Hi!

I'm doing a noise analysis of an amplifier input stage with a MAT02 transistor pair. In the datasheet, I could not find any value for the base spreading resistance, rbb. Does anyone here know what it could be or is there a way of calculating it? The datasheet says what the bulk resistance, rBE, is, but that's something completely different, right?

Thanks for your help!

/stu


bcarso

finding base spreading resistance, and other related things
« Reply #1 on: May 19, 2005, 01:52:07 PM »
If the noise data show e sub n with collector current you can fit to find rbb, as it sets a limit to the improvement at high currents.  Were it not for rbb the e sub n well above the flicker noise region (say 10kHz and up) would be that of a resistor with half the thermal noise of the reciprocal transconductance, for example like a 13 ohm R with 1mA of Ic.  And remember that the rbb thermal noise is uncorrelated with the 1/gm noise.

finding base spreading resistance, and other related things
« Reply #2 on: May 19, 2005, 07:49:48 PM »
I'm not really sure I understand what you mean. Can you explain this to me?

Quote
as it sets a limit to the improvement at high currents


In a graph showing the noise voltage density vs. collector current the noise voltage just keeps rising with increasing current. Am I looking at the wrong thing?

Quote
would be that of a resistor with half the thermal noise of the reciprocal transconductance, for example like a 13 ohm R with 1mA of Ic. And remember that the rbb thermal noise is uncorrelated with the 1/gm noise.


So the squared noise voltage would be the squared thermal noise of rbb plus the squared thermal noise of a resistor with a resistance of re/2? Did I get that right? Probably not, but answer my first question first, then explain this to me. I really appreciate your help! You teach me so much.

Thank you!

/stu

BTW, I changed the title of this thread, since this method allows you to find the rbb for any transistor.

bcarso

finding base spreading resistance, and other related things
« Reply #3 on: May 19, 2005, 08:20:02 PM »
"In a graph showing the noise voltage density vs. collector current the noise voltage just keeps rising with increasing current. Am I looking at the wrong thing?"

I guess---show me this curve.  The noise voltage spectral density should go as the square root of the reciprocal of the transconductance.  Since the transconductance goes as the emitter current, the noise shoud go down as the emitter and collector current goes up, until other effects come into play.

bcarso

finding base spreading resistance, and other related things
« Reply #4 on: May 20, 2005, 01:52:51 AM »
I found the curve.  You are right that above about 3mA things go sour. Although note that the curves are for low frequencies where flicker noise begins to rear its head.  Evidently this is also where some current-crowding effects and other issues arise.  So there is not a lot of data there to pull out rbb.  It would be nice to see the 10kHz curve with current.

But for example consider operation at 1mA.  Re is 26 ohms, thermal noise would be that of a 13 ohm R which is 464pV/root Hz at 300K.  If we attribute the rest of the noise to rbb it has to be enough to get a total of about 900pV/rt Hz.  That is an additional uncorrelated noise source of 771pV/rt Hz which is equivalent to the noise of a 36 ohm R at 300K.

(there is a small additional contribution from the shot and excess noise in the base current flowing through rbb, but this will be small for such a high beta device and a relatively low rbb)

So that's my guess as to rbb: about 36 ohms.  It basically tells us that there is little point to operating at Ic higher than about 1mA.  And this is also likely since AD/Precision Mon. would have been happy to quote an even lower e sub n if they could have.

finding base spreading resistance, and other related things
« Reply #5 on: May 20, 2005, 05:03:20 AM »
Thank you. Now I get it. This was a bit harder than I thought since most datasheets do not have any noise curves at all. That leaves me kind of clueless if I was doing a noise analysis on an amplifier with, say, a BC184 in it. Are there any rules of thumb when it comes to finding rbb for a device without knowing practically anything about its noise characteristics?

/stu

bcarso

finding base spreading resistance, and other related things
« Reply #6 on: May 20, 2005, 01:42:56 PM »
No, unfortunately.  It would seem like higher power devices would be lower becuase of the larger geometry, but then we have examples of extraordinarily low rbb devices (see Groner's 2SC3329 thread) that are quite small-signal.  Also, here and there it has been pointed out that power transistors, regardless of the actual rbb, have sucky beta at modest currents making then generally unsuitable as low noise amps.

One thing:  paralleling devices will always work to reduce rbb and the re component, given the current per device be maintained.  Of course this may not be optimal for a given source impedance since shot and excess noise is going up with the square root of n, and the capacitances are growing linearly with n.

finding base spreading resistance, and other related things
« Reply #7 on: May 21, 2005, 10:49:15 AM »
Ok. But thank you for your help.

Just one more thing I'm wondering about,

In some low-noise design books and papers you sometimes find values for F_sub_c, F_sub_T, r_sub_bb, etc for certain transistors. However, when you read the datasheets those values are not specified. Where did the authors get that information? Are there special low-noise datasheets or did they just make it up to make the books look good?

an example: page 117 in Motchenbacher Low-noise Electronic System Design shows a table of noise parameters for 12 different transistors.

I would be really happy if I could find such a table for some transistors that I already have or that I can get easily. Anyone?

/stu

bcarso

finding base spreading resistance, and other related things
« Reply #8 on: May 21, 2005, 04:13:22 PM »
Motchenbacher measured a bunch of devices for his books, doing us all a great service btw.

Some books just base their discussions on knowing typical processes of the day---Gray and Meyer et al. for example. Often the focus is on ICs so the devices tend to be on the small side compared to discrete components.

As well, the IC designers now have some fairly powerful simulators, which may well extract the parameters from a detailed 3-D modelling of the geometry and dopant profiles, etc.

If you can get hold of an old National Semiconductor Transistors/FETs databook, there are a lot of curves (although rarely if ever is rbb mentioned, and then only in the form of the collector-base time constant, which given Ccb allows you to calculate rbb).  The paperback book has a dark red cover with some transistor layouts in orange. As is often the case there is no date of publication, other than a reference to an earlier edition from 1973.  But I would guess it's circa 1975.

I have suggested that someone undertake to scan the book and post it, but PRR said his copy wouldn't survive the abuse.

National pulled away from giving this much information later, and the blue cover discrete books are very uninformative (except an early FET one).

There are a few On Semi datasheets (PRR found one a while back) which show rbb as a function of collector current (it's a fairly weak function until current-crowding effects get important).

finding base spreading resistance, and other related things
« Reply #9 on: May 22, 2005, 01:20:58 PM »
Ok. Thank you for the tips. I guess I have to do what I can with the information I have.

A short (not) question:

Consider a sziklai connection (complementary darlington, comound pair or whatever you want to call it).

When calculating the total noise voltage, is it correct to assume that:

-the mean square thermal noise voltage of the base resistances of both transistors should be summed

-only the re of the first transistor should be taken into consideration

- I have forgotten something important in doing my calculations

/stu


bcarso

finding base spreading resistance, and other related things
« Reply #10 on: May 22, 2005, 02:25:33 PM »
As a feedback pair the noise should be overwhelmingly dominated by the noise of the input device for Sziklai.  The second transistor adds lots of current gain.  One way to think of it is that the second rbb is driven by a high impedance (the collector of the first Q) so is rendered insiginificant as far as influencing second stage base current.  If there is a base-emitter R for the second device you can make a small correction for its noise and the reduction in current gain---the analysis is a little different.  You would use this resistor to increase the queiscent current in the first transistor to tailor the bias point for lower voltage noise.

Of course you could do a complete analysis for all noise sources, and it will get hairy looking, but still should show the overwhelmingly dominant noise source as the first Q's e sub n and i sub n.

For a conventional Darlington, the noise powers in e sub n of each transistor add (i.e., root sum-of-squares of each e sub n).  So there you definitely need both rbb's and r sub e's.  The conventional Darlington is not a very low voltage noise configuration.

finding base spreading resistance, and other related things
« Reply #11 on: May 27, 2005, 08:15:08 AM »
Quote
about 36 ohms. It basically tells us that there is little point to operating at Ic higher than about 1mA


Can you elabote? Why is there little point in having a higher Ic than 1 mA?

I have been thinking about this: The formula for calculating optimum collector current. It only calculates the shot and thermal noise of the transistor. If this "optimum" current is used, noise at lower frequencies will be quite high due to flicker noise which is not included in the calculations.

For example, calculating the optimum collector current for an LM394 with Rs=140 (not including rbb) gives an optimum Ic of about 3,7 mA (IIRC, I don't have the papers here now). The high frequency noise figure will be just under 1 dB at high frequencies but will start rising as frequency is decreased, already at 1 kHz there is a noticable difference. By lowering the current to 1 mA the high freq NF will be a bit higher but it won't start increasing before about 100 Hz or so.

This implies that for audio use the "optimum" Ic would be lower than the calculated, or?

Is this what you were thinking about or is it something else?

Are my ideas correct or have I misunderstood something?

Thank you for Your help!

/stu

bcarso

finding base spreading resistance, and other related things
« Reply #12 on: May 27, 2005, 10:01:30 AM »
The whole flicker noise subject is vast and still a very active topic of research---it appears that it is even linked intimately with the Riemann hypothesis!.  But considering practical audio applications, one should remember that Fletcher, Munson, and their successors have shown the sensitivity functions vs. level of aural acuity to strongly emphasize relatively higher frequencies, up to around 5-6kHz at least.  The functions are dramatically so shaped at lower levels. This is one of the reasons why the specifications on many pieces of equipment show a broadband flat 20-20kHz or so total noise, and then an "A-weighted" measurement that favors noise in the region of high hearing sensitivity.

So, if you listen with enough gain you may be able to start to hear the noise in a system at low frequencies, in a very quiet room.  But you'll be blasted out of your chair in the louder passages.

In fact even when the extreme emphasis on low frequencies occurs, such as an RIAA EQ'ed phono preamp, it is rarely the ~1/f noise region that one hears coming out of the loudspeaker (and especially after the needle is in the groove, since almost always the noise is dominated by vinyl surface noise).*

OTOH if one can minimize low freq noise all the better.  The good news is devices were getting steadily better for a while, and a few of them continue to be made in the same way so as to preserve the performance.  But the optimal operating point for a given part for low frequency noise is not likely to coincide with the best for, say, 10kHz, so there are design decisions to be made.

It is possible to do a dual-path amp and drastically reduce the low freq noise with a modulator/demodulator approach.  But it is extremely tricky to eliminate the noise at higher frequencies from the mod/demod system, which is most often a "chopper".  There is also a little 1/f noise in the choppers despite the claims of manufacturers, but it's hard to see. It is also tricky to "splice" the two amplifiers seamlessly.

To your question of why there is no point to going much higher than 1mA: the 2kTR squared voltage noise associated with r sub e is already well below the 36 ohm thermal noise at that current.  Then, as well, the curves for the MAT part look like the current-crowding effects are starting to raise rbb much above that current.  Now the 394 is definitely a lower rbb part so its optimal operating point for a low Z source is higher, as evidenced in the Jensen 990 opamp.  I was not making a general statement about the 1mA.

There might be other reasons in a given circuit, such as bandwidth, slew rate, etc. to run at higher current though.


*of course a really lousy preamp can get audible at low frequencies if you really work at it.  Reminds me of what the late Joe Weber, convinced to his dying day that he had detected gravitational waves with what most now believe to be an inadequately sensitive setup, said at a meeting: "The Uncertainty Principle sets a lower limit to how well we can make a measurement.  But it sets no limit on how BADLY [alluding to his colleagues] we can make it."

finding base spreading resistance, and other related things
« Reply #13 on: May 27, 2005, 11:45:43 AM »
Quote
The whole flicker noise subject is vast and still a very active topic of research---it appears that it is even linked intimately with the Riemann hypothesis


Yes. The flicker noise thing was one of the reasons I started thinking about the low-noise design techniques. I can't recall I've heard of the Riemann hypothesis. What is that?

Quote
OTOH if one can minimize low freq noise all the better.


Absolutely. What I am trying the figure out is if there are more advantages in lowering the operating current to a level where flicker noise start appearing at very low frequencies than in to thrust the low-noise design techniques available for calculating the optimum current.

Quote
Now the 394 is definitely a lower rbb part


Are you sure? I've read somewhere that the rbb for the LM394 was 40 ohms. However I'm almost certain that I've also read somewhere that it is 20 ohms. Motchenbacher mentiones that the flicker noise generating part of rbb is significantly smaller (typically half) of the real (thermal noise generating part) base resistance. I feel a bit confused. I'm sorry if I have messed up some of the theory. I should know it without books, but I don't. And I don't have any books with me now.

The little measurements I've made so far seem to support the calculated optimum collector current. There was little gained (or lost actually) in lowfrequency noise by lowering the collector current to 1/3 of the calculated. And of course you're right about the fletcher/munson curves.

Thank you for an interesting discussion! I enjoy it and I hope you think it's interesting too. I've learned a lot from this. I hope that I can contribute in some way.

/stu

finding base spreading resistance, and other related things
« Reply #14 on: May 27, 2005, 01:12:28 PM »
One more question popped up in my head.

Would lowering the operating current (from the calculated optimum) increase or decrease THD, or would it affect the distortion at all?

/stu

bcarso

finding base spreading resistance, and other related things
« Reply #15 on: May 27, 2005, 02:21:24 PM »
I just checked and Horowitz and Hill say 30 ohms for the 394---I'm not sure where they got that.  If so then it isn't much lower that the MAT part.  However, bear in mind that it is subject to variation with collector current and may stay low longer as that increases, compared to the MAT part.

Samuel Groner noticed the Toshiba 2SC3329 (see his recent thread with that in the Subject header) which I had also just learned of, as well as the PNP complement, the 2SA1316.  These claim a typical 2 ohms rbb (!).  If I get the chance to build the preamp I suggested to Samuel then I'll be able to tell if that number jibes with the actual performance. I hope this rbb holds up at higher collector currents where the r sub e gets small by comparison.

At some point you just have to start putting stuff together and measuring.  I've found some glaring errors in authoritative literature, and I'm sure I've made plenty of them too (not usually in print though)!  There's one imposing book published by Academic Press that has a spurious theory of FET noise, and this in an article contibuted by guys at Princeton, although in their partial defense they were astronomers and not solid-state physics experts.  But it confused me quite a bit for a while years ago.

The Riemann Hypothesis is that all of the nontrivial zeros of the Riemann zeta function have a real part confined to a small part of a line in the complex plane.  Yes, how could that have anything to do with 1/f noise, or much of anything else for that matter?  The R.H. has to do with the distribution of prime numbers and is considered to be about the most important unsolved problem in math today.  There's a really carefully written but nearly zero prerequisites book just out by a smart guy who writes really well, one Dan Rockmore, called Stalking the Riemann Hypothesis.

As far as distortion, it depends.  A lot of low-distortion open-loop or at least only-local-feedback bipolar circuits depend on compensating for the exponential/logarithmic dependence of the parts by use of other similar parts. Barrie Gilbert invented some of these. Bipolars can behave to quite a high precision in accordance with these equations over quite a range of currents and voltages.  But there are departures at extremes.  If you go to too low of currents, leakages on or near surfaces, or even in bulk start to produce errors.  If you go to high currents then bulk/contact  resistances start to get important. And then there are high-field effects, hot-carrier effects, blah blah...another nearly endless area.

If you use feedback more, then the more you can apply without screwing up the phase margin the more you make the circuit linearity that of the feedback components---and resistors are usually pretty linear.  So then it matters less what the internal distortion is.  PRR reminds us to look where the big current swings are when we are tracking down the distortion.

There is also distortion that gets important and that most simulators don't attempt to model, and that is so-called thermals.  And here is where running at higher currents/voltages can really hurt you: the signals themselves change the dissipation of the devices and shift the parameters in a messy way.  So you are back to various tradeoffs: higher speed or pursuit of lower noise means more current but more distortions due to thermals, etc.  There are circuit techniques developed by 'scope designers that can be used, where either the thermal swings are reduced or where two devices have matched thermal swings and the effects can subtract.  The best discussions I've seen are in Feucht, Handbook of Analog Circuit Design, who worked for Tektronix for a while.

BTW thermals are a good example of where sine wave testing can be quite misleading.

finding base spreading resistance, and other related things
« Reply #16 on: May 27, 2005, 03:48:24 PM »
Quote
I just checked and Horowitz and Hill say 30 ohms for the 394---I'm not sure where they got that


Probably just a rumor, but someone told me the H&H 30 ohm value was simply the mean of the two other published values, 20 and 40. If you say 30 ohms you can't be too far from the thruth then.

Quote
...the Toshiba 2SC3329 ... claim a typical 2 ohms rbb (!). If I get the chance to build the preamp ... I'll be able to tell if that number jibes with the actual performance. I hope this rbb holds up at higher collector currents where the r sub e gets small by comparison.


Yeah, that would be a fun part to play with! Please let me know how it turns out.

Quote
At some point you just have to start putting stuff together and measuring


That's were I started. Now after a couple of months of reading I feel like I'm ready to get back to building and measuring again.

Quote
As far as distortion, it depends


Of course. Ic isn't the parameter that decides the distortion. But what I meant was that if you have to make a decision about Ic vs noise the decision might be easier to make if there are other advantages/disadvantages involved too.

Quote
If you go to too low of currents, leakages on or near surfaces, or even in bulk start to produce errors. If you go to high currents then bulk/contact resistances start to get important
...
means more current but more distortions due to thermals...


That was exactly what I was looking for. The little testcircuit diffamplifier I've built with two LM394 in paralell says something like that too. THD was lowest with collector current of ~2,5 mA per device. Raising it to 4 mA increased THD from 0,0021% to 0,0034%.

Quote
I've found some glaring errors in authoritative literature, and I'm sure I've made plenty of them too (not usually in print though)!


Now you made me nervous. Someday I'll have to write all my calculations and measurements down and print them...

Quote
The best discussions I've seen are in Feucht, Handbook of Analog Circuit Design




Thank you for the tip! I'll see if I can find it.

/stu

bcarso

finding base spreading resistance, and other related things
« Reply #17 on: May 27, 2005, 06:11:56 PM »
Last time I looked Feucht was out of print but he had a website and was selling new and improved versions on CD-ROM.

Here is a funny quote from one of the great mathematicians of our time, Vladimir Arnold:

(after mentioning a long history of [ultimately productive] mistakes by famous mathematicians...):

"...Kolmogorov's initial definition of the entropy of a dynamical system was wrong, as well as Pontriagin's and Rokhlin's calculations of homotopy groups of spheres.  I would be able to provide dozens of more recent examples of mistakes in celebrated papers if I did not fear for my life."

(from "Polymathematics", in Mathematics: Frontiers and Perspectives, ed. Arnold et al. , AMS, 2000)  The whole article is a riot, although as I have stressed before, I don't get out much.

PRR

finding base spreading resistance, and other related things
« Reply #18 on: May 27, 2005, 06:52:37 PM »
> noise at lower frequencies will be quite high due to flicker noise

Yes, but the 1/f flicker corner is (for clean silicon) usually below 1KHz. And total noise is proportional to bandwidth. And what is the difference between DC-20KHz and 1KHz-20KHz? 19KHz versus 20KHz, inaudible.

Plus of course the ear's mid-high boost, and profound bass-loss at low levels (so our own footsteps resonating our head/neck don't deafen us).

> even when the extreme emphasis on low frequencies occurs, such as an RIAA EQ'ed phono preamp, it is rarely the ~1/f noise region that one hears coming out of the loudspeaker

I ran into a situation where flicker noise overwhelmed everything.

ART Research phono preamp into a commodity (Sony?) HiFi amp. Worked fine at moderate level. But this was a piano studio, the speakers were capable of keeping up with a grand piano, yet when I tried it the amp kept shutting down. Even without the needle in the groove. Only phono, not CD. And the woofer flapped frightfully. On the bench, a 1.5VDC VTVM on the output showed several-tenths volt random jerks. The volt-time product of some of these apparently would exceed the power amp's DC protection threshold as total gain was brought near realistic levels.

The phono preamp implemented the 20Hz corner with a small cap in front of the 47K input resistor. Yes, mega subsonic noise impedance. Looking at the chip's published noise curves, it all made sense.

I swapped some caps around to keep the input well damped to very low frequency, and took a 25Hz cutoff at the output, with a shunt resistor to swamp load variations. Now it was OK all the way to maximum available gain, which on most phonodisks would be well past power-amp clipping.

> Would lowering the operating current (from the calculated optimum) increase or decrease THD, or would it affect the distortion at all?

If everything is scaled, no change (until you get to extremes, as bcarso says). In fact as you go to too-high currents, 1/Gm becomes "small" compared to parasitic resistances, so you actually get more linear. OTOH thermals can bend bass bad.

For the same power output: lower current is sure to hurt, or at least force higher impedances. THD is almost meaningless unless you specify what power you want.

Some things won't scale. Parasitic resistances, and also stray capacitance. In audio and in video, useless stray capacitance often requires more current than we need to drive the real load on a "voltage amp" stage. You can move from metal TO-5 to plastic TO-92 cans, from terminal strip to PCB, to SMT, to IC, and shed some capacitance (in return for tiny eyes and tools), but you can't get rid of it.

Samuel Groner

    Z├╝rich, Switzerland
  • Posts: 2935
finding base spreading resistance, and other related things
« Reply #19 on: July 20, 2005, 07:08:13 AM »
I just read some pages in the National Linear Apps. Handbook and they quote rbb = 40 ohm for the LM394, 20 ohm if you parallel the two sections.

Samuel


 

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