Turbos also enable Miller Cycle, which is really a sort of boosted version of Atkinson Cycle. Some of the drawbacks of Atkinson Cycle operation are loss of volumetric efficiency at high BMEP and loss of low-end torque. Modern turbocharger designs do a very good job of addressing such shortcomings. A couple of current examples include the recent Miller Cycle versions of the VW EA211 1.5L and EA888B 2.0L engines. The EA211 is also using a VNT turbocharger, which helps with torque response and helps increase pressure ratio at low engine speeds.
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