← CIRCUIT ANALYSISCA-5 · 4 LESSONS + CAPSTONE

Capacitors, inductors & first-order circuits

Energy storage and RC/RL transients.

  1. CA-5.1CapacitorsOPEN →
  2. CA-5.2InductorsOPEN →
  3. CA-5.3RC step responseOPEN →
  4. CA-5.4RL step responseOPEN →
CA-5 CAPSTONE

A time constant you can press

Every button on every board you will ever design bounces — its metal contacts chatter for a few milliseconds on each press, and a fast microcontroller reads one press as dozens. The classic hardware cure is this unit's mathematics: an RC circuit that refuses to change faster than its time constant. Design the numbers here; ME-6 wires it into practice.

  1. A pushbutton's contacts bounce for about 2 ms. Choose a debounce time constant of τ = 10 ms — comfortably past the chatter, imperceptible to a human. With C = 100 nF, compute the required R.
  2. Using the charging response, compute how long after a (clean) press the capacitor voltage crosses half of 3.3 V — the threshold region where a GPIO input flips its reading. Express the answer in time constants and in milliseconds.
  3. Check the waiting game the other way: with your τ, how much can the voltage move during the 2 ms bounce window? (Compute 1−e−2/101 - e^{-2/10} ≈ 18% — not enough to cross a mid-supply threshold from either rail, which is exactly the point.)
  4. Open PCB Studio and build a board with the Pico 2 W, a pushbutton, and one LED. Generate the schematic and examine how the button is wired to its GPIO. The Studio's rules engine handles the button's electrical context (you'll formalise pull-ups and debouncing in ME-6); your task-1 RC values are the timing that context implies.
  5. Run "Generate + PCB layout" and export the Gerbers. As you look at the routed board, find the button's trace and consider: the copper itself has resistance and capacitance, which means every trace is a tiny RC — at these speeds utterly negligible, but at the speeds of ME-5's clocks, the interconnect becomes part of the circuit. That is where this course is heading.
CA-5 · Capacitors, inductors & first-order circuits · iLearnSTEM Electronics