One easy definition of a 'high-current' amp, as Monty mentioned, is one that has a continuous-power rating of double its output power as the load halves its impedance. This test is rather strenuous, and many amps just can't do it. The key word here is 'continuous'. For a short-enough period, any amp can double its power when the load halves. To be able to pass twice the current continuously, almost ALL parts in an amp that pass current, and that's at least all the power supply and active circuirty, have to be larger and the entire system has to be able to dissipate the heat*. A few amps are built with large-enough parts that that they'll double output again into 2 Ohms, and fewer still will double again into 1 Ohm. I had a Lazurus HA-1 stereo poweramp that was rated 50WPC into 8, 100WPC into 4, and 200WPC into 2.
So maybe one definition of 'high-current' is having a continuous-power rating into 4 Ohms of double the 8-Ohm power. Others have more-strenuous definitions.
* This requirement is what prevents many multichannel amps such as my Outlaw 770 from doubling its power continuously--each amp module is so close to the next, there just isn't enough airflow over each to remove the additional heat created by the doubled current flow.
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