Level 1½ · builds on chapters 1, 2 & 11. The divider (ch. 11) appears inside this chapter's best trick.
{kids ? <>Meet the gatekeeper. They watch two tanks — one marked +, one marked − — and follow ONE rule: if the + tank is even a drop higher, slam the big output valve ALL the way open. Otherwise, slam it shut. : <>An op-amp has two inputs (+ and −) and one rule: if V₊ exceeds V₋ by even a microvolt, the output slams to the top rail. If it's under, it slams to the bottom. The gain is absurd — a hundred thousand or more.}
{kids ? <>The keeper never gets tired, never says "ehh, close enough," and reacts faster than you can blink. Used raw like this, they're called a comparator — a which-is-bigger machine. : <>Used raw, this is a comparator — a which-is-bigger machine. Thermostats ("is temp below the setpoint?"), low-battery warnings ("did V sag under 3.2?"), night lights ("did the sensor divider fall past dusk?") — all one keeper plus a reference from chapter 11's divider.}
{kids ? <>Here's the genius trick: pipe the OUTPUT back around to the − tank. Now the keeper compares your input to their own output. If the output is too low — open more. Too high — close a bit. The output gets herded until it exactly matches the input! : <>Route the output back to the − input. Now the keeper compares the input to its own output: output low → open more; high → back off. The only resting point is V_out = V_in. This is negative feedback, and it converts infinite slam into perfect obedience.}
{kids ? <>"Why bother? The output just copies the input!" Because the copy is strong. The input can be a whisper from a fragile sensor — the output is the keeper's mighty valve saying the same thing with muscle. : <>A copy sounds useless until you remember chapter 11's loading problem: a divider tap collapses if anything thirsty drinks from it. A follower reads the tap with almost zero sip, and repeats it with muscle. It's called a buffer — the fix for loading.}
{kids ? <>Last chapter you built a divider that reports a FRACTION of a level. Now the trick: put one in the report-back pipe, so the keeper only hears half of what the output really is. To make the report match your input, the keeper must drive the output TWICE as high! : <>Don't feed back the whole output — feed back a divided fraction (chapter 11, reporting for duty). If the keeper only "hears" half of V_out, it must drive V_out to 2×V_in before the loop rests. Gain, set purely by a resistor ratio.}
{kids
? <>That's how a whisper from a microphone becomes a roar from a speaker: the keeper is told a shrunken story, so it overshoots by exactly the amount you picked.
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