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DIY Stompboxes => Building your own stompbox => Topic started by: tca on September 21, 2011, 05:19:44 PM

Hi,
I've been trying to do the calculations in Dimitri's paper http://www.scribd.com/doc/65330169/TriodeEmulatorbyDimitriDanyuk (http://www.scribd.com/doc/65330169/TriodeEmulatorbyDimitriDanyuk).
But I'm always getting
Rs=1.66*Vp/Idss instead of
Rs=0.83*Vp/Idss.
Did anyone tried to repeat the calculations in that paper? Any comments?
Thanks

I forgot that Vp was negative. ;)

Did anyone tried to repeat the calculations in that paper? Any comments?
Not really. I trust the fetzer valve calculator. :)

I never read that paper, but i guess that the fet IV eq can be expanded in a Taylor series, compared to the expanded tube eq, and then one can see under what conditions the fet eq can be "forced" to take the shape of the tube eq.
Under clipping, is this condition satisfied?
Instead of doing this, go high voltage.
mac

I've just managed to reproduce the results (figures included) with a simple numerical script in Octave (http://www.gnu.org/software/octave/ (http://www.gnu.org/software/octave/)). The value o k=0.83 just pops out easily and the precision is enough for all practical implementations.
Thanks.

Actually the exact result is:
Rs=2^(1/4)Vp/Idss= 0.840896415253715...Vp/Idss
Who says that math doesn't pay off?
:D

> "forced" to take the shape of the tube eq.
> Under clipping, is this condition satisfied?
As I read it: no.
In fact it does the wrong thing for any large swing.
His math (confirmed by TCA) shows a 3/2 law but only AT the halfway operating point. Fig 5 plots this for the entire range. The exponent actually shifts from 2.0 toward 1.0, and passesthrough 3/2 (1.5) at one point.
OTOH, an ideal tube in spacecharge is reliably 1.5. Actual tubes are 1.6 to 1.3 depending on geometry, but fairly consistent over a useful range of current.
And I *think* the tube tends to slant the other way from this degnerate FET.
(http://i.imgur.com/lUpV1.gif)
So small signals may be tubelike, but I doubt "fuzztone" is tubelike.
And the big objection: "One of a musicians reported that there is certain quality a tube amplifier must have and this design has not. It is the tubes. The reviewer could not peer inside the ventilation windows in the case and watch the tubes glow."

Actually the exact result is:
Rs=2^(1/4)Vp/Idss= 0.840896415253715...Vp/Idss
Who says that math doesn't pay off?
Congratulations, I looked hard at the explanation in the paper about getting the 0.83 value but couldn't actually get to the exact math behind it.

To add some perspective, Danyuk's triode emulator is intended for music reproduction, i.e. Beethoven's 5th Symphony. In this context, triodes in a hifi amplifier do not get close to clipping limits, and so this circuit doesn't address clipping characteristics. The idea is to add a subtle to moderate amount of harmonic distortion, let's say between 1% to 5% depending on the listener's tastes. There is a mix knob that blends the pure signal with the same signal processed by a JFET circuit that approximates to the 1.5 exponent. If you think about this, a mix of these two signals will no longer follow the 1.5 exponent rule anyway!
The relevant part here is that adding a controlled amount of loworder harmonics (mostly 2nd a bit of 3rd) is pleasant to the ear. Whether these harmonics follow a 1.3, 1.5 or 1.7 exponent rule is not as relevant as having the *right* amount in the mix, which by the way will be different from person to person.
In addition, a practical 12AX7 triode stage with bypassed cathode won't follow a pure 1.5 exponent law either, even if popular knowledge says the triode plate current follows a 1.5 exponent law with regards to the grid voltage. Why?
Let's take Child's law for the plate current: Ip = (Vg + Vp/mu)^1.5
There you have the gate voltage (Vg) and the 1.5 exponent, but you also have another term (Vp/mu) which to make things worse depends on the instantaneous plate voltage as well.
The plate voltage will be something like Vp = Vcc  Rp*Ip
where Vcc is the supply voltage and Rp is the plate resistance (here we assume there is no load on the stage)
Replacing into the first equation you get:
Ip = [ Vg + (Vcc  Rp * Ip) / mu ] ^ 1.5
Notice that Ip is on both sides and cannot be isolated on one side (as far as I know) to obtain a closed equation in the form: Ip = function( Vg, Vcc, Rp, mu )
This shows that in practice you don't get a PURE 1.5 exponent law. In addition we know that Child's law is just an approximation, so the "real world" may differ even more. *** The moral here is that the 1.5 exponent law is not as important as it appears at first sight. ***
If you want to know, I've run many simulations with different triode models comparing with a JFET circuit with different source resistors, and have come to the conclusion that a JFET with a source resistor chosen as Rs = K * Vp / Idss, where K lies between 1.5 to 2.0 is a much closer approximation in terms of the harmonic content of the resulting signal (as seen running an FFT analysis) than the 0.83 or 0.84 "magic value". Of course this is only valid in the central third of the dynamic range, as the JFET won't follow the triode saturation characteristics.
So, do we need to change the paradigm on the 0.83 magic source value? Absolutely not! Based on listening tests I really like this 0.83 value on electric guitar, and I'm sure many other people do. I've also done listening tests bypassing the source resistor in the JFET circuit to approximate to the JFET theoretical 2.0 exponent (and also adding some attenuation to compensate for the extra gain obtained when the capacitor is added, so as to compare things at a similar level). In summary, I don't like much the result with the 2.0 exponent since it gets on the harsh side to my liking. Moving in the opposite direction, I also liked the case where Rs = 1.0 * Vp/Idss, as it sounds fuller than the original guitar signal.
CONCLUSION: The above is proof enough for ME that it is a waste of energy to pursue an EXACT triode emulation. Instead, it paysoff to see which the basic distortion mechanisms are and try to get something similar that's pleasant to the ear. As the saying goes, "there are many ways to skin a cat."

> is intended for music reproduction
No, he says he tried it on "pickups (lead, bass guitar, etc)":
"Several circuits were made in the form of tube simulator (Figs.8,9), active frontend electronics (Fig.6) for various pickups (lead, bass guitar, etc) and microphone amplifiers...."
> There is a mix knob ..., a mix of these two signals will no longer follow the 1.5 exponent rule anyway!
No, of course not..... but more knobs is more to play with.
> practical 12AX7 ... won't ... 1.5 exponent ... Why?
Because there is 100:1 electrostatic feedback inside the tube, and in most any useful rig we have large plate swing.
The opposite extreme is an infinite impedance load. Now the current is fixed, Child's Law does not visit us, gain is exactly Mu and distortion approaches zero.
In most practical cases the exponent is something less, gain is less, and distortion is inbetween zero and the ~~5% of a harddriven tube. In fact it is the load which reduces practical triode THD from 10% (Danyuk's fig 2) to ~~5% at full output.
> where K lies between 1.5 to 2.0 is a much closer approximation ... ... than the 0.83 or 0.84 "magic value".
Sure. Danyuk emulated the shortcircuited triode. Useful triodes distort half as much. Your moreorless 1.7 gives half the distortion of 0.84.
It is interesting that he did not emulate a tube triode's Mu. Would have been simple with that overdone servoload.
> we know that Child's law is just an approximation
Within it's assumptions, it is exact; and cropsup in other contexts. I suppose you mean that real tubes are approximations of Child's assumptions, particularly in being noninfinite (end effects). And (especially on 12AX7) the designers knew how to exploit those "violations" to enhance gain. (12AX7's zerogrid line is far from Child's Law; grid is "too close" to cathode, by design.)
There's other deviations. Tubes at very low current density act like BJTs: 1/Gm is proportional to current. At very high current, some tubes can show "resistance" losses in cathode, making them very linear (but lowgain). (And current flattens at high current, but with oxide cathodes you Never Go Way Up There.) Conversely the 1/Gm proportional to current law in BJTs degrades into a Child's Law at very high current density. Difference is tubes conduct poorly and are usually in Child turf, BJTs conduct well and shouldn't get into Child's territory.
The JFET is actually a very different device. Tubes and BJTs have a "fence across the path". JFET has no fence, it squeezes the sides of the path.
> *** The moral here is that the 1.5 exponent law is not as important as it appears at first sight. ***
We need The Answer. The answer to everything is 42. Use a 2N4242 working at 42V with 42 ohm resistor, the mice will be happy.

You can also have the 3/2 law for any value of the operating point such that k takes the value
k=1/2*z^(3/4)
where z is the normalized input voltage. If z=1/2 one gets k=2^(1/4).

Ip = [ Vg + (Vcc  Rp * Ip) / mu ] ^ 1.5
Notice that Ip is on both sides and cannot be isolated on one side (as far as I know) to obtain a closed equation in the form: Ip = function( Vg, Vcc, Rp, mu )
Just square both sides of the equation and then use the general formula of roots for a cubic equation (http://en.wikipedia.org/wiki/Cubic_function (http://en.wikipedia.org/wiki/Cubic_function)). 8)
.. it paysoff to see which the basic distortion mechanisms are and try to get something similar that's pleasant to the ear. As the saying goes, "there are many ways to skin a cat."
I couldn't agree with you more!

Is there a particular reason for the Fetzer valve circuit to be working in common drain (with only current gain)? I haven't seen any reason in Dimitri's paper for this. Probably because of the "equivalent" triode valve circuit? Is this the only reason?
Thanks.
P.S.
This is a stupid question... see below!

> reason for the Fetzer valve circuit to be working in common drain
?? The standard Fetzer is commonsource: http://www.runoffgroove.com/oldfetzer.html
Dimitri's plan is smothered in added amplification so FET gain is not needed; however it too is wired commonsource.
(http://i.imgur.com/73JUA.gif)

?? The standard Fetzer is commonsource: http://www.runoffgroove.com/oldfetzer.html
You are obviously right... sorry about that question. I was thinking about a buffered version of the schematic!

I've written a small page explaining how the exact value of the constant k, which determines the value of the source resistor, is obtained.
http://www.diale.org/triode.html (http://www.diale.org/triode.html)
Any comments are welcome.
Cheers.

I'm kinda lost here. What "K" should one aim for in a first stage of a Fetzerbased preamp (for example)?

TCA: Thanks for your essay
I'm not qualified to proofread your math. (In a recent post I arrived at "1" when the truth was "2".)
I do know that "real" device equations may have one general trend, and many "minor" trends due to endeffect or other practical construction details.
> The basic equations that governs the behavior of a JFET, in the saturated regime
FWIW:
This is so only for "(infinitely) long channel" JFETs.
Some production JFETs are "longenough channel" to follow the equation closely.
A shortchannel JFET has lower output resistance, but also higher gain in lowimpedance loads. Shortchannel JFETs are popular in RF circuits where all loads are lowimpedance and gain is essential.
We often can not know which type "our" JFET is. Back around 1980 the manufacturers published some clues in their datasheets but the JFET market has been stagnant for years and there is little new data, and not much old data.
If you have curves, you can compare with Silconix's examples:
(http://i.imgur.com/FGV1Z.gif)
From: Designing with FieldEffect Transistors, 2nd edition, Siliconix Inc, Ed Oxner
It should be noted that vacuum triodes also have "long/shortchannel" properties. WE300B is very linear, exponent less than 3/2 over the useful range. 12AX7 is very nonlinear in some areas.
And a vacuum triode's "3/2" law is, in most simple circuits, strongly linearized by load resistance and Mu.
And this Kfudge _approximates_ a 3/2 law only over a limited range. Perhaps goodenough for 10% swings and 0.5% THD. Notthesame for guitar players who routinely slam 30% swings and >5% THD.
> What "K" should one aim for
I suspect start with >0.5 but <1.0, then trim to taste.

it helps to look at the right set of transfer curves ... have a look here:
http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html (http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html)
my approach to achieving similar Platelike wave bending goals based on biasing a jFET anywhere inside
its Vp range while providing full gain/curvature (ie., by avoidance of Source resistance)
Dimitri's plan is smothered in added amplification so FET gain is not needed
(http://i.imgur.com/73JUA.gif)
it's not about gain but more about gain curve ...
the opamp based transresistance amplifier converts Drain current to output voltage (linearly)
and fixes Drain voltage steadily via NFB in opamp // acting like an AC ground for the Drain
the intent is that the widerange (largesignal) nonlinear Grid Voltage to Drain current transfer function
is now mirrored out and converted to (usalble) voltage ... more importantly, the whole nonlinear
current transfer function now gets preserved in shape as it is made to become a voltagevoltage function ...
by providing y = ax type of transform in the transR amp (essentially shapeorder preserving)
the resistance in the Source circuit simply drops the power factor, from a 2 (undegenerated jFET) to 1.5
(undegenerated triode) ... this shows the principle at play (jFET currenttransfer test bed) and shows the ability to
hit a power function curve somewhat lower than 2 (variability)
most musicians, tho, would be happy to have as much curvature/bending (= dynamic harmonics) as possible ...

I'm kinda lost here. What "K" should one aim for in a first stage of a Fetzerbased preamp (for example)?
I would say: 2^(1/4)=0.84 plus/minus 50%.

it helps to look at the right set of transfer curves ... have a look here:
http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html (http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html)
I will read it most carefully. I've started to make the calculations to look for the possibility of getting a cascode version of the Fetzer Valve circuit. My idea is to put a constant current source at the drain of the Fetzer circuit, most like the muamplifier, but maintaining the 3/2 exponent.
Thanks.

it helps to look at the right set of transfer curves ... have a look here:
http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html (http://www.lynx.bc.ca/~jc/transferCurvatureTubeSimulation.html)
it's not about gain but more about gain curve ...
Hi Eb7+9, I do like your schematic!
(http://www.lynx.bc.ca/~jc/jFETCommonDrainBiasShifter.jpg)
I don't know how you got VP/2 (beautiful insight, though). I've redone my calculations for your case and obtained the value of VP/5 for that voltage for an exponent of 3/2. Your circuit is very inspiring: "it's not about gain but more about gain curve ..."
Actually this voltage is given by VP*(2n)/(4n) where n is the exponent. If n=0 I get your result as an extreme case. Neat!!!
In the case of the Fetzer valve circuit for Vin=0 there is not a solution for k (can anyone check this) and, obviously, the value k=0.84 plus/minus 50% is a good starting value for this parameter in this case for that particular circuit. The bias voltage for k=0.84 is 0.08*VP, almost zero for all practical implementations.

I've started to make the calculations to look for the possibility of getting a cascode version of the Fetzer Valve circuit. My idea is to put a constant current source at the drain of the Fetzer circuit, most like the muamplifier, but maintaining the 3/2 exponent.
That would be awesome. I hate the low voltage restriction while working with Fetzer stages.

In the case of the Fetzer valve circuit for Vin=0 there is not a solution for k (can anyone check this)...
Just want to correct this statement that I've made earlier (which is wrong) :[. For the Fetzer valve circuit, which has Vin=0 when no signal is applied, the value of the bias voltage is z=(1+k)^(3/2), (which is not the case in Dimitri work, z=1/2), the exact value for the constant k in this case is the solution of the equation
(1/(1+k)^(3/2)(1+sqrt(1+4*k))/(4*k^2))=0
which is k=0.78644.

I don't know how you got VP/2
well, simply put // when there is no degeneration resistance (ie., Source circuit feedback via resistor) then the total usable input voltage range is "obviously" Vp to 0 ... and so choosing a bias voltage of Vp/2 (same as Vp/2) simply translates the transfer curve so that an equal portion lies on each side of the yaxis (ie., evens out the xaxis range) ... in "this" case we maximize headroom, and that's all // in theory, that's the only purpose one would choose that applied voltage ... but in practice we can set it to whatever we like, which is really just another approach to generalized "biasing" // ie., setting the quiescent current (the first and foremost purpose of biasing) ... in the practical case there is a benefit to biasing for a lower current (one is noise) ... in another, it shortens the positive envelope range and lengthens the negative (that's the part I'm chiefly interested in here) ... since the positive side leads to a clipped waveform nothing is lost beyond the clipping limit, while on the negative side we can give the tail an extended range // this becomes important once we feed that signal to the front of a tube gain stage or another jFET gain stage as it determines the range of dynamic compression produced as a result ...
at least one forum member figured this out last year after I posted, where he applied the idea to produce a fully SS amplifier that mimic'd dynamic tubelike compression // I didn't specify exactly how to do this 'cuz I wanted to give folks room to figure out their own ways of making use of the concept ... the other cool thing about all this is that the exponential input diodelike loading function of Triodes isn't required in order for this dynamic mechanism to take place // in fact, I found that Plate and Grid curvature both "add" in the same direction to produce the compression effects // but, more so, the Plate curvature tends to dominate in this picture (!!) ... a longstanding assumption about what's required for full emulation is that both be present // indeed, peeps were for a long time missing the "what" part in the emulation picture ... ignoring the fact that not all Triodes are equal to begin with, and then the idea of emulating "a Triode" was never properly defined to begin with ...
the key to understanding this is to undo the thinking we were taught in school and textbooks which says the largesignal gain curve "should be as linear as possible"// in fact, one needs to go quite the other way here to get it ... to be honest this biz of applying a voltage directly to the Source/Cathode terminal is not a completely new idea in itself, since tube hifi "extremists" were sometimes known for biasing preamp tube Cathodes directly with batteries back in the day (mainly to get lower noise specs than provided by bias resistors) ... tho, what is new in my case, is the idea of applying that biasing approach to a jFET device for the purpose of offering a greater order of curvature (2 instead of 3/2) to play with // going beyond what Danyuk is doing in his paper ... indeed, this biz about exploiting transfer curvature for wavebending purposes is challenging a long standing paradigm in signal processing and thus further requires a conceptual shift in order to appreciate what this can do for us // indeed, in isolation it seems to really not do much except produce a deformed wave ... it's what happens to the next gain stage "as a result of this action" that is key here, once THAT deformed signal traverses a signal cap to the input of this next stage (and obviously not a linear stage either) ... this is something I discovered in '94 when I started doing my polynomial based modeling work on Triodes, which is fully described in my tube amp book IFMTA ... (see Glass Audio 2/98 for an introductory writeup)
http://lynx.net/~jc/MailletGlassAudio98.PDF (http://lynx.net/~jc/MailletGlassAudio98.PDF)
I'll say it again, getting hung up on the 3/2 power thing is not very useful here once we understand how the negative "lobe" elongation can be used to shift the DC (baseline drift) average of a signal (the first term in a Fourier series) to progressively turn off a successive gain stage // not only that, but pretty much all tube stages do NOT operate in the 3/2 power mode anyway since they typically include degeneration resistance in the Cathode circuit, something I think Danyuk missed in his argument ... in other words, peeps tend to get hung up on the wrong part of the emulation thing as a result of overlooking this greater aspect ... it's not so much the power function as much as the "concave" nature of the transfer that we "want" to make use of once we know how things work in tandem // the curvature order only gives us more curvature per amount of input signal, that's all // and even then that doesn't really matter ... we "primarily" seek to use a device that has similar transfer concavity in the SS realm, that's all really ... as I mentioned before, Danyuk came very close to figuring the whole thing out but unfortunately his approach also doesn't work well in the context of cascading gain stages ... he only looks at things from a standalone point of view
when I so decide, I will reveal my MOJO Booster circuit and fully explain what this mystery MOJO business is all about and how exactly this circuit can be used to duplicate and manipulate the dynamically degenerative mechanism of cascaded commonSource Triode circuits // it will also suggest how the naysayers of MOJO were no more those who copied/applied texttheory by rote and never gave much thought to how transfer curvature can affect/determine dynamicdependent Transient responses ... I guarantee some will flip out once they realize what can be done with this idea // in particular, one singlestage circuit in front of a good tube amp is enough to send things into an exciting dynamic synergy  which I've done at jams by using other player's rigs (axe and amp) and inserting this pedal directly in front of the amp ... it's the first of in a twopart series of interactive SS/tubeamp synergistic circuits

http://lynx.net/~jc/MailletGlassAudio98.PDF (http://lynx.net/~jc/MailletGlassAudio98.PDF)
Thanks for that. Just start reading it.

Eb7+9, I'm starting to understand what you are saying, the value of k, and hence the value of the exponent, is not really important, as long as it is high enough.
The next plots show the values of the normalized input voltage (biased at 0.5), the nonconstant part of the drain current and the FFT of the output signal for various values of k.
(http://www.diale.org/img/k01.png)
(http://www.diale.org/img/k67.png)
(http://www.diale.org/img/k84.png)
(http://www.diale.org/img/k1.png)
(http://www.diale.org/img/k2.png)
The harmonics 2th, 3rd, etc start to appear at roughly k=.67 (another "magic" value) and the relative percentage remains almost constant for higher values of k (this partially justifies the comment made earlier by stm: "...also liked the case where Rs = 1.0 * Vp/Idss, as it sounds fuller than the original guitar signal.").
The plot for k=.01 does not contain 2th harmonics because the input voltage is not high enough.
Note:
This plots were not made with a simulator.

JC (Eb7+9), I sure do wish you great financial reward for your discovery/realization.
However, I fear that you are revealing too much without any means for adequate recognition/compensation.
I guess you might have to settle for a tribute page on Wikipedia as the 'dude who finally killed the tube amp'. :\
You deserve better. I say this as the guy who has built a SS amp based on your technology.

'dude who finally killed the tube amp'.
I guess that is an over statement.
As the work of Eb7+9 shows, the only way to understand these things is to work out the math, e.g., http://lynx.net/~jc/MailletGlassAudio98.PDF (http://lynx.net/~jc/MailletGlassAudio98.PDF)
For adequate recognition/compensation only time will tell, but I do think that the best way to get all those things is to share knowledge.
Cheers.

...a fully SS amplifier that mimic'd dynamic tubelike compression...
Eb7+9, can you pin point this entry? Thanks.

I can't recall where BubbaFet mentioned finding his working example, plus the exact details weren't revealed if I recall // doesn't matter, this is an open ended problem that should be explored individually  as a result more circuits ideas will crop up ... I can give working hints when I get a chance // for now it's sufficient to say that we can produce the desired result by simply sticking a working circuit in front of a CommonCathode gain stage (frontend of a tube amp) or any CommonSource jFET gain stage based circuit ... simple enough !
as far as making dough with this idea, turns out this is not my lifetime for making that happen it seems // either I get a straight job and secure some comfort, or gamble my health in exchange for my rewards of discovery  can't have it both ways unless some form of patronage gets set up (paypal?!) ... I was destitute as a math student in university, pacing for weeks to solve a single problem, year after year // same thing with last 20 years playing electronic fantasy // honestly, I much prefer living on this side of the fence, I feel fortunate despite the many hardships along the way ... certainly, I have barely paid rent for years building my Bass preamps and other inventions but let's face it this old jet plane has had its belly rubbed real hard on the ground many times and I'm a little banged up by now (LOL) // sometimes it's not fun, but then again my sense of discovery seems to come out more when I'm not doing too well in the comfort dept. // that's just how it is for me ... I'm into the hunt for what it is, sheer thrill of discovery, and the pleasure of sharing ... but I should say, this Triode transfer emulation stuff turned out to be more than just fancyful academia in action // this is an idea that has a very fun practical side if you're a guitar player ... you'll see what it can do once you start playing with it // myself, I prefer not to look at this as tube amp replacement therapy but rather enhancement type stuff ...
if anyone feels like they could setup a donation plan for me to continue surviving that would be nice, but me and money don't seem to jive in that sense (my marketing skills simply suck too much), plus the way things are going I think I'd be waiting a long time to see any return // it's too dog eat dog anyway once you try getting into all that) ... life is finite and I have no expectation to make money from my discoveries (some of which has been many times plagiarized over and over by one of the stars on this forum) ... ultimately, that's not so important to me, I'm not here for that reason ... one thing I have thought of doing is releasing the MOJO Booster idea in the form of a kit // I'm trying to get that done before I get evicted next month ... we'll see if I can pull it off
without trying to sound too immodest I'll just say this, plugging the MOJO Booster in front of a tube amp leads to a pretty neat synergistic effect, and that is real fun for me // the idea of emulation leading to an additive dynamic push of sorts ... indeed, playing with dynamic compression goes beyond the typical blockmode compressor circuits we all know // not that they (character type circuits) are BAD or anything, for sure they have their place  but this is a little on the newish side ... for one, there is no "trailing" effect via the diodeandcapacitor charge/relaxation combo commonly seen in these types of circuits, as a result it's very natural feeling ... I had one guy race back in the club from his cigarette break after giving me his rig to play a tune on wondering "wtf" I did to get that response ... those little situations make it kinda fun, it's not just a bunch of pretentious blather but realworking stuff ... sonic rocket fuel in a little box ...
tca, I commend and thank you for your (real time) plots // they suggest bone fide classA Triode circuit action ... I bought a Nano DSO a few months ago and just realized I shoulda got the dualtrace version // with that I plan on demonstrating the idea in action in terms of a timevarying transfer profile in a somewhat similar way to how these guys did their testing of nonlinear circuit transfer:
http://www2.hsuhh.de/ant/dafx2002/papers/DAFX02_Moeller_Gromowski_Zoelzer_measurement_nonlinear.pdf (http://www2.hsuhh.de/ant/dafx2002/papers/DAFX02_Moeller_Gromowski_Zoelzer_measurement_nonlinear.pdf)
in essence this type of analysis would constitute a substantial departure from taking the (ubiquitous) SteadyState analysis approach we have all been taught in school // I could go into details why this is so, but that's a long story ... in a nutshell this is a new approach to characterizing Transient response activity in signal processing circuitry // it took many years after leaving school for me to ponder just exactly why all they teach in school is smallsignal (System) theory ... I'm parked outside a cafe and it's getting cold // I gotta cut this short, but when I get a chance we can get into the nittygritty of all that other stuff ...
cheers // and thanks for following me down this rabbit hole
~jc