Are You Smarter Than an Op Amp?

Let me shatter your confidence in simplicity! You think that applying an op amp is as simple as using a non-inverting circuit:

Or an Inverting circuit:

NOT SO FAST!

Let me introduce you to a complication – the open loop response characteristic of a typical op amp:

For reasons I will not go into here, because this could easily turn into a complex treatise in feedback theory, I will present the REAL gain equations for op amp gain circuits:

Inverting:

Non-Inverting:

OUCH – those equations are UGLY!

In all practicality, you almost never have to worry about them. But if you try to make a very high gain amplifier stage, particularly at high frequencies (assuming it didn’t oscillate for other reasons), these equations explain why you didn’t get the gain you expected.

For the inverting case, with an open loop gain of 80 dB:

When the designer attempts a gain of -1 with Rf = Rg, the open loop gain only contributes 0.02% error. If the designer is using 1% resistors, the error will never be noticed. Even at a gain of -10, the error is only 0.1% – still lost in the resistor tolerance. But at a gain of -100, fully 40 dB below the open loop response, the error has become 1% and could be noticeable. The designer can compensate by tweaking resistors a bit, but by the time a gain of 10,000 is attempted, the error balloons to 50%! And no reasonable amount of tweaking will help. If the designer did something ridiculous like use 1 Ohm for Rg and 1 TOhm for Rf – the highest gain the stage will provide is still less than -10000. Just like the speed of light, you can theoretically get as close as you want, but you can never achieve it.

This is a similar table for the non-inverting case.

This may all sound esoteric and theoretical – far removed from most designer’s experience, but keep it in the back of your mind when you are designing gain stages. This is the way op amps really behave, and those simple gain expressions you are used to are only approximations, and they can mislead you.