DIY OTA questions

[R.G.]

Beta and Vbe will do for a start. Since both are variable, you're going to need to match them at the desired operating point, which gets tricky when the operating current varies a lot, as it does in the OTA.

As a practical matter, one could grow old quickly trying to match discrete devices for a DIY OTA. What you want is two transistors formed side by side on the same slice of silicon at the same time by the same processes - that is, monolithic pairs, trios, quads, etc. as needed. My stuff on a DIY OTA was based on the idea that inexpensive matched pairs were available.

This is really critical in the input diffamp. Matches for the current mirrors are less critical. You want the two or three transistors within a current mirror to be matched, expecially for the two-transistor version, but the smaller the current errors are in the current mirror, the less the exact nature of the Vbe and gain are within the current mirror. You just have to have enough and let feedback take its course.

It is possible to make the input diffamp be less sensitive to matching by putting emitter resistors in the emitters of both input transistors before the emitter currents join. Effectively, the V=I*R losses in the emitter resistors make any differences in Vbe not matter so much. But this directly cuts down the gain of the diffamp at the same time. It's worth trying though.

[antonis]

Should the power supply really be +/-12...?

Not at all..
Bipolar supply is used for convenient Bases bias to GND and for eliminating other bias configurations errors..
(after all, the vast majority of discrete diff amps are fed from symmetrical bipolar supply so the author wisely tries to match transistors as close as possible to their future use..)

[jonny.reckless]

It is possible to make the input diffamp be less sensitive to matching by putting emitter resistors in the emitters of both input transistors before the emitter currents join. Effectively, the V=I*R losses in the emitter resistors make any differences in Vbe not matter so much. But this directly cuts down the gain of the diffamp at the same time. It's worth trying though.

Don't you lose the exponential relationship between VBE and IC by using emitter degeneration resistors? You really care about transconductance being directly proportional to current in an OTA topology, and as far as I am aware, this means no emitter degeneration?

[antonis]

I presume R.G. refered on small value "balast" resistors for counteracting any Collector 1 - 2 current difference by acting each one to its particular V_BE and not as overall diff pair series feedback items (like "common" resistor in long tail pair configuration)..

[Rob Strand]

Don't you lose the exponential relationship between VBE and IC by using emitter degeneration resistors? You really care about transconductance being directly proportional to current in an OTA topology, and as far as I am aware, this means no emitter degeneration?

I guess the question is:  if you allow some non-linearity in gm vs Iabc (transconductance vs ail current) by adding a small amount of emitter degeneration does it help matching?   In a compressor we could handle some non-linearity in gm vs Iabc.   Off hand I thought the emitter resistors helped but it's actually tricky to compare apples vs apples.

Suppose we compare two designs:  one with 2xRE's and one without.  For apples to apples comparison we want the gm to be equal at some high-ish Iabc setting and we adjust Iabc so the gm on the two designs match.   Iabc will be higher when RE is present.  We are assuming RE isn't so large that we can't reach the target gm.   With the gm requirement, it turns out when the transistors are mismatch you get the same offset in the output current when Iabc goes from 0 to the point where the gm's match.  So when the comparison is done apples to apples like that we don't gain anything by adding RE's, even if we let gm be a non-linear function if Iabc.   Surprising result, it's like there is a Vbe offset and gm multiplies it.

As for the current mirrors emitter resistors can help the mirror help keep unity current gain when one of the transistors is mismatched.   However, it only help at high currents, high enough that the voltage drop across RE becomes significant compared to the Vbe mismatch.    At low currents it doesn't help.    I worked on a project once which used current mirrors which need to track over a wide range of currents.  The only way to do it was with good matching.   We ended-up using THAT chip transistor arrays.

[R.G.]

Don't you lose the exponential relationship between VBE and IC by using emitter degeneration resistors? You really care about transconductance being directly proportional to current in an OTA topology, and as far as I am aware, this means no emitter degeneration?

You do change the exponential relationship of collector current to Vbe by inserting a linear term (i.e. the voltage across the emitter resistor). However, that's less of an issue in an OTA. I think it principally lowers the gain of the diffamp stage, and that's not all that's going on in an OTA.

An OTA datasheet generally has some warning about not running the differential Vbe any higher than 25-50mV to keep distortion down. That distortion is the onset of Vbe-Ic exponentiality, and is generally not wanted. For these small offsets in Vbe, the diffamp input stage steers the emitter current from one collector to the other mostly linearly. There's a lot of math in OTA analysis, but for simple OTAs like the 3080, 3094, and 13700, it comes down to the differential transconductance being gm = 19.2 * Iabc. The expectation is that you will feed the inputs small differences to keep the diffamp gain linear, and modulate the gain with Iabc. The final voltage gain is gm times any load resistor. All the vbe to Ic nonlinearity for the diffamp transistors is assumed away in the analysis of that factor of 19.2, generally as "small" Vbe changes.

Iabc can be linear or not. Most of the applications I've seen feed a linear-ish or linear-ized current to Iabc; generally what you want is a linear modulator, so that you can effectively multiply the input signal times a linear current at Iabc. But it doesn't have to be that way. You >can< make this relationship exponential so the gain is linear in db (as opposed to voltage) by feeding Iabc a voltage, not a current. In this case the exponential nature of Vbe to Ic does come into play, but in the Iabc curren mirror, not the diffamp. For voltages starting at zero and increasing linearly up to the maximum current that Iabc can handle, the gm and hence gain of the OTA is an exponential function of the Iabc terminal's voltage. True, this takes some tinkering to be sure you feed it a zero based voltage that can never go over the Iabc limit for the whole OTA to keep from destroying the OTA, but it can be done. And this results in an exponential gain versus Iabc pin's voltage.

That's a long way around saying that small resistors in the individual emitters of the diffamp transistors are probably OK, and don't damage the gain proportionality too much.

er, I think. 

[PRR]

Emitter resistors limit the maximum gain at maximum current, and do "nothing" at low currents (either for gain or for balance).

If you are varying current to change gain, you get short-changed at high gain and no advantage at low gain.

Recall the intrinsic emitter impedance may vary from 100 ohms at 300uA to 10,000r at 3uA. Adding say 10 Ohms will improve balance at the top (3mV drop will better-match most modern BJTs) but have "NO" effect at 3uA (0.03mV).

In variable-gain, ballasts are generally a poor idea. They sometimes appear as a band-aid for available parts with high-level mis-match.

In fixed gain, up to a point, ballast resistors or equivalent are often used. But then an "OTA" (3080 type) is not often the best idea.

[Rob Strand]

If you have two transistors, the mismatch shows up at different Vbe's for the same collector current.   That's what is measured by the jig in the link 11-90-an posted in reply #19.

The way the mismatch appears at the transistor level, is a difference in Io.  For the two transistors,

Q1:     Ic = Io1 exp( Vbe1 / Vt)
Q2:     Ic = Io2 exp( Vbe2 / Vt)
Vt = k T / q ; k = Boltzmann's constant, q = electron charge, T = temperature [in K]

If you want the Ic of both transistors to track we set those equal to each other and we get,

  Vt * ln(Io1/Io2) = Vbe2 - Vbe1 = dVbe

What that says is for the collector currents to track (at any current level high and low) we need a constant Vbe offset between the two transistors.

In the context of the OTA tracking collector currents means no feed-through of the control current Iabc at the OTA output.

So if in theory if we add a DC offset adjustment the should track for all currents.

Unfortunately that's only a first order approximation.   The ohmic drops in the transistor can throw that off.   Think about 1mA and 1ohm difference, an impedance we would normally ignore on a small transistor, that already adds another 1mV of offset.

Some LM3080 compressor designs have an offset adjustment for exactly the reasons above and in practice the adjustment has minimal improvement  on audible feedthrough.

Another point is if you want to match transistors you should make sure that are at the same temperature,  every 1C temperature difference is about 2mV on Vbe.   So don't touch them too long.

[PRR]

> Some LM3080 compressor designs have an offset adjustment for exactly the reasons above and in practice the adjustment has minimal improvement on audible feedthrough.

Yes, because the pair is baked-in on a single die. I think this thread is about using loose transistors to avoid the high(??) cost of '3080/'13700? Then a trim may make more sense. OTOH today BJTs are baked 100,000 to a wafer, and the dopants are very consistent, so today there is a very high chance two BJTs from the same reel of tape will be near as matched as chips struggled to yield in 1974.

[jonny.reckless]

> Some LM3080 compressor designs have an offset adjustment for exactly the reasons above and in practice the adjustment has minimal improvement on audible feedthrough.
Yes, because the pair is baked-in on a single die. I think this thread is about using loose transistors to avoid the high(??) cost of '3080/'13700? Then a trim may make more sense. OTOH today BJTs are baked 100,000 to a wafer, and the dopants are very consistent, so today there is a very high chance two BJTs from the same reel of tape will be near as matched as chips struggled to yield in 1974.

I found using a pair of transistors off the same reel worked pretty well in practice. I just pulled another couple of BC549s off the reel and put them in my component tester. They are within 5mV VBE at 1mA collector current at room temp. It's good enough for me. If you're trying to build a temperature compensated high precision synth or piece of test equipment that is one matter, but for a general purpose current controlled amplifier / filter, it'll likely be more than adequate. The poor man's compressor idea was predicated on the concept of using off the shelf penny transistors because an LM13700 was over $2 at Tayda  The OTA in the PMC cost me $0.07. I'm not claiming it's the best VCA in the world, just (one of) the cheapest, and sounds OK for guitar...

[Rob Strand]

FWIW,  the ETI compressor in this thread has input offset adjustments on the OTAs,

https://www.diystompboxes.com/smfforum/index.php?topic=125145.0

No doubt the text in the original article explains the adjustment process.

[jonny.reckless]

FWIW,  the ETI compressor in this thread has input offset adjustments on the OTAs,
https://www.diystompboxes.com/smfforum/index.php?topic=125145.0
No doubt the text in the original article explains the adjustment process.

I used to love that magazine. I got my start in audio electronics building kits from there as a teenager in the 80s. That, and Maplin, had some really nice kits for very reasonable prices at the time.

[Rob Strand]

I used to love that magazine. I got my start in audio electronics building kits from there as a teenager in the 80s.

Yes, those were the days.   The magazines were the world of electronics. 

[11-90-an]

I used to love that magazine. I got my start in audio electronics building kits from there as a teenager in the 80s.

Yes, those were the days.   The magazines were the world of electronics. 

Gah! Wasn't born at that time yet...