AC Filters & Resonance

Oscilloscope X-Y Lissajous Phase & Frequency Ratio Lab

Use X-Y dual-channel oscilloscope mode to measure phase angles and harmonic ratios visually from straight lines, ellipses, and figure-eights.

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

sin(φ) = Y_intercept / Y_max

Plotting CH1 horizontally (X) against CH2 vertically (Y) traces a tilted straight line at 0° phase shift, an inclined ellipse at 45°, and a pure circle/upright ellipse at 90° quadrature! Connecting two independent AC generators with 1:2 or 2:3 frequency ratios draws classic harmonic Lissajous knots.

Interactive Lab Procedure

  1. Click "Mode: Y-T" above the oscilloscope to switch immediately to "Mode: X-Y (Lissajous)".
  2. Sweep VAC1 frequency from 10 Hz (almost 0° straight diagonal line) to 106 Hz (45° ellipse) and 1000 Hz (nearly 90° axis-aligned ellipse)!
  3. Add a second AC source at 240 Hz on CH2 to draw a 1:2 figure-eight Lissajous curve!

Technical FAQ

What is the core governing formula for Oscilloscope X-Y Lissajous Phase & Frequency Ratio Lab?

sin(φ) = Y_intercept / Y_max — Plotting CH1 horizontally (X) against CH2 vertically (Y) traces a tilted straight line at 0° phase shift, an inclined ellipse at 45°, and a pure circle/upright ellipse at 90° quadrature! Connecting two independent AC generators with 1:2 or 2:3 frequency ratios draws classic harmonic Lissajous knots.

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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