I have a question about the cubic law component. Like everyone else, I
assume that fets are square law devices, and this is supported by the
clean second harmonics we get when we are only varying the Ids current
with the Vds voltage remaining constant. When Vds is allowed to vary with
signal, we start seeing some 3rd harmonic creeping in, and when the gain
variation due to Drain resistance matches against variation due to
transconductance, we see that "sweet spot" has clean 3rd harmonic with
the second having been cancelled.
Is this related to what you are talking about? Otherwise I'm somehow missing
that in the distortion readings of these devices in ordinary analog use.
Well, Nelson, in the end, you have far more experience with how these guys will work in the amplifier, so I won't pretend to know the answer.
But there is plenty of theory about what we can expect. The cubic law is not a "law" in my mind because there is not a physics-based reason for preferring that relationship. But the same is true for the so-called square law unless we are talking about MOSFETs. An idealized but common derivation for the long-channel MOSFET transfer characteristic is a square law. What happens in real devices is another matter. According to practically every text book, the rectangular channel JFET is not expected to have a square law, except as an approximation to the actual physics. That approximation is often observed empirically, at least for the low power variety of JFET, so you are not necessarily wrong for assuming that. Nevertheless, I did work out the Taylor series approximation to third order as recommended by Sze, and it is clear from the form of the derivatives that all terms above linear are non-zero. The square term is dominant, but the cubic term is there. No surprise that faint cubic harmonics are reported in RF mixers. I'm assuming we got em too.
A SemiSouth JFET channel is trapezoidal (an artifact of manufacturing) and heaven knows what the actual transconductance shape should be because of manufacturing variation. Thus, whatever you see has to be assumed to be device dependent. This is really what I am reporting in the article. As you get closer to threshold, the experimental data clearly deviates from a square law. The Spice model doesn't and thus gets it wrong. But up in Id where you usually bias them, the curve fits pretty well with a quadratic polynomial. It's all in the bias point and how far you modulate away from it.
But that's the transconductance. The modulation of drain current by drain-source voltage involves potential barrier modulation caused by field penetration into the channel. The shape of the output curves vary from part to part because the geometry and doping vary from part to part. Incidentally, I think this is part of the fun of playing with your amps with different JFETs and bias points. Lots of possibilities exist for optimization.
My conclusion from all of this is that we need to take quality data of the output curves and then analyze them simultaneously for Vgs and Vds variation, because that is what the amplifier will do. I have a curve fit process for doing that that I will post in the next article. I've been using that to help me understand calculated residual distortion in an amplifier. I have not experimentally checked the analysis yet, so frankly I'm not sure what will be the outcome. But I'm basing the analysis on experimental data taken from actual parts, which must be relevant. Stay tuned!
We save that BS for discussion over in the Pass Pub....
This stuff here iz the real deal and I won't describe my degree of excitement about reading it....
Wonderful article Dr. Mike - thank you very much for taking the time to write it and share it with us!!!
Hmmm, two of my favorite topics, women and wine. I'm now old enough that I can't remember which comes first.
Hmmm, two of my favorite topics, women and wine. I'm now old enough that I can't remember which comes first.
Then you have arrived
Dr. Mazzola, the knowledge in your current article and that in The Sweet Spot article by Mr. Pass go hand in hand. But; a few audio DIYers have the equipment to test and characterize semiconductors per your teaching and Mr. Pass. May I suggest that SiC JFETs etc.. be characterized for their sweet spots. This impotant performance attribute will simplify our lives and speed up our activities.
I will be starting on extensive F6 amp thingie and will be doing a lot of variation with the r100 and its operating points. I would argue that Nelson's points of operation are probably a pretty safe bet to work with. I have 8 transistors and will test them all for Yfs and leakage before putting them in the circuit and playing with rail voltage and bias.
Hmmm, two of my favorite topics, women and wine. I'm now old enough that I can't remember which comes first.
There is a nice little lounge tune called "Fast Cars, Naked Women", which sums
it up nicely.
Thanks for the explanation. Its been 22 years since I operated at the
Threshold (that's a joke, son!) it explains why I don't see much cubic.
Thanks for the explanation. Its been 22 years since I operated at the
Threshold (that's a joke, son!) it explains why I don't see much cubic.
Attachments
Thanks buzzforb. Your results will be valuable. You will be dedicate fun time and energy to determine their sweet spot. A small risk of inadvertent burnouts is probable for this valuable semi. I hope that you publish the findings.
The sweet spot of R100A in diy F6 is approximately: [Vds = 23 V, Idss =1.4 A, and Vgs ~1.2 V]. Thanks to Mr. Pass, lhquam, Zen Mod, buzzforb, flochinni, generg, and countless others for disclosing and practicing this valuable characteristic. Some of you may need to know the sweet spot for R085A!.
- Can I deduce the "average sweet spot" from published data sheets of typical performance. Variability?
- Is the sweet spot of a single R100A important; or use an average value for the R100A family due to the unavoidable intrinsic variability of their characteristics?.
- Is there a mathematical expression emanating from the Physics of the device which one could use to determine the average sweet spot.
- The sweet spot methodology is also applicable to MOSFETs e.g. [IRFP240], and BJTs e.g. [2SC4004]. How do I arrive at their average sweet spots.
Best regards
Hmmm, two of my favorite topics, women and wine. I'm now old enough that I can't remember which comes first.
Mike
Remember that being associated with a university skews the curve. Those in your classroom and labs keep you thinking young.
For me, at some point, it didn't matter which came first.Best
Bob
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Mike
Remember that being associated with a university skews the curve. Those in your classroom and labs keep you thinking young.
Best
Bob
Ha Ha! You got that right. The average age of this town plummets every August.
But the risks for not practicing defensive driving are in anti-phase. I do have a dim memory of those days. I seem to recall the latter (wine) helped with the former (women), but then I got married.
all you need is THD measuring shebang , along with few braincells dedicated to it's use
I'm always lacking in at least one of these two
when your F6 is going to sing ?
Thanks Zen Mod. I am still collecting parts for my diy F6; I am the slow diy step; but thanks to Mr. T and Mr. b for the high caliber of their service and offerings.
The published idle operating points and junction temperature of each semiconductor in [for examples] BA3 Front End, F5 and F5T, L'Amp a simple SIT etc., are their sweet spots. I believe that you are saying not to bother with the sweet spot of the individual device; but rather with the net outcome %THD of the resulting [multi-semiconductor] amplifier; regardless of the potential variability of their intrinsic sweet spots.
Mr. T and Mr. b. and others supply audio DIYers with matched power devices for FW amps. I'll go back to a past E-mail and determine whether the matching of R100A was done at the sweet spot. I vaguely remember the answer to be yes. I'll post the results.
The buzz is the sweet spot.
N.B. The following are the results for matching the R100A
The Semisouth R100A transistors have been sorted. They are ready to ship.
They were measured at 1.55-1.60A @ 23V on a heatsink that varied from 54-56c. This is the assumed voltages and current for both the J2 and F6.
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My simplistic understanding of certain points made in Mike's article boils down to this: I still don't understand why he spent all that time on the BJT?
Certainly the area of operation around the threshold is a non-linear area. Looking at the "You Won't Find a Linear Transistor Hear" box I see Gate/Base voltage as it relates to Id/Ic with constand Vd/Vc. A rising bias I, correlates to a higher Gate voltage and a change in the fx. In a typical transistor (IRF240) we apply enough bias to get good linear "sound" wich ussually means .5A to 1.5A or higher. Just as the paper points out. The first area to avoid is low threshold. Does this come down to the relative "size" of the device? If we use a 100A transistor we are cutting our throat from the begining because we wont be far enough up on that Vgs threshold curve operating at 1.5A Iq? N.P. always says we want that bias as high as we can stand it. Or is it, above that knee in the Vgs vs Ids curve?
When N.P. asked about the fx being measured as a square law funtion, I thought 2SK170, well Hell, we are operating at .1Vgs, way up on the curve from pinch-off (threshold) it's a nice strait line up there. Trying to do that with an output part is different... I guess that explains his answer
These ideas were all with the Drain Voltage held constant. I beleive N.P. was eluding to and interaction with the drain behaviour that allows for 2nd order H cancelation I didn't really get that from this article
Certainly the area of operation around the threshold is a non-linear area. Looking at the "You Won't Find a Linear Transistor Hear" box I see Gate/Base voltage as it relates to Id/Ic with constand Vd/Vc. A rising bias I, correlates to a higher Gate voltage and a change in the fx. In a typical transistor (IRF240) we apply enough bias to get good linear "sound" wich ussually means .5A to 1.5A or higher. Just as the paper points out. The first area to avoid is low threshold. Does this come down to the relative "size" of the device? If we use a 100A transistor we are cutting our throat from the begining because we wont be far enough up on that Vgs threshold curve operating at 1.5A Iq? N.P. always says we want that bias as high as we can stand it. Or is it, above that knee in the Vgs vs Ids curve?
When N.P. asked about the fx being measured as a square law funtion, I thought 2SK170, well Hell, we are operating at .1Vgs, way up on the curve from pinch-off (threshold) it's a nice strait line up there. Trying to do that with an output part is different... I guess that explains his answer
These ideas were all with the Drain Voltage held constant. I beleive N.P. was eluding to and interaction with the drain behaviour that allows for 2nd order H cancelation I didn't really get that from this article
In all fairness, Dr. Mazzola presented new and valuable [measured] data for R100 in his paper as shown in the Figure which is entitled "You won't find a linear transistor here". The like Figure 4 of the attendant datasheet of R100 is of lesser value to DIYers; but shows clearly that Vgs is ~1.1 V. Also, Figure 1 of the attendant datasheet [Id vs. Vds with variable Vgs] did not show the region of interest for audio.
Dr. Mazzola. Please consider generating a Figure 1 and a Figure 4 like in the official data sheet; but for audio application. Noting that the approximate sweet spot for R100A is [Vds ~ 25 V, Idss~1.5 A and Vgs ~1.2 V]. Thank you.
NB. The curves like in the Figure of the paper are tremendously valuable. This Figure has data for sweet spots. For example, the last curve to the right: [Vds constant ? [cascode] , Ids = 0.5-0.6 A, and Vgs ~ 1.4 V].
Dr. Mazzola. Please consider generating a Figure 1 and a Figure 4 like in the official data sheet; but for audio application. Noting that the approximate sweet spot for R100A is [Vds ~ 25 V, Idss~1.5 A and Vgs ~1.2 V]. Thank you.
NB. The curves like in the Figure of the paper are tremendously valuable. This Figure has data for sweet spots. For example, the last curve to the right: [Vds constant ? [cascode] , Ids = 0.5-0.6 A, and Vgs ~ 1.4 V].
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