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

#### duckduckgo

Joined Aug 4, 2013
4
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?

#### bountyhunter

Joined Sep 7, 2009
2,512
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.

#### crutschow

Joined Mar 14, 2008
34,073
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).

#### Ron H

Joined Apr 14, 2005
7,061
I agree with Carl.

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

#### #12

Joined Nov 30, 2010
18,224
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.

#### LDC3

Joined Apr 27, 2013
924
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.
If I understand correctly, than a unity gain voltage follower is a example with a worst-case stability.

#### crutschow

Joined Mar 14, 2008
34,073
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.
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.

#### Ron H

Joined Apr 14, 2005
7,061
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.
And a zero-gain inverting amplifier is just a "ground follower".

#### WBahn

Joined Mar 31, 2012
29,885
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.

#### Ron H

Joined Apr 14, 2005
7,061
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.
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.

#### crutschow

Joined Mar 14, 2008
34,073
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.
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.

#### ramancini8

Joined Jul 18, 2012
473
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.

#### Ron H

Joined Apr 14, 2005
7,061
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.
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.

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#### crutschow

Joined Mar 14, 2008
34,073
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.

#### ramancini8

Joined Jul 18, 2012
473
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.

#### crutschow

Joined Mar 14, 2008
34,073
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.
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.

#### MrChips

Joined Oct 2, 2009
30,518
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.
Hey, I got the impression any discussion about over unity was verboten.

#### duckduckgo

Joined Aug 4, 2013
4
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.
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.

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#### Ron H

Joined Apr 14, 2005
7,061
Z is the symbol for impedance. When impedance is purely resistive, Z=R, NOT Z=1/R, as you stated in your equations.