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We're working on a project that requires a stable +6 and -6 and +3.6 and -3.6 volts from a 12 volt battery. It has to be stable, even when the voltage of the source goes down. We came up with this:

schematic of proposed stabilization system

But this doesn't work because the 6 volts aren't stable when the 12 volts drops. We can not use software in our project.

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    \$\begingroup\$ Of course it does. You only have 12V of potential. \$\endgroup\$ – Ignacio Vazquez-Abrams Jun 9 '16 at 18:00
  • \$\begingroup\$ Put a DC-DC step-up converter between the battery and your +/-6V. That will stabilise the input voltage to 12V if it drops. \$\endgroup\$ – Tom Carpenter Jun 9 '16 at 18:17
  • \$\begingroup\$ I'd also use two 3.6V precision references to your artificial ground to get your +/-3.6V - zeners don't make particularly stable voltage references. \$\endgroup\$ – Tom Carpenter Jun 9 '16 at 18:18
  • \$\begingroup\$ You forgot to mention how much current you will draw from those voltages. The opamp with the two 100 k resistors is a good choice as long as you only draw a few mA from the +/- 6 V lines. For the +/- 3.6 V I would use voltage regulators like LM317 and LM337, you can set their voltage with a couple of resistors. \$\endgroup\$ – Bimpelrekkie Jun 9 '16 at 18:41
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    \$\begingroup\$ To get stable +/- 6 V from a varying 12 V you need something much more elaborate. I would use a boost converter to make 18 V. Then the 2 resistors + opamp to make that +/- 9 V. Then some LM317/LM337 regulators to make +/- 6 V from than and the same for making +/- 3.6 V from that. This is not the only way of course. \$\endgroup\$ – Bimpelrekkie Jun 9 '16 at 18:46
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Switch-mode regulator chips are readily available and easy to use. They are easily configurable to produce bipolar output voltages. And they will continue to produce the desired voltages even as the battery drains down to even below what is safe for the battery.

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