EASA / GCAA Part-66 · Module 16 · Piston Engine · 16.7
Objective: a piston engine makes power from the mass of air it swallows, and air gets thinner with height. Compressing the charge before it reaches the cylinders restores that mass, but only up to the critical altitude. Above it the compressor runs out of capability and manifold pressure falls away like anyone else's.
Power follows the mass of charge in the cylinder, and that mass follows manifold pressure. On a naturally aspirated engine the best manifold pressure you can ever have is ambient pressure, less a little induction loss, so as you climb the manifold pressure and the power fall away together. By roughly 18,000 ft the atmosphere is at half sea-level pressure and so, near enough, is the engine's output.
Charging restores the pressure. A supercharger is driven mechanically from the crankshaft through gearing, so its output depends directly on engine speed: it responds instantly and works at any altitude the gearing allows, but it costs crankshaft power to drive. A turbocharger is driven by a turbine in the exhaust stream, so it recovers energy that would otherwise be wasted and costs the crankshaft nothing directly, at the price of some exhaust back pressure and a slower response.
The critical altitude is the whole point of the topic. Below it the compressor has capability in reserve, so the wastegate is partly open, dumping exhaust past the turbine (or the system is otherwise regulated) to hold manifold pressure at the value the pilot has set. As you climb, less and less needs to be dumped. At the critical altitude the wastegate is fully closed and the compressor is doing everything it can, and that is the highest altitude at which the selected manifold pressure can still be held. Above it manifold pressure falls with ambient pressure just as it would on an unsupercharged engine. Note also the hazard in the other direction: at low altitude the compressor can deliver more than the engine can safely take, so an overboost is a real risk and detonation is the consequence.