The P-38 had only a single stage single speed crank
driven centrifugal supercharger, there were no multi
speed superchargers on Allison engines, hence the
lack of power at high altitudes for anything but the
P-38 turbocharged engines.
The GE turbochargers were:
B-2 120#of air per minute 21,300 RPM
B-13 130# of air per minute 21,300 RPM
B-33 165# of air per minute 24,000 RPM
These same turbochargers were used on several different planes, including the P-38 and the P-47, and on the the B-17
and the B-24 as well.
Each model was a detail improvement on the previous model, with improvements in efficiency and maximum turbine RPM. They
were all very similar, and in fact, to my knowledge, were interchangeable as far as the physical installation goes.
However, due to power differences, they had to be installed in matched pairs on the plane.
Unlike modern installations, the GE turbochargers in use then
were not specifically designed for a particular engine with a particular power level. They were designed around a general power level alone. The GE turbocharger was at best about 65% efficient, as opposed to the current efficiency of correctly sized turbochargers that reach or at least aproach 90%.
The limiting factor with the Allison was octane. The turbocharger provided air at a rate regulated to equal sea level. Allison actually slowed down the mechanical supercharger because it could make enough boost with the turbocharger to exceed the limitations of the available fuel. When they slowed the mechanical supercharger down, the RPM required of the turbine in the turbocharger to maintain sea level pressure increased, and exceeded the limit. The wastegate could not dump enough boost from the turbocharger to keep the pressure down at low altitudes, so the mechanical supercharger had to be slowed down.