opamp common-mode distortion - effect of source resistance

I'm trying to learn more about common-mode distortion in BJT opamps.  I read in Douglas Self's Small Signal Audio Design, pages 104-108, that common-mode distortion is only a concern with a reasonable high source impedance (several kiloohms).  So, if I'm driving an opamp follower from another opamp's output, for example, I don't need to worry.

However, Samuel Groner's paper on opamp distortion seems to imply that CM distortion is a concern even with negligible source impedances–see the test setup for CM distortion on page 8.

Unfortunately, I lack the equipment and/or the ingenuity to do my own tests.

Now I don't know what to believe and who to trust, and my dreams are haunted by shadowy non-linearities.  Won't someone hold my hand and reassure me that everything is going to be all right?

All op-amp distortion is a measure of linearity of input to output voltage transfer function (open loop).

If you inspect the internal design of any opamp you will see an obvious voltage swing constraint, while the discrete parts that make the input stage will only behave well over some lesser range of total power supply swing.

So CM affects will surely matter, what voltage the opamp input is expected to work over.

Why exactly are you concerned about this... CM behavior is generally dominated by external feedback network,

JR

Of course you shall believe* me! 8)

It's all a function about the maximum distortion you can/want to tolerate, plus of course the expected maximum common-mode level and the given performance of the chosen opamp.

As my measurement series shows, common-mode distortion will dominate in a follower configuration (with reasonable output load) for essentially all opamps, even with zero source impedance. However, for many applications the performance may nonetheless be good enough.

One thing to think about is that if the source impedance is low, a follower/buffer is not usually required.

Samuel

* In fact, I had hoped that the opamp measurement series moves the "believe" towards the "know".

Maybe my terminology is wrong!  I don't think we're talking about the same thing.

I thought that "common-mode distortion" meant distortion that arises from some portion of the signal voltage appearing in common across both inputs, like in the case of a non-inverting unity gain follower.  This thread:  http://www.groupdiy.com/index.php?topic=10865.0 discusses this, as do the texts I mentioned in my OP.

I realize this effect is probably not one's biggest concern in normal life, but I'm trying to educate myself, and thought it would be good to gain a better understanding of what to look out for.

Samuel Groner said:

Of course you shall believe* me! 8)

It's all a function about the maximum distortion you can/want to tolerate, plus of course the expected maximum common-mode level and the given performance of the chosen opamp.

As my measurement series shows, common-mode distortion will dominate in a follower configuration (with reasonable output load) for essentially all opamps, even with zero source impedance. However, for many applications the performance may nonetheless be good enough.

One thing to think about is that if the source impedance is low, a follower/buffer is not usually required.

Samuel

* In fact, I had hoped that the opamp measurement series moves the "believe" towards the "know".

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Interesting, thanks.  I was being a little bit tongue in cheek  , but I was curious to what extent the effect relies on source impedance.  Not very much, then?  Perhaps Douglas Self's measurements, mentioned earlier, are conflating two different problems?
I was thinking, specifically, about increasing the drive capability of an opamp by adding followers in parallel with the output, like in the Burr Brown app note that I can't seem to find at the moment.

EDIT:  app note ab051

Of course "what Sam said"...

A unity gain follower has the maximum benefit of open loop gain to reduce distortion via negative feedback and loop gain margin, but with the largest potential input voltage swing... so the worst case for practical input swing limitations.

Source impedance may have some secondary impact, but it will generally be dominated by the inner limitations of the opamp circuitry.

This is subtle stuff and why a unity gain inverter "might" slightly beat a unity gain follower for low distortion, while the distortion for either may be too small to quantify with some uber-opamps.  I don't know how far Sam has dropped his measurement resolution floor. The popular trick to characterize uber opamps at elevated noise gain then divide the distortion product to extrapolate an effective number, ignores or introduces other input effects, while this may just be a personal problem of mine... (Should we trust what we can't verify? Then again does distortion at -150 dB matter,,? not much IMO).

JR

I was curious to what extent the effect relies on source impedance. Not very much, then?

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No no--it drastically increases with source impedance! There's a fixed floor at zero source impedance, and a component which is proportional to source impedance. Check the "input impedance linearity" plots and chapter 2 of the opamp measurement series.

Let's take an example--TI NE5534 configured as follower.

As shown in the opamp measurement series, at 10 kHz/+20 dBu "Common-Mode Linearity" is about 0.5%. This is for 60 dB noise gain (as noted by JR to enable much higher measurement resolution). A follower has unity noise gain, so the effectively observed distortion, with zero source Z, at the output of the follower is 1000x less, or 0.0005%. Plenty low for most ears.

Now there's a graph showing "Input Impedance Linearity", saying 0.025% (again at 10 kHz/+20 dBu). This is for a 100k source Z, at unity noise gain. So for a NE5534 follower driven from 100k we get 0.0005% distortion from the basic zero-Z common-mode distortion, and 0.025% from the component which is proportional to source Z. Obviously the latter is far more important.

If we reduce the source Z to 1k, the second term drops 100x to 0.00025%. Now the first is more important, and total distortion back at a point where it is likely inaudible. That's how/why Self came to his statement.

Just for comparison the same opamp configured as unity gain inverter: The measurement series says 0.035% for "Transfer Linearity" (nearly the same with heavier loading). This again is at 60 dB noise gain, but the inverter has itself 6 dB noise gain (even with 0 dB signal gain). So effective distortion referred to the output is 500x lower, or 0.00007%. Almost 10x lower than for the zero-source-Z follower, and a zillion times better than any follower with multi-kOhm source Z.

I know this is rather complicated at first (and probably also at second and third). I'm working on a revised test setup (don't hold your breath--at least a year from now, probably more) which will make the isolation of the various mechanisms more obvious, and the estimation of effective output-referred distortion for a specific opamp configuration/implementation much easier. But it won't change the fact that distortion is a second-order effect and thus much more difficult to model and understand than first-order ones (e.g. DC parameters and noise).

Samuel

OK, that explanation helps a great deal. You separate out those two problems ("common mode" and "input impedance" non-linearity), and Self doesn't explicitly.

For people in my position who are relatively new to electronics this stuff is certainly very complicated, and I expect it will be mysterious well past the third look  .  However, your writing does a great deal to shed some light.  Thanks!

> common-mode distortion is only a concern with a reasonable high source impedance

That's not generally true.

I don't have the cite handy. I suspect either you didn't read it clearly, or Self was writing on a specific problem.

Take a basic (3-transistor) op-amp with a resistor for the long-tail. Wire as follower. Swing the input very close to the rails. It will probably stop working well before it hits the rail. It will show "increased" non-linearity compared with the same opam wired inverting. Track the currents in Q1 and Q2 over the input swing. As input nears the tail rail, both transistors are starved for current. As input nears the collectors' rail, Q1 must suck double-current while Q2 is running out of current just when it needs to goose Q3 with more current.

And in that simple-opamp case, aside from Q1 Q2 unbalance, you will see large base current unbalances which cause an additional error in the source impedance. But zeroing the source impedance does not fix the other problem.

If the tail is a perfect current source, these effects are less. There are no perfect current sources. You can build better ones. When you do, you find similar stray effects at Q1 Q2 collectors (which are not really infinite impedance), and Sam will know other errors.

is this the reason for FET input?

PRR said:

...
If the tail is a perfect current source, these effects are less. There are no perfect current sources. You can build better ones. When you do, you find similar stray effects at Q1 Q2 collectors (which are not really infinite impedance), and Sam will know other errors.
...

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All that said, it makes you wonder why are some of the "most wanted" discrete opamps having a plain resistor in their tail. It "sounds diferent".

CJ said:

is this the reason for FET input?

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Actually FET i/ps are often the cause of "source resistance related CM distortion".

http://www.diyaudio.com/forums/analog-line-level/218373-discrete-opamp-open-design.html

This is a huge thread but halfway through, Guru Wurcer finalizes his FET i/p stage and points out that it needs to be cascode to avoid this particular evil which is due to non-linear Cgd in the i/p FETs.  Bipolar i/p do suffer from this but not as much as the BF862s.

I, err, apologize for being such a smartass, but I think that the crowd over at diyaudio has vastly different priorities compared to, well, "studio" crowd over here. Hence, I think that groupdiy-ers actually want DOAs with hair-and-mojo, while diyaudio guys want clean, with tight bass and silky highs.

Groupdiy-ers, in my opinion, will opt to BUY a clean opamp in a chip form, if they want one, whereas diyaudio-ers will also want to (at least) spice it (and argue about possible nonlinearities and their sources, and of course the accuracy of their models), then build a prototype, and later organize a PCB groupbuy.

Groupdiy-ers, on the other hand, will mostly argue whereas it sounds thin or phat (provided it works in a first place). Am I right? IMO, the resistors in the LTP gives the opamp ability to potentially sound phatter. What do you think?

tv said:

I, err, apologize for being such a smartass, but I think that the crowd over at diyaudio has vastly different priorities compared to, well, "studio" crowd over here. Hence, I think that groupdiy-ers actually want DOAs with hair-and-mojo, while diyaudio guys want clean, with tight bass and silky highs.

Groupdiy-ers, in my opinion, will opt to BUY a clean opamp in a chip form, if they want one, whereas diyaudio-ers will also want to (at least) spice it (and argue about possible nonlinearities and their sources, and of course the accuracy of their models), then build a prototype, and later organize a PCB groupbuy.

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I am reluctant to stereotype entire communities.

Groupdiy-ers, on the other hand, will mostly argue whereas it sounds thin or phat (provided it works in a first place). Am I right? IMO, the resistors in the LTP gives the opamp ability to potentially sound phatter. What do you think?

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Adding degeneration resistors in the LTP reduce the transconductance of the input stage so you can reduce the compensation cap for similar stability with higher slew rate. Of course there is no free lunch so adding resistors there increase noise and degrade DC performance.  The degeneration resistors can make a slow opamp cleaner while all things equal it reduces open loop gain. The classic Deane Jensen opamp design used inductors there for the best of both worlds worlds, high gain and good DC performance, but stability with high slew rate. 

JFETs have lower transconductance than bipolar transistors so naturally deliver higher slew rate performance. (this is a bit of an oversimplification).
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Different strokes for different folks. but some of the legacy designs people are attracted to for their "color" were attempts to design a clean path with inferior technology.

YMMV

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@ CJ the reason for FET input opamps is mainly the very low input currents (noise, bias, offset), along with very high input impedance. High slew rates were nice too. Prior to the '70s FET inputs were too noisy for general use. As Ricardo mentioned they are not free of operating point constraints wrt input voltage range.

JR

PRR said:

> common-mode distortion is only a concern with a reasonable high source impedance

Take a basic (3-transistor) op-amp with a resistor for the long-tail. Wire as follower. Swing the input very close to the rails. It will probably stop working well before it hits the rail. It will show "increased" non-linearity compared with the same opam wired inverting. Track the currents in Q1 and Q2 over the input swing. As input nears the tail rail, both transistors are starved for current. As input nears the collectors' rail, Q1 must suck double-current while Q2 is running out of current just when it needs to goose Q3 with more current.

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Is this the same problem?  Forgive me if I'm misunderstanding, but I read both Self and Samuel Groner's paper to use "common mode distortion" in reference to non-linearities arising from some portion of the signal appearing at both inputs when using an opamp in non-inverting configuration, regardless of whether the signal is large or small.

Apologies if I'm being dense!

@JR - I didn't mean degenerative resistors in a LPT, but rather like PRR said, a resistor as a current feed for a LTP. The varyiing current in LTP will have all sorts of "colorful" effects (ok, and most probably also a lower noise vs. a CCS). If in a noninv. config, input signal is large enough, it will most likely also modulate the LTP bjt's hFE.

As for stereotypizing, I think I'm "close enough", hehe.. of course not 100%.

I ran some simulations in LTspice, with models of BJT-input opamps, as well as a "DOA", stepping an inline resistor at +input as "source impedance", in range from 5k to 100k, and my findings are that with higher the "source" resistance (or impedance), the higher are amounts of 2nd and 3rd harmonics, which is to be expected because of nonlinearities regarding bjt base current.

Simplified, the interaction of "source impedance" and input LTPs base current causes a "distorted" wavefom to be injected into the input "signal", (Ib x Zsource; while deltaIb is nonlinear), and this is something that I personally wouldn't call "common mode distortion", but hey, who am I in the grand scheme of things? Actually, it has been known for ages that you should "balance" the impedances that an opamp's +/- inputs see to optimize performance, and that running unbalanced impedances (like in my "test jig" below) will degrade performance.

But hey...

This is something that I personally wouldn't call "common mode distortion".

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Drive your opamp as inverter with otherwise the exactly same setup (i.e. ground R1 and move the source to R2). If the extra distortion with larger R1 disappears, it was a common-mode effect.

Samuel

Well, THB, the effect IS there, but, compared to the non-inv config, it is orders of magnitude lower (both in absolute terms and relative terms). So, I would say, "not plausible". To me, this looks exactly like I described, and it's almost stupidly simplistic. Probably the same "mechanics" behind it that caused designers to add "linearizing" diodes to OTAS, but here predominantly manifested on the "positive" input BJT of the LTP, i.e. its base getting non-linearly current-hungry at positive swing.

Of course, I might have done something very wrong there..
Also, the accuracy of "models" in question..

Well, THB, the effect IS there, but, compared to the non-inv config, it is orders of magnitude lower (both in absolute terms and relative terms). So, I would say, "not plausible".

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Before we dismiss SPICE let's do another little experiment--could it be that the observed distortion (in noninverting mode) is proportional to frequency? Check at 100 Hz and 10 kHz. If yes, it will be 20 dB lower/higher than at 1 kHz.

Samuel