# Opamp output voltage in negative feedback

Assume we have an opamp in negative feedback just like this:

This is for an ideal opamp which its VCC pin is connected to some positive voltage(15V) and its VEE pin is connected to some negative voltage(-15V).

The equation of Vout=-Vin*Rf/Rin

When working with microcontroller the lowest voltage is GND.

If we connect the VEE pin of the opamp to GND the equation of Vout can't be the same because the lowest possible voltage is GND. Which is the equation for the new 'state' of the opamp?

• It's the same equation, but that doesn't account for the limited range of the output voltage swing. WIth the ancient uA741 for example, on +/-15V supply rails, the output swing is +/-12V. On +/-10V supply rails, the 741 output swing is +/-7V. And with +5V/0V supplies, the 741 output voltage swing drops to... zero, it's stuck at 3V. Its output can only get within about 2V of the supply rails. That's not part of the feedback equation, that's only going to be found in the Output Voltage Swing specification in the op amp's Datasheet Electrical Characteristics table. Commented Dec 2, 2020 at 21:07
• So it will have an output of 0V? Commented Dec 2, 2020 at 21:14
• Right, probably near 0V unless Vi is very small or slightly negative. Why don't you use a non-inverting op-amp configuration? Commented Dec 2, 2020 at 21:17
• Because this is actually a part of a digital to analog converter and need to control the gain. Commented Dec 2, 2020 at 21:19
• I mean a non-inverting configuration like this: eecs.tufts.edu/~dsculley/tutorial/opamps/opamps2.html. Do you mean you need to be able to have a gain of less than 1? Commented Dec 2, 2020 at 21:40

If this is an ideal op amp, connecting the negative supply pin to ground will not affect the equation

$$\V_{OUT} = -V_{in}*R_f/R_{in}\$$

as long as $$\V_{OUT}\$$ calculated by that formula satisfies $$\0 \le V_{OUT} \le V_{CC}\$$

• Not all opamps will reach 0V when VEE = 0. You will need something like the ubiquitous LM358, the typical 741 will definitely have its output restricted.
– S.s.
Commented Dec 3, 2020 at 2:39
• The OP asked about ideal op amps. Commented Dec 3, 2020 at 2:43

Unless many things are stated explicitly, all opamp circuit equations for inverting gain, non-inverting gain, active filters, integrators, etc. assume that the input and output signal voltage ranges stay within any particular device's input and output voltage ranges. For example, an LM741 output stage can get up to only about 2 V below Vcc while a contemporary rail-to-rail opamp with a light output load can get to within 0.1 V of Vcc, but none of this figures into the gain equation.

Note that the voltage rails do not always equal the max signal range. Many device input stages are designed such that the low value of the input common mode voltage range extends below the device's negative rail. And, Linear Tech has parts that can handle input voltages way above the positive rail. As always, read all of the datasheet.