TDIs that use the VE pump still have mechanical injectors. The only thing the solenoid does is control how much fuel gets into each line by a solenoid controlling the flow from the pressure side of the pump to the pump head/rotor, which is what bumps it up to the super high pressure to the injectors.
there's a single solenoid controlling the flow to all 4 injectors.
The quantity adjuster is a servo which moves the control collar. The control collar is what covers the spill ports on the plunger. With the spill ports covered the fuel pressure cannot bleed off back into the pump housing and isntead the pressure heading to the injectors will rise further. The increased pressure and fuel volume will extend the injector duration until pressure in the line drops back below the opening pressure of the injector.
The quantity adjuster can make small adjustments to regulate fuel on a cylinder by cylinder basis. This is how the ecu adjusts for injector variances and smooths the idle.
The cummins 24v bosch VP44 pump can control timming and it has mech. injectors. There is a very fast acting solenoid that opens and closes when each cylinder is to be fired. I don't know the exact details but they do it.
Seems like it would be easier to make a common rail system with 4 individualy controlled injectors.
yeah you can't control duration (with vp37), only advance.
duration is fixed to the combination pumpcam/plunger/injector(pressure and size)