Matching Transistors For Good CMRR

[Samuel Groner]

Hi

I'm currently looking into matching discrete transistor pairs for good CMRR of a differential input stage. According to Gray & Meyer (page 384-385 in the 1984 edition) it is the base width mismatch that causes a change in saturation current and hence finite CMRR (even if the tail current source and collector load is assumed to be perfect). My semiconductor knowledge is too limit to exactely follow the argumentation--why does saturation current appear in the discussion..? And for which parameter would I match transistors? Early voltage (which seems to be correlated to base width)? Thanks for your help...

Samuel

 

[zapnspark]

FWIW, I have experimented with all sorts of transistor matching test fixtures.
A lot of those test fixtures were very finicky.

I found that using a simple meter with an hfe function, will allow matching transistors pairs very closely. The matching I got was very similar to the more complicated methods.

ZAP

 

[JohnRoberts]

I don't know a theoretical answer for your question but would be inclined to experimentally make a differential circuit to test devices in. Perhaps even select devices for best CMRR while in that actual circuit.

Then work backwards to see how those devices with good CMRR matched parameters compared to a pair with bad CMRR. Kind of low tech, but that is the answer you're looking for.

Perhaps swap the devices around in the test jig to confirm text fixture is symmetrical.

JR

 

[bcarso]

[quote author="Samuel Groner"] According to Gray & Meyer (page 384-385 in the 1984 edition) it is the base width mismatch that causes a change in saturation current and hence finite CMRR--why does saturation current appear in the discussion..? Samuel[/quote]

I may have the '84 ed (2nd?) somewhere. But in the early sections of the 4th (which include some Early discussions) Is is introduced and used in fundamental expressions for collector current as a function of base-emitter voltage, without calling it saturation current. Later on in discussions of CMR the term saturation current is used without reference to the early sections. Maybe it appears somewhere in between.

It's not the finest hour for Gray (Hurst, Lewis) and Meyer, but then there are always other more physics-oriented texts (Sze et al.) which are longer and probably more accurate.** In many of those, Is is called saturation current and explained as the asymptotic-with-reverse-voltage current of an ideal P-N junction. Ideal, because it is a bulk current, with edge effects and other onset-of-breakdown and second-order effects ignored.

Anyway, Is as a determinant of Vbe is not really a directly measurable quantity,* and has nothing (well, nearly nothing) to do directly with a transistor in saturation, in the conventional sense, i.e., heavily conducting with a small collector-emitter voltage. So you may as well measure Vbe.

Gray et al. give the normal-bias equation for collector current as a function of Vbe as

Ic = Is (1 + Vce/Va) exp (Vbe/Vt),

where Va is the Early voltage and Vt is the thermal voltage kT/q. They mention that the expression is approximate, but is "a common means of representing the device output characteristics for computer simulation".



*that's to say, you can reverse-bias the junction and measure the very tiny current, but because of the non-ideal effects it won't lead typically to a good measure of Vbe versus bias behavior. Most of the time the current measured will be a good deal larger than the somewhat-hypothetical Is.

** but won't be of much direct use in designing analog circuits, integrated or otherwise.

 

[Samuel Groner]

Thanks. So it is reasonable to assume that Va is sufficiently consistent amongst discrete transistors of the same part type?

Samuel

 

[bcarso]

[quote author="Samuel Groner"]Thanks. So it is reasonable to assume that Va is sufficiently consistent amongst discrete transistors of the same part type?

Samuel[/quote]

I've never seen data on that. It would be worthy of study. Beware of the accompanying thermal effects!

 

[JohnRoberts]

I love it when you guys talk technical... :grin: Not that I recognize what Va is (no matter).

I'm guessing that looking at saturation effects is not concerned with the last diode drop of CMR range, but looking for a general marker for base width and perhaps by extension beta vs. Vcb (?). Like the full curve tracer display. Beta change with voltage will look like an impedance change with voltage reflected back to the input (base) so differences should impact CMRR.

If saturation behavior tracks with the entire family curves it may be a short cut way to match devices. Should be easy enough to prove or not, if willing to spend some bench time.

JR

 

[bcarso]

See http://en.wikipedia.org/wiki/Early_effect (Va is the so-called Early voltage).

Again, just to make sure people understand the distinction, saturation in the usual sense of low collector-emitter voltage is not the sense used with reverse current. And the reverse current for a typical input transistor's base-emitter (or base-collector) junction is hard to measure, as it is in the low picoamp range or less, and very temperature-sensitive. In fact the ADI varactor-bridge amps (310, 311) used selected bipolars for the varactor diodes rather than normal varactor diodes, because of the low leakage.

Off-topic: Searching for that wiki led to another ADI patent of interest to current source aficionados, US 6194886.

 

[bcarso]

PS: A really good discussion I just found of the detailed reasons for diode deviation from Is with reverse voltage is in Neudeck, The PN Junction Diode, in the Modular Series on Solid-State Devices (ISBN 0201053217). One result mentioned is that germanium diodes follow the first-order reverse-current law much more accurately than silicon ones---not that that is of much use for us!

(He calls Is Io btw)

 

[JohnRoberts]

I need to stop typing since I'm in over my head, but thanx for the link... I've never seen the Ic vs Vce slopes carried back to a common intercept point. It's been years since I looked at a curve tracer and gave mine away years ago.

My recollection of power devices was pretty flat curves suggesting an early voltage way down the negative axis.

I never had the sense from observation that there was a single common intercept.

Interesting stuff.

JR

 

[bcarso]

Actually, I've always found the Early effect expressed as that imaginary voltage intercept as less than intuitive---but it caught on and insured that Mr. Early will be remembered :grin:

EDIT: even though he will eventually be known as the late Mr. Early

 

[PRR]

> base width mismatch that causes a change in saturation current

To whip the dead horse, and mis-state the definition....

If you apply NO voltage to a junction, and short it, current flows.

It flows because of thermal agitaton. (At Ab-Zero of temperature, it would not flow.)

This does not create Perpetual Motion: the external terminals are short, zero voltage, thus zero power.

At the same temperature, this current is a function of juction area. No big surprise.

All the useful current magnitudes of a diode or transistor are proportional to this "saturation current". A 2N3055 has higher Isat than 2N918; two "identical" 2N918s will have different Isat because making junctions is like ink dots on paper, you never get the exact same size dot because of ink and paper variation.

So yeah, it should be a best-match parameter. All normal currents slant up from Isat at a fairly well defined slope.

Isat is never specified. Why? What size of a number is it?

Shockley showed that (Silicon) junction voltage varies ~~20mV per octave or ~~60V per decade. Say we have a transistor which shows 600mV at 1mA. Then to get to zero voltage we need 600/60= ten decades of current. So staturation current is near 10^-13 Amps.

A very small value, and always masked by leakage and other stray effects. However by careful measurement we could confirm Shockley, get the exact value of junction voltage at medium current, get the exact (slightly process-dependent) value of "60mV/decade" of our device for several decades down, and extrapolate recklessly. Or if you build a very sharp meter, you can go 7 or 8 decades down from a mA and then see the steady slope deviate, as-if other small leakages were beginning to dominate.

I think the name "saturation current" is a mis-use of thermionic terminology. We normally run a thermionic cathode over-hot, and use grid and space-charge to control current. However we can also control cathode temperature and control current; this leads to some different effects. Since cathode temperature is a high-power low-speed input, it is not a lot of use except in a "noise diode". By controlling the tenperature-limited saturation current we can adjust the noise power output, which makes a handy and very cheap secondary reference for noise testing.

Early voltage may be related, but I think the value you can measure in a real world has more to do with stray leakage than intrinsic junction action. (Tho Cherry-Hooper seem to think intrinsic Early can be demonstrated directly with 1960s devices). (Recall too that the Jensen 990 has a couple useless diodes in the dead side of the diff-pair. Turns out the 1.2V offset in Vce due to second stage input DC level Early-s down to over 10mV offset at the bases. "Fixing" this the obvious ways causes worse errors, so he (approximately) fixed t at the source.)

I wonder how much CMRR you need for Music. Or even measurement tools for music systems. Sayeth the preacher, in Ecclesiastes: Of the making of many measurements there is no end.

 

[recnsci]

[quote author="PRR"]Recall too that the Jensen 990 has a couple useless diodes in the dead side of the diff-pair. Turns out the 1.2V offset in Vce due to second stage input DC level Early-s down to over 10mV offset at the bases. "Fixing" this the obvious ways causes worse errors, so he (approximately) fixed t at the source.[/quote]

Dont know what obvious ways were you referring to, but making that PNP
mirror slightly more complex (741 alike) would solve problem. Instead of
diode connected Q10, one fast PNP (lets call it Q12) feeding current
mirror base currents, with its own base connected to Q10 collector.
Additionally, one diode between Q12 emiter and Q10/Q3 bases and
one 2K resistor from Q10/Q3 bases to Vcc. Remaining offset problems
would be mismatch of Q5 and Q12 base currents and (reduced by
degeneration) mismatch of PNP mirror pair.

What I cant figure out as easily is impact of this addition on stability.
On first glance this should push mirror pole upward, but in reality it
would probably introduce additional pole and ruin stability (impedance
at Q12 base rather high, thus Q12 emiter impedance acting
inductive).



And still, this would not have CMRR comparable to cascoded input
topology, to go back on topic.

cheerz
Urosh

 

[clintrubber]

[quote author="zapnspark"]I found that using a simple meter with an hfe function, will allow matching transistors pairs very closely.[/quote]
Got away so far with indeed a simple DMM-with-a-BJT-socket and was able to get good matching pairs for both hFE & Vbe, so life could continue.

But for some reason (and without further thinking yet) I get the impression that matching for best something#1 (say CMRR) parameter#A is important (say Isat) and for something#2 (say -FWIW- DC-offset) it's parameter#B, so a different BJT-property.
Would be interesting (at least for technical reasons) if this thread managed to end up with a few agreed-upon conclusions about what to match for which spec.

Like for instance:
'Goals': CMRR, THD, DC-offset (FWIW, but why not),...
Parameters: Isat, hFE, Vbe,...


[quote author="PRR"]I wonder how much CMRR you need for Music.[/quote]
Interesting thread, but indeed, in general I'm more & more wondering to which extend improving specs still noticably serves the purpose (which is music if I'm not mistaken), and from which point on spec-mania actually starts to degrade the 'actual performance' (despite then having near-perfect rejection of the unwanted stuff, which becomes more & more FWIW then).

This is obviously an old discussion that doesn't need repeating, so I apologize for this OT addition.


Regards,

Peter

 

[Samuel Groner]

Would be interesting if this thread managed to end up with a few agreed-upon conclusions about what to match for which spec.

It is my personal conclusion from this thread that matching for Vbe (offset, CMRR, might have a theoretical influence on THD as well) and hFE (offset current) is all that is required in practice (assuming that other topological errors such as the mentioned current-mirror issues are handled). If you want it better, get dual transistors.

I wonder how much CMRR you need for music.

I'm investigating common-mode distortion and not CMRR per se. There are many IC opamps that have one or two order of magnitude higher distortion in noninverting configuration than in inverting, so I don't believe that this is a non-issue.

Samuel

 

[recnsci]

[quote author="Samuel Groner"]
It is my personal conclusion from this thread that matching for Vbe (offset, CMRR, might have a theoretical influence on THD as well) and hFE (offset current) is all that is required in practice (assuming that other topological errors such as the mentioned current-mirror issues are handled). If you want it better, get dual transistors.
[/quote]

With two transistors from same process, matching Vbe(Is) and hfe
will cover enough geometry/chemisty ground that other parameters will be
close enough.

[quote author="Samuel Groner"]

I wonder how much CMRR you need for music.

I'm investigating common-mode distortion and not CMRR per se. There are many IC opamps that have one or two order of magnitude higher distortion in noninverting configuration than in inverting, so I don't believe that this is a non-issue.

Samuel[/quote]

Once I checked situation of otherwise perfect opamp with simple
resistor in long pair tail. IIRC distortion was more than 80 dB below,
4dBu input for +-15V supply. Almost exclusively second harmonic,
very nice 1/x rolloff.
Any semi decent current source in tail will make distortion induced
by tail current modulation negligible.


OTOH I guess you've seen this:
http://www.analog.com/UploadedFiles/Application_Notes/742022599AN232.pdf

there are two remarks of my own regarding that paper:
using complementary feedback pair instead of single pnp follower
for bootstraping should improve things, especially in no-buffer
topology.

second: Mr Jung mentions that this is mainly a problem for high
source impedance followers. However, since both opamp inputs will
have nonlin input impedance in noninverting topologies, and considering
average 10K resistors in feedback networks, this will result in nonlin error
in output sensing and induce distortion no matter how perfect opamp
amplification is. That is, me thinks that this distortion mechanism is worth
considering in all noninverting configurations where feedback network
impedance is not "small" (what ever small exactly is in this case).

cheerz
urosh

 

[bcarso]

That ADI app note propagates tacitly the idea that the problem is the nonlinearity of the capacitance change with voltage*, which irks---all that is needed is that the capacitance changes. Now, it's true that it is also not usually (or maybe ever) a linear change with voltage---but it could be and you would still have distortion, albeit with a different spectrum.

If the impedances seen at two inputs with variable input C are equal, and the C at each varies equally, then you get cancellation of the distortion at lower frequencies. Of course most of the time the effective Cs are not equal. I empirically compensated for the distortion in a 072 voltage follower with a parallel RC between the output and inverting input, and it helped a lot but was not nearly as good as the intrinsic distortion of the opamp with no common-mode swing.



*One of my pet peeves, along with the misuse of the term "linear beta", which is almost always used to mean "beta constant with collector current".