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Lesson 14
The moment a probe touches a node, it becomes part of the circuit: a capacitor to charge, an inductor in its ground lead, and two more poles before the screen. Commit to what the scope will show first, then fire up the scope and see how much of it was the probe.
Predict · 1 of 2 · the ring
A 3.3 V CMOS output (20 Ω, 1 ns edges) is probed with a P2220 at 10× (10 MΩ ∥ 17 pF) and its 6-inch ground clip, on a 200 MHz scope. Every rising edge rings, and the node itself barely does. A wire is about 20 nH an inch. What frequency is the ring on the screen?
Result
Waiting on your call.
Make your mark, then lock it in. The answer, your error and the reason behind it land here, and the scope and every view below fire up.
Engine: the Lab's exact state-space solver (the matrix exponential), with the Lab's own probe models; the probe's and the scope's bandwidths are single poles, solved as extra states. 1,200 exact samples a sweep. Checked against the closed forms by scripts/probe-check.mjs, and against SPICE: its numbers show once you're in the lab (they'd give the answers away).