 1.65 V.

  3. Step 3

    Do
    In the circuit canvas, use the resistor and capacitor labels to calculate the time constant R × C.
    You will see
    Source panel: "f = 1 kHz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 120.1 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.647 V"; "C = 1 μF". Output wire panel: "V = 1.647 V".
    Why it matters
    Expected: 10 kΩ × 1 μF = 0.01 s, or 10 ms. Meaning: A 10 ms time constant is long compared with one 1 kHz period (1 ms).

  4. Step 4

    Do
    In the circuit canvas, use the resistor and capacitor labels to calculate the cutoff 1 / (2πRC).
    You will see
    Source panel: "f = 1 kHz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 194.44 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.651 V"; "C = 1 μF". Output wire panel: "V = 1.651 V".
    Why it matters
    Expected: 1/(2π × 0.01 s) = about 15.9 Hz. Meaning: The 1 kHz ripple is far above this first-order low-pass cutoff.

  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
    Source panel: "f = 1 kHz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 52.728 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.653 V"; "C = 1 μF". Output wire panel: "V = 1.653 V". Live scope labels: "Max=1.85 V" (input); "Max=1.656 V" (output).
    Why it matters
    Expected: At 1 kHz, ideal steady ripple is 0.2/sqrt(1+(1000/15.9)^2) = about 3.18 mV peak. Meaning: The settled output is near 1.65 V; the scope’s 1.656 V maximum includes earlier transient samples.

  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
    Source panel: "f = 1 Hz"; "Vmax = 200 mV"; "Voff = 1.65 V". Resistor panel: "Vd = 21.935 mV"; "R = 10 kΩ". Capacitor panel: "Vd = 1.477 V"; "C = 1 μF". Output wire panel: "V = 1.477 V".
    Why it matters
    Expected: At 1 Hz, ideal gain is about 0.998, so a settled full cycle should follow the input closely. Meaning: The captured first milliseconds after the edit show the new frequency, not a completed 1 Hz cycle.

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