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What's All This Transconductance Stuff, Anyhow?

Nov. 21, 1994
Bob debates a reader's assertions regarding the beta and transconductance of transistors.

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Recently, I received this letter: Sir: I haven't written you in a long time since you give me the "Taguchi Treatment." This is the typical "professional correctness" approach in our industry.

I was being laughed at for calling for reduced voltages applied to the output circuits of active devices OVER thirty years ago; today, two to three volts or less is becoming standard in computing. I was able to get a two-to-one change in output current in FETs, with 18-mV change in gate voltage, and with drain supplies of a few tens of millivolts applied (20 mV, for example). I knew the physics of how to do this even then.

The LM4250 op amp made by NSC is an excellent example of why this works (+/–1.5 V supply voltage). Unfortunately, I need some more of them. In measuring currents with bipolar devices, it is desirable that the current be measured with a voltage burden of not over about 5 mV. Which means that a semi-precision op amp capable of boosting a voltage of 0.5-5 mV to 20-200 mV, with a precision 5-10%, and an offset error at the input of probably not more than 0.5 mV is needed. Where can one get such beasts (instrumentation amplifiers)? Note that a burden of 200 mV measuring the current in the collector of a bipolar transistor increases device voltage gain by about 7.5, which can be enough to generate instability occasionally. Clearly, we need to be more open-minded in our profession.

Very truly yours, Keats A. Pullen

I was compelled to reply: Dear Mr. Pullen, I don't criticize anybody because of political correctness, or the lack of such correctness, but because of a lack of technical correctness.

I have noticed that for many years, you have strongly criticized engineers who think that the beta of transistors is important. In your mind, that may be a matter of political correctness, or technical correctness. BUT in many technical areas it is important to have bipolar transistors with good, well-controlled beta. In other cases it's important to have well-matched beta. If you want to argue that's not true, let's talk. But, if you persist in your insulting of any engineer who talks about "beta," and who uses beta to analyze circuits, I shall rebut you with great vigor.

I will even be happy to send you some LM4250s, as free samples, but you should be cautious because the input transistors have high beta and are matched. The internal transistors have high, matched betas, too.

I was reading recently about the "good old days" of 20 years ago, when many people were building digital circuits, computers, calculators, etc., using FETs whose thresholds might shift and move several volts over their lifetime. So, 9-V power supplies were needed to make systems that would not stop working right away. You could demonstrate that a 2-V supply was enough on any given day, but the product would not keep working. Stability of operating bias isn't trivial today and it was a serious deal 20 years ago. A scientist might be called a person who can show something working once. An engineer must figure out how to make products that will last considerably longer than the warranty period.

I will certainly agree that the transconductance of transistors is very important. We usually take it for granted because it's so consistent. But you should not say, as you usually do, that we engineers don't appreciate the gof devices just because we don't talk about it a lot. We take it for granted.

However, I have heard your claims, over the past several years, that FETs have a transconductance so good that you can get a two-to-one change in output current for an 18-mV change in the gate voltage at room temperature. Of course, that's the same as 60 mV per decade, and is equivalent to saying that the gm/mA is 38.6, which is a well-known theoretical maximum amount of gfor bipolar transistors at room temperature.

Okay, Mr. Pullen, I'll call your bluff: on EXACTLY what FET device that you have bought, or borrowed, or fabricated, have you ever measured a transconductance as good as 18 mV per octave? Or, have you seen anybody else measure such a FET? I agree that 18 mV is a theoretical limit, never to be exceeded. No FET device ever made is that good, whether MOSFET or JFET. Not just by a few percent, but by a factor of 2 or maybe, at best, 1.5. So you won't find an octave change of drain current per 18 mV; you'll find, perhaps, at best, a factor of 27 or 36 mV per octave----not NEARLY as good as 18.

I asked a large number of my friends: What is the best published data, in all of the technical literature, that indicates the transconductance of any FET----MOSFET or JFET----is as good as XX mV per octave of output current? Some of them said that the gm per mA can get extremely high, considerably higher than gm= 38.6 X I. That's if you trust your computer simulation, and if you operate the transistors at extremely low density down to the sub-threshold region, such as 0.1 µA through a transistor 1 micron long by 5000 microns wide.

I explained to these people that the story their computer tells them is untrue, because their computer is using an oversimplified model for FETs, with bad accuracy at starved levels. At high levels, every time you decrease the drain current by a factor of 4, the gm/ I does improve by a factor of 2----but that runs out of gas before you get to gm= 38 X I. The gm doesn't ever exceed 38 X I; in fact, it never attains 38 X I, yet does approach it. But not very closely. Other people knew that gm/mA approaches 38.6, and doesn't exceed it----but they agreed that they didn't know how closely, nor why. Nobody recalled reading any "best published value." Several guys pointed out that they have seen 100 mV per decade on big MOSFETs operating below 0.01 µA. That's about 30 mV per octave. Nobody had ever seen this number in the 20s.

I was helping to interview a young engineer recently, and I bounced this question off him, not expecting an answer. He simply explained that there's a virtual gate, under the gate oxide of a MOSFET. If the capacitance of this gate to ground (or, to Vsource) is relatively large, the capacitance of the C0X would cause a capacitive voltage-divider effect, so the virtual gate never sees all of the gate voltage's change. In this case, the gm/ I will typically be reduced below 38.6 by a factor of C0X/ (C0X+ Cgs ). This factor rarely gets better than 0.6. Even in cases where the gate oxide is very thin, as thin as 50 Å, the capacitance from the virtual gate will still be almost as big as the C0X. So the gm/ mA will be poor for devices with thick gate oxide----and it can get better when the gate oxide gets thinner. However, the gm/mA never gets very close to the maximum theoretical value. Has anybody seen better than 30 mV per octave on a MOSFET?

And JFETs (junction FETs) aren't very good, either. I measured some 2N5486s----a modern, high-performance N-channel JFET----and found the gmas good as 25 mV per octave, but no better, not even at starved levels such as 0.1 nA. JFETs don't give high gm/ mA, because the back gate has inferior sensitivity to the front gate. If you use a tetrode FET, with the back gate brought out separately from the front gate, the gm is even worse.

I once saw some JFETs that had gm about 38 X I, because they were implanted with such a light channel that they wouldn't conduct any current until they were forward-biased. Then they ran like a bipolar transistor, with injection and with finite base current, too. They were Enhancement-Mode JFETs.

Well, after this interview, the first thing I told my boss was, "We want to hire this guy who understands the glimitations of MOSFETs." And then I wrote down this letter.

So, Mr. Pullen, if you know where to measure any FET with a millivolts-per-octave ratio better than 25, please let us know exactly where and how we can repeat this experiment.

Yours truly, /Robert A. Pease

 p.s. Operational amplifiers with offset voltage better than 0.5 mV, such as the LM308A and many others, have been around for over 20 years. If you just connect a trim pot and optimize the offset, it's not hard to trim an op amp's offset within a few microvolts of zero. These days, offsets less than 0.025 mV or 0.010 mV, on an OP07-type amplifier, are not news----these have been around for at least 10 years. So, I don't see what your problem is. /RAP

 Then I mailed the letter.

 When I was a youngster in Connecticut, and knew almost nothing about electronics, I recall, VERY PLAINLY, reading in the Hartford Courant (about 1958), that somebody had invented a "spacistor" that would put out its current better than any existing transistor. Well, what the heck does that mean?

After about 15 years, I realized that these guys were probably talking about the first JFETs. All very good. And to this day, JFETs do many tasks very well. And MOSFETs, by the hundreds of billions, also do their jobs. They have small input currents. But, while their gm/mA is adequate, it's not astonishing. Does anybody remember the "spacistor?" Who made it?

When I began measuring real transistors back in 1961, I was really impressed with the bipolar transistor's wide range, in which the transconductance is nicely proportional to the IC , from 1 mA to 1 nA, or even lower. Hey, that's pretty impressive. And I have to concede some more respect for the late Bob Widlar, for showing that a transistor's gcan work even when the emitter voltage is higher than the base voltage, on an npn (bipolar) transistor. You can measure this on any germanium transistor at room temperature, or on any good npn at about 250ºC. So the transconductance of a bipolar transistor is a very useful, well-known, and predictable quantity. In fact, it's only when the gm gets worse than 38.6 X I that we take notice.

Ah, yes----when we work with transconductance, why do we talk about "gm?" Well, in basic circuit theory, just as the resistance of a circuit is labeled r, the conductance of a circuit is labeled g. And when vacuum tubes came along, their gain, ∆Iout/∆Vin, was in the form of a conductance. Furthermore, this was considered a mutual conductance----the voltage was applied between the grid and the cathode, and the output current flowed between the plate and the cathode. Vacuum tubes thus were characterized in terms of their mutual conductance, or gm , at a given bias. When transistors came along, we kept the same term. So that's why we have the term gm , and we still use it because it's much more compact than the phrase "transconductance."

Keats Pullen showed me an old clipping from a 1966 IEEE Proceedings, indicating that he had measured the gof some of the first experimental JFETs he ever saw, back in 1964, and he claimed they did have 38.6 milli-mhos per milliampere. But there wasn't any technical information on the device, no type number or model or part number----not even the manufacturer. In other words, this was not exactly a reproducible experiment.

More recently, Mr. Pullen argued that if we're just able to build FETs out of perfectly pure silicon, it stands to reason that the gwill behave perfectly. Sorry, but that kind of appeal to passion falls apart when you remember that you won't have any transistor at all, unless the "perfectly pure silicon" gets doped.

Furthermore, Mr. Pullen argued that vacuum tubes also have a gm of 38.6 X I. But this gm is only applicable at 25º C, where the value of q / kT is 38.6. At higher temperatures, gm falls. Why would a vacuum tube's gnot correspond to the much hotter temperature of the orange-hot cathode, or the warm space-cloud of electrons swarming around it? In fact, a vacuum tube's gm / I is rarely better than 4, which is a long way away from 38.

Then I got another letter from Mr. Pullen, pointing out that the millivolts per octave of these 1964 FETs was not 18 or 19----but 20 mV in one case, and 25 mV in the other case. All of these years, Keats has been telling us that the millivolts per octave that he had measured was 18, when actually it was 25 or 20.

I went back and measured some 2N4393s (a basic 30-Ωswitch). They had 21.5 mV per octave----a considerable ways away from 18----but not much different from the ones Keats saw in 1964.

Keats Pullen has always insisted that FETs could show an octave change of IDper 18 mV. Finally, he had to admit, when pressed, that the ones that he thought were best weren't actually as good as 18 mV per octave, but 20 mV. Well, if you mean 20, say 20, not 18.

Now, everybody I talked to said that JFETs were worse than MOSFETs, and the millivolts per octave was always worse than 25. And I was sure of that, too. And they were wrong. And I was wrong. Just goes to show... "what everybody knows" can be wrong. There's nothing like a real experiment, with real tests and real data, to puncture "what everybody knows." If any reader can tell me of any published or unpublished data, preferably from an experiment we can reproduce, showing gm better than 20 mV per octave, on any MOSFET or JFET, at 25ºC, I'd be interested to hear about it. Any theoretical analysis that explains the reasons why a JFET's millivolts per octave never gets too close to 18 would be greatly appreciated, too. Is that limitation due to doping, or geometric factors? Or something else?

All for now. / Comments invited!  RAP / Robert A. Pease / Engineer


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Santa Clara, CA 95052-8090

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