# Many op amps are unstable at gains of less than unity ? Why ?

Discussion in 'General Electronics Chat' started by duckduckgo, Aug 10, 2013.

1. ### duckduckgo Thread Starter New Member

Aug 4, 2013
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The paper 'A Single-Supply Op-Amp Circuit Colletion' written by a TI engineer named Bruce Carter says ' This method is not recommended, because many op amps are unstable at gains of less than unity.'

And the famous handbook <op amps for everyone> also says 'it is important to have a gain of more than 1 on the Vref gain channel or instability may result'.

I just want to know, Why?

2. ### bountyhunter Well-Known Member

Sep 7, 2009
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Because to obtain unity gain stability, the internal compensation has to be larger which reduces bandwidth and usually slew rate. If you want wider bandwidth, the part is decompensated (compensated less) and that forces a minimum stable gain greater than unity be observed in the design.

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3. ### crutschow Expert

Mar 14, 2008
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If an op amp is stable for a non-inverting gain of one (which most are) it will be stable for an inverting gain of less than one. It's a fallacy to say otherwise. The worst-case stability is when you have maximum feedback and that occurs for a non-inverting gain of one (output connected directly to the minus input). All inverting feedback configurations have feedback less than that so are also stable.

The formula for minimum offset is also in error. With the Cin capacitor, R3 = R2 for minimum offset voltage due to the input bias current (since there is no bias current flowing through R1).

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4. ### Ron H AAC Fanatic!

Apr 14, 2005
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I agree with Carl.

They shouldn't assign rookie engineers to write app notes.

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5. ### #12 Expert

Nov 30, 2010
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I've seen this warning a hundred times, but never suffered a project that didn't work. I thought I was just lucky. Thanks for the explanation.

6. ### LDC3 Active Member

Apr 27, 2013
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If I understand correctly, than a unity gain voltage follower is a example with a worst-case stability.

7. ### crutschow Expert

Mar 14, 2008
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It's interesting how an incorrect technical statement can propagate because it "sounds" correct. I think it comes from the knowledge that some op amps are stable for gains of greater than one (such as 2 or 5) and if you go below that gain value the op amp will likely be unstable. So it may seem "logical" that if an op amp is stable for a (non-inverting) gain of 1, then a gain of less than 1 would also be unstable. But you can't get a non-inverting gain of less than one. For example an inverting gain of 0.1 is equivalent to a non-inverting gain of 1.1.

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8. ### Ron H AAC Fanatic!

Apr 14, 2005
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And a zero-gain inverting amplifier is just a "ground follower".

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9. ### WBahn Moderator

Mar 31, 2012
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This isn't an issue that I've ever had need to really look into, so I'm just making an observation on the cited references, not making an claim as to what is correct or incorrect. But it seems relevant that the second author was pretty explicit about always saying that the gain of the Vref channel -- not the overall gain or the gain of the Vin channel -- needs to be over unity.

10. ### Ron H AAC Fanatic!

Apr 14, 2005
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The R1-R2 attenuator, being out of the feedback loop, has no effect on stability. The gain from +in to output can never be less than unity.
Some op amps are designed to be only be stable with higher feedback ratios, e.g., 10 or more. These allow higher bandwidth than would an otherwise identical op amp that is compensated for unity gain.

11. ### crutschow Expert

Mar 14, 2008
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The second author may be explicit but that doesn't make him correct. If the Vref input has a gain of <1 it would be due to the input attenuator consisting of R1 and R2 and that has no effect on the closed-loop stability of the op amp.

Edit: Ron H you beat me by a minute.

12. ### ramancini8 Member

Jul 18, 2012
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Loop gain determines stability! Loop gain for all op amps is aZg/(Zg +Zf) where a is the amplifier open loop gain, Zf is the feedback impedance, and Zg is the inverting input to (ac) ground impedance.

Zf = Zg for an inverting gain of 1, thus the loop gain is a/2; this means that the loop gain intercept is lower on the Bode plot leading to lower 0dB crossover frequency resulting in increased stability. A non-inverting gain of one is by definition a voltage follower, so the loop gain is a. High loop gain decreases error while it decreases stability.

If you want more detail and pictures look at Op Amps for Everyone (free on TI web) chapter six. Bruce interprets the circuit different and tries to make a case out of his interpretation; I think Bruce correct, but he complicates the subject while adding little of value.

If an op amp is compensated by the manufacturer to be stable at a closed loop gain of one, odds are that it may be stable at gains less than one, but there is always the critter that has a little too much open loop gain and rings or possibly oscillates at gains less than one. Remember, overshoot and ringing occur when a circuit is on the verge of instability.

13. ### Ron H AAC Fanatic!

Apr 14, 2005
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How do you make an amplifier with a noninverting closed loop gain of less than 1 (loop gain>a)? You could add an amplifier in the feedback path, but I think that is outside the scope of this discussion.

Last edited: Aug 11, 2013
14. ### crutschow Expert

Mar 14, 2008
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ramancini8, you (and many others) seem to not understand that a non-inverting gain of 1 is the worst-case for op amp feedback stability (without added reactive components). It's equivalent to an inverting gain of zero (which is certainly less than 1). Bruce from TI may do a lot of arm waving in his analysis but it can't counter that fact.

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15. ### ramancini8 Member

Jul 18, 2012
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Ron H.---I never claimed to make a non inverting gain other than one, and that was a voltage follower.

Crutschow---Please read my post carefully because it says exactly what you are saying.

If either of you guys want to discuss this further lets do it in email so we don't disturb others.

16. ### crutschow Expert

Mar 14, 2008
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The last paragraph in your post mentioned a gain of less then 1 as possibly being less stable than a gain of 1 so it didn't appear that you were agreeing with what I said, but if you do, then there's nothing more to discuss.

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17. ### MrChips Moderator

Oct 2, 2009
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Hey, I got the impression any discussion about over unity was verboten.

18. ### duckduckgo Thread Starter New Member

Aug 4, 2013
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When I see 'Loop gain determines stability! Loop gain for all op amps is aZg/(Zg +Zf) where a is the amplifier open loop gain, Zf is the feedback impedance, and Zg is the inverting input to (ac) ground impedance' I know this is the answer I really want. My English is so poor that It's too difficult for me to express it clearly and briefly. The largest mistake I have made is that I didn't spend time reading TI's Op Amps for Everyone (certainly, and ADI's Op Amp Applications Handbook).

Certainly, it's easy to get the Uo/Ui (KCL,Visual short,Virtual ground). I just want to show the SFG(Signal Flow Graph) is useful, too.

Last edited: Aug 12, 2013
19. ### Ron H AAC Fanatic!

Apr 14, 2005
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Z is the symbol for impedance. When impedance is purely resistive, Z=R, NOT Z=1/R, as you stated in your equations.

20. ### duckduckgo Thread Starter New Member

Aug 4, 2013
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So sorry for my carelessness!
I just corrected it.

Last edited: Aug 12, 2013