The improvement in the power output observed from different turbo matching is manifest in a couple of things. The biggest effect is, as you stated, by improving the delta-P between the intake and exhaust manifolds. This has the direct effect of reducing pumping losses which can be read as the lower work loop in an indicator or P-V diagram. The smaller the area of this negative work loop, the lower the pumping losses.

Secondly, better turbo matching results in the compressor operating in a more efficient operating point, meaning simply that the charge temperature going out of the compressor and into the engine is at a lower temperature and therefore higher density for a given absolute pressure. I won't go into the details as to why this is good as there should be pretty good intuitive understanding as to why this is so.

Now, here is the part is less well understood: Many people have the (erroneous) understanding that charge temperature and turbine backpressure are governed by the physical size of the turbocharger. I constantly hear terms such as "I get a cooler charge with a bigger turbo," or "I get less exhaust manifold backpressure with a bigger turbo." After hearing these for so long by so-called experts and reading the same over the Net, I started

a thread some years ago in the Forced Induction forum at VWVortex that caused quite a stir.

The fact of the matter is, both charge temperature and turbine backpressure are related ultimately to efficiency and what effects efficiency. In the case of charge temperature, it can be calculated as nothing more than

T

2/T

1 = (P

2/P

1)^((k-1)/k)),

Where k is the specific heat ratio and approximated with the value 1.4, and the subscripts 1 and 2 refer to compressor inlet and outlet, respectively. All values of temperature and pressure must be absolute (Kevin or Rankine; kPa, bars or PSI absolute).

However, the calculation above assumes a perfectly isentropic compression process, which can never be achieved. We define an isentropic or adiabatic efficiency, whose limit of 100% would denote a truely isentropic or adiabatic process.

hs = (T2s - T1) / (T2 - T1 )
T2s denotes what the temperature would be at the compressor outlet if compression occured isentropically. T2 is the actual compressor outlet temperature and what we're trying to find.
What this equation shows is that as you approach an insentropic process (higher isentropic efficiency), the compressor outlet temperature reduces, with T2s being the lower limit.
On the turbine side, it can be shown that the dP you ask about is a function of the net efficiency of the turbocharger, or simply the product of all the discrete efficiencies (isentropic efficiency in the turbine and compressor, and the mechanical efficiency).

dP a hTOT,NET = hMECH * hS,C * hS,T

Edit: In the above equations the letters come out incorrectly. *"a" that follows dP is supposed to denote the proportionality symbol, while "h" is supposed to the Greek letter "eta" that is synonymous with efficiency.*

Note that the physical size of the turbo does not directly factor in to either the equations for T

2 or dP at all. Where size would play a decisive role in dP is if the mass flow rate is approaching the choked region of the turbine. Here, a larger cross sectional flow area or a larger A/R turbine would certainly help.

Now, since you don't have the option of changing the efficiencies of the turbocharger at will, the practical question is, how can I minimize T

2 and achieve the most favourable dP? The answer is by maximing the efficiency at which the turbocharger operates for each given operating point of the engine. That is the science of turbo matching. The parameters you have ample licence to play with are selection of wheel sizes, trims, and A/R ratios for both the compressor and turbine sides of the turbo. By proper selection, all you are doing is trying to make sure that mass flow and pressure ratio (boost) demands of the engine intake, and the mass flow and enthalpy (heat) of the engine exhaust are operating as much as possible in the most efficient parts of the turbo maps. The basis of turbo matching doesn't get any easier than that. It is NOT about stuffing the biggest turbo you can between the engine and the firewall!