Electronic – Simple voltage regulator circuit with 7805c outputs very low voltage

Using an op-amp is probably the best way to deal with this requirement but you might be better with an emitter follower circuit: -

The op-amp will drive the NPN so that its emitter (Voltage across the load) is the same voltage as the +Vin pin on the op-amp.

I borrowed "The Photon's" drawing because although it was wrong, it was easily amended to show an emitter follower. If you did use a FET (N channel with source to load) this would work but you might find that Vin needs to be higher for it to work. BJT base drive only needs to be 0.6V above the emitter - I'd still recommend using an op-amp with rail-to-rail output capability so that Vin can be a bit lower.

I'm also assuming the op-amp is powered from Vin and GND.

The requirement basically translates to the ability to source high current at a specified reference voltage.

A low component count way to implement this is to use a high power high current op-amp as a voltage follower, with the reference voltage at the non-inverting input.

For instance, the Burr Brown (now TI) OPA549 can deliver 8 Amperes continuous current with a suitable heat sink. With its 300,000 open loop gain, this should be sufficient for using the available low current reference to generate a stable high current output.

There are many other such high current op-amps, which dispense with the need for the external MOSFET.

From this page:

In other words, a voltage regulator IC is not required.