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Are there any commonly accepted algebraic models for vacuum tube operation (triode, tetrode, and pentode)? In the same way that BJTs have a Gummel-Poon or Ebers-Moll model, and (macroscale) MOSFETs have a cutoff/linear/saturation algebraic model, is there a similar model for vacuum tubes? A DC-accurate model plus some dynamic components (dominant capacitances) would be excellent, but I'm having trouble finding any references. Higher order effects (equivalent to something like the Early effect in BJTs) would be good to know about as well, especially if they tend to impact practical designs.

I am one of the developers of CircuitLab and vacuum tubes are one of our most requested features, and I'm investigating whether it'd be practical to implement in our simulator. Thanks!

stevenvh
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compumike
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    I cannot help, but congratulation for the nice tool! – clabacchio Mar 02 '12 at 21:31
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    [An AC model of a triode tube](http://web.eecs.umich.edu/~mmccorq/diversions/simulation/index.html) - is this a good start? – Adam Lawrence Mar 02 '12 at 21:45
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    Did they even have math back then? –  Mar 02 '12 at 21:49
  • Thanks! The AC-only (small-signal) model is a start, and is helpful for showing dominant capacitances for dynamic effects, but they've already taken linearized derivatives (such as gm, rp). What I really need next is the full non-linear equations from which you could calculate those derivatives. – compumike Mar 02 '12 at 21:50
  • David is right: simulating a vacuum tube could break the space-time continuum – clabacchio Mar 02 '12 at 21:54
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    could you simulate the vacuum part using 'void'? =P – JustJeff Mar 02 '12 at 23:35
  • Jokes aside, you probably want an ancient book, like one of [these](http://www.positive-feedback.com/pfbackissues/0603/Sfbiblio.6n3.html). I have one or two of the books on that list, but I don't currently have them with me. The Chaffee book or something similar likely has what you want and more. But like Bitrex says, models useful for simulation are going to be phenomenological in nature because stuff like space charge effects are expensive to model from first principles. – mng Mar 03 '12 at 00:49
  • Actually, I have such a book, just won't have access to it until Monday. Had all the models you could want for designing amplifiers, etc. If I think of it on Monday, I might try to dig into it and post something back here. – JustJeff Mar 03 '12 at 01:46
  • +1 on http://www.circuitlab.com/ – MarkSchoonover Mar 03 '12 at 04:37
  • Another parameter to consider is the "wear" that occurs over the life of the tube. Plate current decreases for one. Another is that air leaking into the tube makes it "gassy". A real-world design probably has to consider some of this, just as transistor design considers the variation in gain among "like" parts. – gbarry Sep 17 '12 at 15:00
  • @gbarry: I wonder how such models work with circuits that adjust gain by varying the filament temperature (as Theremin's early instruments did). – supercat Jun 23 '13 at 01:37

1 Answers1

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The general small-signal model of a tube is pretty much outlined at the link Madmanguruman posted: a current source in parallel with a plate resistance and the associated inter-electrode capacitances.

For non-linear time domain analysis, the situation is more complicated as outlined here. As the article states, it's possible to derive a mathematical model of a triode or pentode based on the Langmuir-Child law, but that model doesn't accurately represent the real behavior of a tube in certain areas of its operation. The best models are "phenomenological" i.e. designed to fit a tube's actual performance curves as closely as possible without regard to underlying physics.

There is a program I've used available that will let you take published tube curves, fit the model to the curves, and then spit out a SPICE subcircuit. It works well for triodes, I don't know if it can be used for pentodes though. There are also many, many ready-to-run SPICE models of varying quality for a variety of different tubes on the web.

MattyZ
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  • That first link, and the [finding parameters](http://www.normankoren.com/Audio/Tube_params.html) page linked from it, are great. It'll take me some time to dig in to all of it, but this seems to be just what I was looking for. Many thanks! – compumike Mar 03 '12 at 05:46