AC Filters & Resonance

RC Low-Pass Filter & Phase Lag Lissajous Simulator

Sweep AC frequency through an R = 1 kΩ, C = 1.5 µF passive low-pass filter (fc ≈ 106 Hz) to measure −3 dB attenuation and phase shift.

Speed
Compare the AC input wave (CH1) against the filtered capacitor voltage (CH2). Increase the AC frequency to see attenuation and approach -90° phase lag (switch Scope to XY Lissajous!).
● CH1: CH1
● CH2: CH2

Engineering Theory & Mathematical Model

fc = 1 / (2πRC), |H(f)| = 1 / √(1 + (f/fc)²), φ = −arctan(f/fc)

Because capacitive reactance Xc = 1/(2πfC) decreases inversely with frequency, a shunt capacitor passes low-frequency signals unattenuated while shunting high-frequency noise to ground. At the cutoff frequency fc = 1/(2πRC) ≈ 106.1 Hz, output amplitude equals 70.7% (−3 dB) of Vin and lags behind Vin by −45°.

Interactive Lab Procedure

  1. Select AC source VAC1 and sweep frequency from 20 Hz (almost zero attenuation) up to 600 Hz (strong attenuation).
  2. Click "Mode: Y-T" on the oscilloscope to switch to "Mode: X-Y (Lissajous)" and view the phase ellipse live!
  3. Verify Vmax and Vrms readouts directly below the scope graticule.

Technical FAQ

What is the core governing formula for RC Low-Pass Filter & Phase Lag Lissajous Simulator?

fc = 1 / (2πRC), |H(f)| = 1 / √(1 + (f/fc)²), φ = −arctan(f/fc) — Because capacitive reactance Xc = 1/(2πfC) decreases inversely with frequency, a shunt capacitor passes low-frequency signals unattenuated while shunting high-frequency noise to ground. At the cutoff frequency fc = 1/(2πRC) ≈ 106.1 Hz, output amplitude equals 70.7% (−3 dB) of Vin and lags behind Vin by −45°.

Can I modify component values and rewire this circuit live?

Yes! The schematic above runs a live MNA SPICE engine. Click any part to adjust parameters, add or delete wires and components, and click Share URL to save your custom topology.

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