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Modelling a vacuum tube?

  1. Nov 21, 2007 #1
    Hi all!

    OK, hopefully this will be a very quick question. Basically, I want to know how to model a vacuum tube (both triode and pentode) in terms of creating a dynamic system model. For example, if were to look at the voltage in an inductor as a function of time, I would employ the relation


    and then use something like Kirchoff's (current) law to generate a model for the entire circuit--whatever it may be.

    So, basically, I guess I have two questions now that I think about it;

    First, what sort of relations (like the one above, for example) describe the action of a valve?

    Second, what sort of relation (a-la Kirchoff's laws) would apply to the valve as it appears in the circuit? For example, if the amplifying element is an op-amp, the basic (voltage) equation is a constant-times-the-voltage-difference equation--what would I use if my amplifying element was a valve instead?

    Many thanks in advance!
  2. jcsd
  3. Nov 21, 2007 #2


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    I can't help you directly--vacuum tubes as you know are no longer part of modern technical life. I know there are some complexities--current flow at full on, for instance, is limited by space charge (electrons in the vacuum between cathode and plate repel each other...), so Child's Law comes into play.

    You can find the information you want in any old EE text. Go to your local university library and look up books like
    RCA Radiotron Handbook
    any of Frederick Terman's books
    any of the many books on vacuum tubes from the 50's and 60's

    Hmm, just went online and there are many references there, too. Here's the 2nd one I opened:
    http://www.john-a-harper.com/tubes201/" [Broken]

    Have fun!
    Last edited by a moderator: May 3, 2017
  4. Nov 21, 2007 #3
    Thanks for the author reference, I will try to make it to the library tomorrow.


    PS: I found a few online references, including the one you pointed me to, but the underlying theme seems to be to have a bunch of chit-chat with very little / no math, hence why ended up posting here, since it's actually the math I'm after :)
  5. Dec 2, 2007 #4
    I'm pretty sure the 12AX7 has been modeled. Do a Google on it.

    But, why?
    Last edited: Dec 2, 2007
  6. Dec 5, 2007 #5


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    there is still quite a market in the audio and music instrument industry for the "warm" distortion or even the real heavy-duty power chord distortion that comes from these older amps with different vacuum tubes.
  7. Dec 28, 2007 #6
    Yes, I know about that. But, if that is the intended purpose, why model it? That doesn't seem as if it would help.

    For example, probably the first heavily distorted guitar chords came from simply tearing the speaker cones. I can't imagine modeling that or putting it to any use if I could. I would simply tear the cones till I heard what I wanted.
  8. Dec 28, 2007 #7


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    Real musicians would not ruin their speakers to produce distortion. You have been misinformed. There are loads of books about how to maintain, tune up, and/or build guitar amplifiers, including some pretty good ones by Gerald Webber and a nice book about the functions of tube amp sub-circuits (with lots of Fender schematics) by Bob Funk.

    The distortion from an over-driven tube amp comes from the amp's inability to accurately produce the input signal. At one time, that was thought to be a bad thing, then distortion began to be used for effect in blues and rock and in some jazz. When you clip a transistor output stage, the wave-form is flat-topped with very sharp transitions (harsh-sounding distortion), but when you clip a tube amp, the output wave-form is more rounded with softer transitions (more pleasing distortion). Sometimes, also, rectifier tubes are chosen that cannot deliver the full power demanded by loud notes, so the volume sags on the initial attack and then blooms (sustains) as the note is held.
  9. Dec 28, 2007 #8
    Let me see if I got this right. You're saying Bo Diddley was not a real musician?
  10. Dec 28, 2007 #9


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    If you can come up with one example of a person who liked playing through damaged speakers, I can give you a thousand who wouldn't dream of damaging them. This is not how musicians achieve tube distortion. It might be distortion, but it has nothing to do with tubes. People like Stevie Ray Vaughan, Eric Clapton, Kid Ramos, cherish (-ed, in the case of SRV) their tube amps. Such musicians employ tube amp technicians to keep their amps "tuned" to give them their favorite type of distortion depending on what kind of guitar they're using (single coils usually aren't as hot as humbuckers) and what kind of modification (if any) they are making to the guitar's signal before sending it to the amp. I have restored/repaired dozens of fine old tube amps for prominent local musicians, and believe it or not, not a single one of them asked me to tear their speaker cones. Instead, they had me looking for period-correct antique speakers to replace speakers that had been damaged (usually due to water damage or an overheated voice coil). They would tell me what kind of changes they wanted in their tone, including onset of distortion, and I would bias their output tubes hotter or colder, maybe let them play with a couple of different types of output tubes/rectifiers and experiment with higher/lower-output preamp tubes, including tubes that were nicely-balanced and some that were unbalanced. I'd also substitute a potentiometer for the negative-feedback resistor and dial it in until they found their "sweet spot", read the resistance of the pot and permanently install a neg-feedback resistor of that value. This is what amp techs do - it's not a static go-it-alone process. Amp techs are intimately involved in helping their clients establish their signature tones.

    The OP's post is an intriguing one to me, because even in the plain-vanilla production of 12AX7s, in which tubes from one manufacturer were bought by the car-loads and rebranded to satisfy large contracts, the tubes made by some manufacturers were magic. Telefunken and Mullard tubes, especially, along with some of the RCA's. Due to rebranding, the only way to properly identify the manufacturer is to examine the plates, spacers, getters, etc.

    I hosted a 12AX7 ID site for a while, but eventually parked it at another tube-nut's site.
    http://www.eecs.berkeley.edu/~loarie/12ax7.html [Broken]
    Last edited by a moderator: May 3, 2017
  11. Dec 28, 2007 #10


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    I was intrigued by your question and started hunting around and found this site on vacuum tube models for SPICE. I hope it meets your requirements, or leads you to more pertinent resources.

  12. Dec 28, 2007 #11
    Oh, I quite agree with you that most musicians would never poke holes in their speakers. I've run enough 6L6s hot enough to land planes by that I understand the idea of distortion. I even used to use a coupla of Ampex amps just for that soft sound. And, yes, I remember the days before Leo Fender when we had to juice up old Lafayette amps to get decent sounds.

    But, I gave the speakers as an example of something that inherently you could not model at a useful level. And you said I was misinformed about that, so I gave you an example of someone who (I think) was a good musician who did that.

    All that said, I'm glad there are still tube people out there. I haven't built a tube amp for probably 30 years now, but I still enjoy that sound, though I prefer Howling Wolf to Stevie Ray Vaughn.
    Last edited by a moderator: May 3, 2017
  13. Jan 1, 2008 #12
    Modeling a vacuum tube (in the field called a triode or at least a simple diode), forget all of the nonsense you just read. Take an old time salt shaker, empty the salt and seal off the end and then evaculate the air. Install a plate and a cathode but don't forget the grid. If you want to advance to a pentode then I may have the answer.
  14. Jan 1, 2008 #13
    try reverse engineering

    the only thing that comes to mind is to buy a couple old tubes of different power ratings. makes sure you have the factory spec sheet and then take them apart and measure everything. reverse engineeer them to your application. there is so much that can cause you problems if you do not know what you need to do and some of the parts contain things that you can not buy. you may be stuck before you start. but if you have a ton of money to throw into a big hole I can help.
  15. Jan 1, 2008 #14

    oops....... I just read your original question again.
    tubes are current switches controlled by voltages i believe. the capacitive and inductive properties depend on each tubes physical properties. the manufacturer spec sheet would provide you with that. say a characteristic rise time when you use it to generate a square on pulse. say a modulating anode klystron. to turn the klystron current on you must apply a voltage to the anode that is constant wrt the cathode voltage to get a square wave current pulse. now the equation of the" tube as you ask" is really the sum of the whole circuit. and the klystron characteristic part is available from the spec sheet.
    i think i am probably confusing you as much as me so good luck
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