What each one does
A passive crossover sits after one amplifier. Capacitors, inductors and resistors split the full-range signal so each driver gets only part of the band. An active crossover (analog filters or DSP) sits before the power amps. Each driver gets its own amplifier, and the amp’s output goes straight to the voice coil through the speaker cable. Siegfried Linkwitz put the contrast bluntly: passive RLC networks are cheap, but their behavior changes with the drivers’ signal-level dynamics, and they keep the amp from taking maximum control of cone motion. Rod Elliott (ESP) makes the same engineering point from the driver’s side: with a passive network, the impedance the driver “sees” looking back toward the amp is often far higher than the amp’s own output impedance, especially near the crossover frequency — so damping of the driver’s back-EMF is weaker than the amp’s damping-factor number suggests.
What you need for each
Passive: one amp (or one amp per speaker), the network parts, and enough layout care that coils don’t couple and the board doesn’t sit in the woofer’s magnetic field. See crossover layout mistakes and the first crossover that actually measures. Order matters: first vs second-order crossover. Active: a crossover or DSP, plus one amp channel per driver (two channels for a 2-way, three for a 3-way). That is more boxes and more gain structure to set. DSP is one way to do the filters; start with DSP for DIY speakers: where to start and keep this page for the decision, not the DSP walkthrough.
What measurement tells you either way
Neither topology skips measurement. Run a gated sweep and an impedance curve (REW basics; speaker impedance curves, explained). Passive networks interact with the driver’s impedance, so a textbook formula on a complex load is only a start. Active filters remove that interaction at line level, but the acoustic sum at the listening position still has to be checked — baffle step, driver offset and room all remain (baffle step explained).
When passive is the simpler build
Elliott notes situations where going fully active would be silly: a clock-radio bookshelf, a second TV, or any non-critical listening system. A well-executed passive 2-way is still a normal first DIY project: fewer amps, one cable per box, and parts you can buy as a kit. If power is modest and you are willing to measure and tweak the network, passive can be the shorter path.
When active earns the extra work
Linkwitz’s preference is line-level active dividing networks ahead of the power amps: the amp connects almost directly to the voice coil, clipping in the woofer amp is not dumped into the tweeter, and sensitivity / EQ corrections are easier without fighting driver impedance. Elliott argues the same control advantage and that each amp works over a narrower band with a simpler load. Active also makes high-order acoustic slopes practical without a large, expensive passive parts card. If you already own a spare amp and a DSP or analog crossover board, the incremental cost can be small. If you do not, count channels and cables before you commit (see matching amp power).
Checklist
Which kind of capacitor? See crossover capacitors: film vs electrolytic. Which kind of inductor? See crossover inductors: air core vs iron core.