The invention combines the features of a supercharger, a turbocharger and turbo-compounding into one system, utilizing a hydraulic or mechanical continuously variable transmission to drive the turbocharger up to a specific speed or intake manifold pressure and then holding the ideal speed to keep it at the right boost pressure for the engine condition. The benefits of a supercharger, which is primarily good for high torque at low speed, and a turbocharger, which is usually only good for high horsepower at high speeds are merged. Once the exhaust energy begins to provide more work than it takes to drive the intake compressor, the invention recovers that excess energy and uses it to add torque to the crankshaft. As a result, the invention provides the benefits of low speed with high torque and the added value of high speed with higher horsepower or better fuel economy all from one system.