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Usually the way to operate an opamp is to feed a +V and a -V of the same magnitude but opposed polarity. Or, just +V and GND.

But now, I need an opamp's output to be In a different range. About -1.25V to +28V. The opamp i have is an MC4558, which has a supply voltage (max) of ±22V.

Can I supply this with, say, -3V and +33V? The configuration I'm using is drawing "B" in this answer: Setting LMC6001 offset voltage

Some opamps, like the LM324, say supply can be 0-36 or ±18V. This one only mentions ±22V. It doesn't say 0-44V.

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    \$\begingroup\$ DO the chip only have one + and one minus power pin? Or also a 0V pin? Remember voltage is all relative. There is no difference between powering something -20V to +20V than powering it 0V to 40V or 1000V to 1040V. \$\endgroup\$ – Myforwik Dec 12 '13 at 5:54
  • \$\begingroup\$ @Myforwik One of the inputs may be at 0V, connected to ground. [This is more of a general comment.] \$\endgroup\$ – Nick Alexeev Dec 12 '13 at 7:10
  • \$\begingroup\$ @NickAlexeev yes that's my fear. In my case I don't have a "hard" ground anywhere but if I connect one of the inputs directly to 0V then the amplifier will have a 0V reference there (and will see +30V at the input). But i don't know if this also applies to "GND through a resistor". Does the resistor make the opamp "float"? \$\endgroup\$ – hjf Dec 12 '13 at 14:33
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The opamp itself won't notice any difference in -10/+30V or -20/+20V power rails as the 0V is not connected to the device, only to the surrounding circuitry. It is up to you to define 0V somewhere in your circuit and you can change it at any moment. Just beware that all other node voltages change with that decision.

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The only issue you may run in to is input and output swing limitations. Op amps generally do not work as well near the power rails. How near depends primarily on the design of the op amp but also external parameters such as load resistance.

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It's not uncommon to supply the OpAmp with rails that have different magnitude.

The operating conditions* in the MC4558 datasheet are ±20V. It's safer to assume that they meant -20V to +20V. I wouldn't read that 0 to +40V.

Of course, there are OpAmps that can work off higher voltage rails.
You can also consider boosting the output range your OpAmp with an additional stage made with discrete transistors. Some details here. However, I'm not suggesting that in your case this is more convenient than finding an OpAmp for higher supply voltage.

* operating conditions is not to be confused with absolute maximum conditions. Operating conditions imply that the device will meet the specs. Absolute maximum conditions imply that the device will not take permanent damage, but not necessarily perform.

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    \$\begingroup\$ @hjf I think, jippie is correct in his post. Consider the 1st case with ±20V supply and a -10V input. It's a valid situation, which fits the operating conditions. Consider the 2nd case with -10V and +30V supply and 0V input. From the OpAmps perspective, it's the same as the first case. Potential differences are the same. \$\endgroup\$ – Nick Alexeev Dec 12 '13 at 21:02

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