Basic stepper driver question

Hi,

I have a question about the internal workings of stepper drivers, such as the StepSticks found on RAMPS boards.

I know the drivers modulate power through the stepper coils to achieve stepping and microstepping of the rotor. But do they do this using linear constant current circuitry, essentially dropping the voltage supplied to each coil by burning off excess power as heat, like a linear regulator? Or is it achieved in a more complex way, more akin to a switched-mode DC-DC converter?

Does the answer to this question depend on the type of controller used on the StepStick? The variants I can easily find are DRV8825, A4988, and TMC2100.

I can't seem to find a straightforward answer by searching online.

Current is regulated in PWM-switching mode not in linear mode. We are running the steppers at 3-4 times their required voltage. No way, those tiny chips would be able to deal with the excessive energy.