They do it by altering intake closing and LSA which changes dynamic compression ratio and overlap. More overlap resultes in a more exhaust diluted mixture which equals less torque output via less air/fuel charge to burn. EGR is an inert gas that does not change air/fuel ratio. Less charge density with the inert EGR means a torque reduction which means the throttle plate is more open and the engine is not having to fight as much vacuum to pull the pistons down, leaving more power to drive the load. Here are a couple intake cam phasing tables for a Nissan VQ40DE. They changed the phasing for given applications. The intake phasers advance the intake cams. On my 2007 G35 with the VQ35HR it adds exhaust cam phasing. The exhaust cams are retarded as needed. There is whole map there as well. The factory envineers main concern is emissions, power and mpg are secondary and take a back seat to emissions output.
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VQ35HR
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I setup a cam phasing change on my G35 through testing. Let another tuner use it on a near stock car because he doubted the gains would be signifigant. Near stock automatic 350Z test subject with my cam phasing I was running on my 2007 G35 proved him wrong. My car came alive alot quicker with the change and delivered increased fuel economy, also easily held overdrive and even accelerated in OD on one section of uphill road it always downshifted to 4th on just to maintain speed. My car saw bigger gains from the phasing adjustments and alot more power overall because it has headers with merge collectors, high flow cats, dual 2.5" exhaust with a X-pipe and straight through magnaflows as well as a less restrictive intake setup.
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