30 A 50 Hz AC current source for impedance measurement

take a 30A capable 3V transformer and put a light-bulb or power resistor in series with the primary (to limit the short circuit current) .

Instead of regulating the current use a current-transformer or a shunt to measure the actual current.

^{simulate this circuit – Schematic created using CircuitLab}

Use some sort of ratio meter to compare the shunt resistor against the DUT.

If you want 12VRMS maximum output voltage, that's 17V peak. With a linear circuit as described in the question (ie, MOSFETs) with an optimized gate drive it would need say +/-20V supply. If the load is 50mOhm plus 50mOhm current sense resistor, then voltage on the load will be 0.1 ohm times 30A, so 3V, and the rest of the voltage has to be dropped by the power transistors. This corresponds to a dissipation of about 500W average in the transistors.

So a linear solution will need to use several MOSFETs in parallel (say 6 pairs) and a good chunk of metal, plus a large heat sink and fan if it intended for continuous use.

What I'd do instead:

First, I'd use a voltage output amp. Current output amps are a can of worms, difficult to compensate and keep stable, because the load inevitably has some inductance (wires... or worse it's a coil) which adds a zero to the response, so you need a custom compensation network to keep it stable. Combining a current source and an inductive load always needs some care.

Then, I would connect that voltage source directly to the load and current measurement resistor, and simply ramp up the amplitude until the target current is reached.

As the 30 amps signal source, a class D amp, for example based as IRS2092S. This chip does not operate in bridged mode, which is what you need in this case. It needs adequate support components. A ready made alternative is a used class D amp rated for 1kW/1Ohm like Behringer iNuke.

Note if you can use a more civilized current like 1A, then the problem becomes much simpler. You can use a chip power opamp like LM1875 to drive it, and measure the current with a current sense amp. The signal will be 30x smaller, but you can just add more gain. It will be noisier, but you can average the measurement over several periods.

Perhaps you don't need to have perfect current control as long as you can accurately measure the current?

In that case, just about any professional audio amplifier will do. You can get them as a rackmount module. They will output 30A happily, with compliance voltage much higher than 12V.

You'll need to set the signal amplitude low enough not to overstress the load. Otherwise it should work well. Beefy pro audio amplifiers are IMHO under-appreciated creatures. One belongs on every bench if you ask me. They can be used for so many things.

12/30= 400 mohm load. The driver ought to be same or less than a 50 mV current sensor of 1.5 mohm. These values are your choice.

The typical linear amplifier uses cascaded current gain of emitter followers.

With a 10k Zin and a 3 mohm output impedance requires a current gain of 3.3 e6. How you achieve that depends on choices of high hFE drivers with some reduction from feedback of excess voltage gain to reduce Zout.

Alternative design uses a current control Buck regulator.