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You'd be better off using two 12V supplies, but if you insist...

#1 won't work.

#2 (given the very limited information you have supplied) might require the op-amp to dissipate as much as 600mW and stability would likely be an issue with capacitive loads. There are dedicated rail splitter chips which take stability seriously but they are not jellybean parts and, for example, the TLE2426 cannot handle the dissipation or current involved.

I suggest something more like this (assuming you have power to spare on your 12V supply:

This uses a ubiquitous TL431 shunt regulator and boosts it with a generic PNP power transistor.

The combination is like a precision power zener. Or just use a zener as below. Set Vo = 12V.

Then use this circuit:

^{simulate this circuit – Schematic created using CircuitLab}

Note that if you excessively load the GND to -V the +V to GND voltage will increase to as much as 24V. Usually that's acceptable but take care about capacitor voltage rating and so on. You can add a higher voltage zener (say 14V) across R1 as a preventative measure.
R1 will dissipate less than 1W, under normal conditions, but the zener could dissipate as much as 1.3W if 50mA flows from +V to GND and there is no corresponding current from GND to -V.

You could use two 6.2V 1W zeners in series, for example. Keep the leads short, attach them to some PCB area and keep them apart so they run cooler.

Given your desire for as low power as possible, and my realization that this common problem is seldom approached this way. I came up with a self-oscillating switching solution just for the fun of it.

As with any switcher, single-tone emissions/ripple have to be considered (around 20kHz with these values). But if there is any significant ground current, I doubt you can be much more efficient (a more formal switcher with a separate oscillator can be made more efficient and could use a single inductor, but it would require more parts).

^{simulate this circuit – Schematic created using CircuitLab}

It is basically a relaxation oscillator that modulates the average current through L1 so that it oscillates around the required ground current. M1 and M2 are switched on and off relatively quickly (some acceleration capacitors would help with efficiency) and C12 provides positive feedback so that the opamp/comparator saturates on crossing the threshold (otherwise the load would damp the oscillator and it would become a linear regulator instead).

L3, C10, and C11 are there to filter the ripple and to isolate the oscillation from the load, so as to avoid dampening it too much. C10, and C11 also do double-duty as the regulator input capacitance. Excess energy in L1 and L2 would be returned to the required rail and stored in them. M1 and M2 source-drain diodes are conducting in this design.

R3,R4,R5, and R6 are chosen so as to keep M1 and M2 below threshold when there is no ground current. Unfortunately this also reduces the overall gain of the oscillator loop.

I have not done a very careful analysis of all of the implications of this design (particularly because of it being self-oscillating), so overall stability considerations on load changes might be an issue.

I don't think there are ICs for this type of configuration, which unnecessarily increases the part count and the design constraints. The only ones I know of are the DDR memory termination voltage regulators, but those are intended to work at very low voltages.

The regulators won’t work. You have zero dropout allocated to them and your ground impedance is excessive.

The op amp is a better option, but it all depends on how much current you have going through ground. If the current is low enough you can just use a resistor divider with a couple of capacitors in parallel, if it is high you would need a hefty op amp.

You have a couple more options:

1. You could use two zeners with series resistors to reduce ground impedance


2. You could put together a class AB source follower with a few resistors and two transistors (basically what the op-amp is doing but with higher impedance)


3. If your ground current has a well-defined and consistent direction, you can use a positive or negative 12V regulator or even a transistor off one of the rails (making sure to put a bypass diode).

But regardless of what you do, any ground current will result in wasted power (unless you figure out how to design a ground-switcher regulator of course).

If your 24 V is well regulated you could just use a 7812 to create a mid point and call that your 0 volt rail.

^{simulate this circuit – Schematic created using CircuitLab}

This will only work if the 24 V is independent of whatever you're powering, and as per Edgar Brown's comment, positive linear regulators like the 7812 can't sink current.

I think NJM4556A would work

you can draw current from negative and positive rails but there difference not to exceed the OP amp output current.

Note: I'm not experienced, i suggest you to read the following post

EEVBLOG - my-negative-voltage-rail-doesnt-work

There are many low-cost methods. But switching method may help you with a minimum component that available everywhere.

you can use a flyback converter with a minimum circuit:

Edited: The main circuit:

Ref: a mix of two links (http://uzzors2k.4hv.org/index.phppage=flybacktransformerdrivers, https://wiki.analog.com/university/courses/electronics/text/chapter-6)

Component list:

• Zener diode




• 555 IC




• Mosfet




• A toroid, the transformer can be made with wire and a toroid core




• Diode in output




• some capacitor




• some resistor




• some wire

Benefits:

• you can generate any voltage in output even bigger than your first voltage




• these components are available everywhere




• you can generate any voltage even isolated voltage




• you can increase your power by changing the Mosfet and selecting a bigger toroid.

The main references:

http://uzzors2k.4hv.org/index.php?page=flybacktransformerdrivers

Additionally, you need a Zener diode for 12-15volt and a 555 IC.( your coil feed with 24Volt but for 555, you should generate a 12-volt power with a Zener diode).

in the output, you need a diode with a capacitor.
link: https://wiki.analog.com/university/courses/electronics/text/chapter-6

It is dual polarity Full-wave rectifier using a center tapped transformer and 4 diodes