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Is it possible and reasonable to make a voltage reference that outputs 0.675V +- 0.005 over an input of 6 to 40 volts?

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Yes.

.675V +/- 0.005V is +/- 0.7%.

Digikey lists a lot of voltage references at 0.5% or better regulation.

Once you choose a reference, you can adapt the input voltage (if necessary) with a preregulator, and you can adapt the output voltage (if necessary) with a resistor divider.

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    \$\begingroup\$ That 0.5% is usually also initial accuracy. They're generally much better with regard to drift. You would just need to trim the output voltage once, when you first assemble the system. \$\endgroup\$ – Connor Wolf Sep 9 '13 at 22:55
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    \$\begingroup\$ Someone should explain why accurate references are less favored over ones with controlled drift/tempco. Connor Wolf's comment deserves a separate answer \$\endgroup\$ – HL-SDK Sep 10 '13 at 1:26
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    \$\begingroup\$ I would like to see @ConnorWolf expand into a full answer as well. Trims have their own costs and drawbacks. If a spec can be fulfilled with fixed components of reasonable cost, that makes a better design. \$\endgroup\$ – markrages Sep 10 '13 at 3:20
  • \$\begingroup\$ @markrages - I certainly wouldn't argue that something you can do that doesn't involve manual trimming is a lot nicer from the assembly process. However, it tends to be more expensive.As usual, it's a matter of where your priorities are (accurate, easy, cheap - pick any two). \$\endgroup\$ – Connor Wolf Sep 11 '13 at 3:52

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