Electrical – Does a power amplifier output constant current or constant voltage

Be aware that you could badly damage or kill your subject and that this should only be done with suitable ethical, moral and legal oversight.

There circuits velow from question (not answer) here give a starting point BUT for something involving anatomical subjects, something with a bit more control of safety would be very very very advised.

The circuits are ground (negative) referenced but equivalent "high side" circuits can be created if desired. The control voltage here is shown as PWM, which would need to be filtered if it was used, but a DC input voltage would be even better.

Yes, it's very easy to construct a constant-power supply.

Take, for example, an ordinary switchmode boost converter.

^{simulate this circuit – Schematic created using CircuitLab}

Let's assume it is operating in discontinuous mode and does not have synchronous rectification (i.e., just a diode). If the switch is operated with a fixed duty cycle (i.e., no feedback), it puts a fixed amount of energy into the inductor each time it is closed. The amount of energy depends only on the input voltage, the inductance and the on-time. That energy gets dumped into the load when the switch opens.

Constant energy per cycle × constant number of cycles per second = constant energy per second = constant power.

Regardless of the resistance of the load, the voltage and current levels will adjust themselves to match that value of power.

In terms of practical limits, if the output of this supply is shorted, then the current will be limited by the resistance of the internal components (the inductor and diode). If the output is left open, the voltage will be limited by the distributed capacitance of the components — the inductor will "ring" with some high voltage at the self-resonant frequency.