Measurement of Vp and Idss

[Rob Strand]

the so-called 3/2 power function is a very poor approximation to triode output curves
...
super impose the 12ax7 Leach graph against tube data
and easily conclude that a 3/2 power expression

You won't get much resistance from me on that topic.   I guess the appeal is it does a reasonable job without the equations getting unmanageable.

I have used these models in the past,  they try to move a small step forward,

http://www.excem.fr/download/usergui5.pdf

we all know there are two quadratic functions used to describe jFET Drain current functions
So, my point:

comparing non 3/2 power output response of tube (triode)
against sorta quadratic input response of jFET

... like comparing bananas to hotdogs

Yep.  Even the JFET model is an approximation.  Interestingly  the Fetzer largely avoids the Triode region  as Vds is not allowed to be small.  So it relies on shaping the curvature with Rs.

Another difference is the JFET is the Va dependency is somewhat weaker than a Triode outside of the Triode region.

One way to look at it is we only have a few parameters to play with but we are trying to make one thing approximate another.  Like if you try to approximate a square with a circle, you only have control of the radius.  There's a zone where it's sort work but approximations will only ever be that (I mentioned that in an earlier post),

IMO, a more proper basis of comparisons between "tubes" and jFETs can/should be established as follows:

as far as large signal behaviour is concerned a somewhat similar concavity in the input circuit response of jFETs and both types of tubes (Triodes and Pentodes) can be said to exist - tho with one important difference: in the jFET case the turn-off voltage is fixed whereas w tubes
this point moves w anode voltage

I agree with the approach but I'm much more cynical about it.    If you look at JFETs and tubes the non-linearity isn't *that* much.  Before you start clipping things the waveforms are fairly clean, especially when you have drain or cathode resistors present.   Where I see the difference is the soft-clipping region of the triodes (and pentodes for that matter) at low Vak.   Also the softness of the grid diodes.   Those are the things which come into play when you start pushing tubes.

If you look at the Peavey transtube stages they use transistors.   They model the grid diode and some duty cycle behaviour when it clips.  Maybe those things are more important than curvature, well at least for the overdrive case.

instead of getting hung up on emulating device characteristics have a look here for a DC-coupled solution to approximating the classic triode-circuit response:

http://www.lynx.net/~jc/transferCurvature-TubeSimulation.htmlTo

I've read that in the past.  I really like the idea of the modelling the first derivatives.   When you think about a 300Hz signal having harmonics under clipping up at 4kHz we might need more derivatives to capture the shape.  This type of softness is what you need to capture the soft-clipping regions and grid-diode of  tube.  A resistor in series with a silicon diode to get the first derivative doesn't quite get there.

[PRR]

> the so-called 3/2 power function is a very poor approximation to triode output curves

It's a fair approximation, though the ideal 1.5 (3/2) exponent is closer to 1.4 in commercial tubes.

This does not matter. We do not climb the lines up-right, but impose our own line up-left. Child's Law says nothing about the *spacing* of these lines in that direction.

[Rob Strand]

The Koren model is another one.

This page has a nice overlay of Real Tube vs  Koren Model  vs Leach Model,
http://hosenlander.nl/triodecalculator/index.html

The Koren model has a less convenient form for humans but no problem for computers.
In the past I didn't spend much time on it because you really need a full set of data
to feed into the curve fitter.

[fryingpan]

the so-called 3/2 power function is a very poor approximation to triode output curves
...
super impose the 12ax7 Leach graph against tube data
and easily conclude that a 3/2 power expression

You won't get much resistance from me on that topic.   I guess the appeal is it does a reasonable job without the equations getting unmanageable.

I have used these models in the past,  they try to move a small step forward,

http://www.excem.fr/download/usergui5.pdf

we all know there are two quadratic functions used to describe jFET Drain current functions
So, my point:

comparing non 3/2 power output response of tube (triode)
against sorta quadratic input response of jFET

... like comparing bananas to hotdogs

Yep.  Even the JFET model is an approximation.  Interestingly  the Fetzer largely avoids the Triode region  as Vds is not allowed to be small.  So it relies on shaping the curvature with Rs.

Another difference is the JFET is the Va dependency is somewhat weaker than a Triode outside of the Triode region.

One way to look at it is we only have a few parameters to play with but we are trying to make one thing approximate another.  Like if you try to approximate a square with a circle, you only have control of the radius.  There's a zone where it's sort work but approximations will only ever be that (I mentioned that in an earlier post),

IMO, a more proper basis of comparisons between "tubes" and jFETs can/should be established as follows:

as far as large signal behaviour is concerned a somewhat similar concavity in the input circuit response of jFETs and both types of tubes (Triodes and Pentodes) can be said to exist - tho with one important difference: in the jFET case the turn-off voltage is fixed whereas w tubes
this point moves w anode voltage

I agree with the approach but I'm much more cynical about it.    If you look at JFETs and tubes the non-linearity isn't *that* much.  Before you start clipping things the waveforms are fairly clean, especially when you have drain or cathode resistors present.   Where I see the difference is the soft-clipping region of the triodes (and pentodes for that matter) at low Vak.   Also the softness of the grid diodes.   Those are the things which come into play when you start pushing tubes.

If you look at the Peavey transtube stages they use transistors.   They model the grid diode and some duty cycle behaviour when it clips.  Maybe those things are more important than curvature, well at least for the overdrive case.

instead of getting hung up on emulating device characteristics have a look here for a DC-coupled solution to approximating the classic triode-circuit response:

http://www.lynx.net/~jc/transferCurvature-TubeSimulation.htmlTo

I've read that in the past.  I really like the idea of the modelling the first derivatives.   When you think about a 300Hz signal having harmonics under clipping up at 4kHz we might need more derivatives to capture the shape.  This type of softness is what you need to capture the soft-clipping regions and grid-diode of  tube.  A resistor in series with a silicon diode to get the first derivative doesn't quite get there.

Necro'ing the thread.
What if the source resistor were replaced with a FET used as a variable resistor, with its resistance a function of the incoming level? This way you could vary the k as needed. I don't know whether FETs are able to be used so finely.