Fundamental tube characteristics

[TheKT88KilledJFK]

Sorry if this is in the wrong area.  I am not sure where to post this.

I can't seem to find a definitive answer for characteristic equations of a tube like the 12ax7, or others.  I know they're out there because everyone seems to be using them.   I'd rather be able to predict what I should be seeing on a pin than going by a schematic. 

Does anyone have the characteristic equations for various tube models?  I just want the fundamental relationships so I can calculated circuit parameters of my own design. 

[sluckey]

Take a look at this site. Maybe buy a book or two...

     http://www.valvewizard.co.uk/

[drgonzonm]

ge published "ge essential characteristics" I have it a PDF copy on my computer.

There are some spice models for selected tubes.  I am not a user of spice.

And there's Pullen_Conductance, that might be of help.  also a free download. 

[PRR]

> characteristic equations of a tube

Messy. Non-linear.

"ALL" tube-work is done with approximations.

Or plotting on the tube graphs.

Or simply copying "Resistance Coupled Amplifier Table" suggestions. (Good enough for Leo.)

> everyone seems to be using them.

Name three. (Broskie, Merlin, and..... ?)

> predict what I should be seeing on a pin

Grid-Cathode voltage will be "about half" of Plate-Cathode voltage divided by Mu. Test this by looking at many different plans. "About half" may be more like 0.6 due to Child's Law curvature. On power pentodes, for Mu use V(g2) and Mu(g2): 10 for 6V6 6L6 EL34 etc, 18 for EL84.

Final cynical note. When I approximate live voltages for friends, they think it is a party trick. Almost NObody is willing to work-up from Fundamentals (circuits, Ohm's Law, voltage dividers) and get to where they can usefully analyze non-linear active circuits.

[TheKT88KilledJFK]

> characteristic equations of a tube

Messy. Non-linear.

"ALL" tube-work is done with approximations.

Or plotting on the tube graphs.

Or simply copying "Resistance Coupled Amplifier Table" suggestions. (Good enough for Leo.)

> everyone seems to be using them.

Name three. (Broskie, Merlin, and..... ?)

> predict what I should be seeing on a pin

Grid-Cathode voltage will be "about half" of Plate-Cathode voltage divided by Mu. Test this by looking at many different plans. "About half" may be more like 0.6 due to Child's Law curvature. On power pentodes, for Mu use V(g2) and Mu(g2): 10 for 6V6 6L6 EL34 etc, 18 for EL84.

Final cynical note. When I approximate live voltages for friends, they think it is a party trick. Almost NObody is willing to work-up from Fundamentals (circuits, Ohm's Law, voltage dividers) and get to where they can usefully analyze non-linear active circuits.

KCL and KVL, norton, thevenin, etc with DC and AC analysis are the techniques I am used to doing.  Of course, voltage division/ohms law are components of this.  I am used to solid state circuits with transistors that have approximated relationships with a given set of assumptions, but they're pretty accurate.  One of my main concerns is making sure a circuit is stable under feedback, like with a presence or depth circuit.  I also hear oscillation can also occur under specific conditions with the grid of a preamp tube.  With the typical circuits I design, I just make sure there is no poles/zeros on the wrong side of the Nyquist then test from there unless the circuit is faster than 500 KHz.   These are things I just wanted to be able to quantify.  I don't like the idea of running typical 470k grid resistors in high gain amps just because everyone else is, without testing the merit of the idea.

But yeah, the more math involved, the easier this will be for me. 

[PRR]

> KCL and KVL, ...  techniques I am used to doing.

Then you are exceptional in this crowd.

The problem with these basics (which must be mastered) is they assume linearity. Superimposed currents do a simple thing, etc. Vacuum tubes are non-linear. To a fair approximation, current rises as 1.5 power of voltage. Well, 1.2, 1.6, it varies. And then look at the lower-left of 12AX7 curves where something else is happening.

I can't find it now, but one of the early Bell papers on thermionic devices concluded that (hand) calculation was not useful because of nonlinearity.

Kuehnel's 5F6a book rather confirms this. He sets up matrixes and solves them in a way which was impractical before computers. (I'm not seeing this in the 3rd edition; did he drop it?)

Plotting on curves is the time-honored way to estimate tube operating point. With enough lines you can extract voltage gain and signal impedances; with enough eraser you can check for trouble with supply and resistor variations.

A modestly useful guide is Graphical Constructions for Vacuum Tube Circuits www.tubebooks.org/Books/Preisman_graph.pdf
Chapter I outlines the problem of analysis of circuits with nonlinear elements. Natch the rest shows how good-enough answers may be derived from available graphs. Not only for "normal amplifiers" which are not very nonlinear, but even for the Dynatron and its sharp breaks (which tend to blow-up simple analysis, even SPICE can choke if not eased over the discontinuities).

> making sure a circuit is stable under feedback

That seems rather different than what your post asked? IAC, amplification and phase are all the same whether we use transistors, tubes, horses, or tiny demons. (Feedback theory really starts with steam engine flyball governors, though with electronics we have more choice/control of values and so the theory got very deep.)

> I don't like the idea of running typical 470k grid resistors in high gain amps just because everyone else is, without testing the merit of the idea.

What difference does it make??

Well, all grids leak, so a real-high grid resistor will bias-up somewhere other than where we expected for Vg=0. Many specs give a "Max" value which is not likely to foul-up a self-bias design. Some tables suggest grounded cathode and a very large (10Meg) Rg, "using" grid leakage to make bias. Turns out this is fairly stable for healthy triodes with large plate resistors.

OTOH, a very low Rg will load-down the previous stage. You should remember that "gain is cheap" but just throwing it away does no good. Rg should be significantly larger than the driving stage output impedance.

And of course since Rg is most of the impedance, it directly figures on the size of coupling cap. And in bulk, 0.01 is cheaper than 0.02. Since essentially all audio companies eventually go broke, saving the pennies is sound wisdom.

But in many cases, 330K or 1.5Meg (with according cap values) is all the same.

[PRR]

http://tubebooks.org/technical_books_online.htm

[drgonzonm]

I agree the PRR, about ...jfk, he can handle those equations. (check his introduction)
The books on tubebook website is an excellent source.

Mathlab, Mathcad, excel, can be used to evaluate data and handle those non-linear equations.

Hardy Cross in the 20's developed pipe network analysis techniques to handle non linear equations, using lagrange multipliers to linearize non linear 2nd order equations.

Then there is spice, which I believe if you have the models can be used to evaluate amps and tubes. 

There is program, METSIM (Metallurgical Simulator), written in APL, that could probably handle the fundamental characteristics information and formulas.  (If it can't, I would be totally surprised).  The beauty of Metsim, you can use this program and create JSCHEM like drawings, provide specific information for each component, and run calculations similar to duncan. 

I am sure ...jfk, has other programs that he can use. 

Good Luck, post your results. 

[shooter]

Then you are exceptional in this crowd.

I 2nd that remark, for just the cost of shipping you can have all my math, and it has been quite extensive.  I have found the historical aspects of those before, the giants, great inspiration....for theft
If you are competent with mathlab, was a great tool for modeling the odd math, back when.  enjoy, because that's what passion is

[HotBluePlates]

... Mathlab, Mathcad, excel, can be used to evaluate data and handle those non-linear equations.
... Then there is spice, which I believe if you have the models can be used to evaluate amps and tubes. ...

It's not so much about whether there exist simulation programs (there are at least several) or whether one should analyze a circuit (they should, then view the analysis with suspicion), but whether there is benefit from using computer simulation for gnat's-ass calculation of a tube circuit.

(Apologies to the OP if I misunderstood the intent; RDH4 is available in the Library for a thorough discussion of tube characteristics and equations for common circuits).

I understand the mathematical relationships of tube characteristics, but that's also just a starting point. As PRR mentioned, I personally use characteristic curves on tube data sheets for most analysis. That's because each of the tube's characteristics changes depending on operating point, so the single numbers printed on the sheet for a single operating point may hold no relevance to your proposed circuit. Instead, they can be graphically-derived from the curves.

Except... the graphs are a convenient fiction. The curves are drawn using French curves connecting points plotted from measurement of (or theoretically representative of) a "bogey tube". The actual behavior of a tube is easily +/-20% of anything depicted on the graph. When building a circuit developed from analysis of graphs, I get pretty excited when the actual circuit behaves "close enough" to the predicted performance.

... I am used to solid state circuits with transistors that have approximated relationships with a given set of assumptions, but they're pretty accurate.  ...

Transistors & opamps have high Gm and large gain-bandwidth which enables circuit performance to be strongly defined by the external circuit resistances. But that's not the world of tubes.

That said, there are many equations to predict circuit performance of tubes (books full; over 1k pages in the case of RDH4).  Which is why we keep referencing the books... It's just too big a topic to handle in a discussion thread, unless you have a more specific question.

[mresistor]

Welcome to the forum...  that said, it's somewhat over my head when we talk about Kirshoffs laws and modal analysis..   

[drgonzonm]

... Mathlab, Mathcad, excel, can be used to evaluate data and handle those non-linear equations.
... Then there is spice, which I believe if you have the models can be used to evaluate amps and tubes. ...

(Apologies to the OP if I misunderstood the intent; RDH4 is available in the Library for a thorough discussion of tube characteristics and equations for common circuits).

Except... the graphs are a convenient fiction. The curves are drawn using French curves connecting points plotted from measurement of (or theoretically representative of) a "bogey tube". The actual behavior of a tube is easily +/-20% of anything depicted on the graph. When building a circuit developed from analysis of graphs, I get pretty excited when the actual circuit behaves "close enough" to the predicted performance.

When you deal with data known to have errors, there are techniques that allow you to account for these errors, one of my old bosses insisted that least squares was the best. This included taking data and assigning coefficients of variance to the data points.  Redundant data also provides improves overall quality of conclusions. 
 If my memory serves me, There have been several people, that have taken several  real tubes and created their own data and then compared the new tubes to old data.  from this new data spice models are created, fundamental characteristics formulas are verified.  Pure friction, if so, why use the data? 

[HotBluePlates]

... There have been several people, that have taken several  real tubes and created their own data and then compared the new tubes to old data.  from this new data spice models are created, fundamental characteristics formulas are verified.  Pure friction, if so, why use the data?

Cause "Bogey Tube" or "median value".  You design the circuit knowing that gain/Gm/self-bias voltage/etc will likely never be exactly what was calculated, but within so many % of the predicted values.

Tube manufacturers drew the original curves, and they had 10's of thousands of tested samples (and many times that actually made). But when you read information written by engineers at a manufacturer (Getting the Most out of Vacuum Tubes, 8.3MB download; see Chapter 4) you see acknowledgment that published values may not exactly align with any given tube sample.

I suppose there's no harm in generating a computer model which serves the same function as the data sheet curves: close-enough approximation.  I might be overly dismissive of computer simulation because I do the "pencil method" of drawing on data sheet curves, but within a computer graphics editor.

If SPICE models are desired, search "Norman Koren Spice Tube Model" and you'll turn up links to some. If general equations are desired, RDH4 (and the approach described in the book PRR linked) has most you'll likely ever need.

[vibrolax]

Ronald Dekker of Philips Research has done a lot of nice work making a modern curve tracer kit (uTracer 3).
http://dos4ever.com

His associate Derk Reefman http://www.dos4ever.com/uTracer3/uTracer3_pag14.html has done interesting work in extracting data from uTracer for improved LT spice models.

[drgonzonm]

If you find a tube that means bogey values you have one in google tube. 

If you take five tubes of the same manufacturer, and determine there values, you can have an estimate at what the current values and characteristics of that manufacturers bogey values. 

[HotBluePlates]

If you find a tube that means bogey values you have one in google tube. ...

Dafuq? 

If you take five tubes of the same manufacturer, and determine there values, you can have an estimate at what the current values and characteristics of that manufacturers bogey values. 

Unless all your samples skew high or low of true "bogey values" for that tube/manufacturer. You can develop bogey values for the sample-of-5 you have in-hand, but the next time you buy a tube it may not conform to the sample-of-5 predictions.

For triodes you have Gain (Mu), Gm (transconductance) and rp (internal plate resistance) which can all vary when tested at the same operating point. Overall Mu = Gm * rp, but none of those quantities is constant even for a single tube. Mu shows the least variation, so it is common to sort/grade triodes based on a measurement of Gm (and assume Mu will be constant among all samples), but that's using an assumption to simplify the matter.

I have ~100 12AU7's made by Sylvania in the mid-60's. I tested both sections of all of them using the same tube tester (to establish the same test condition) to sort them for Gm. I have them sorted in 5 different bags where each bag itself is a range of measured Gm values. All tubes are as-new, but very few out of 100 measure exactly the same. And I only measured Gm, I didn't measure in-circuit gain when placed in an amplifier. So even where Gm is exactly the same between several samples, I expect there would be some (at least small) differences of measured gain in-circuit, indicating rp was different between samples even where Gm is identical.


The point of all of the above is that with calculators, computers and digital meters, users very often develop misplaced confidence in the calculation, analysis, or measurement, simply because of the increased precision (generally, more-digits) of the result. I'm trying to flash a big spotlight on the fact that the convenient fiction of a SPICE model and computer-generated analysis is likely no better or more useful than the convenient fiction of a pencil and a data sheet curve.

The computer model may also take less work/interaction to get an answer, which also leads to the trap of not recognizing when simulation lies to you.

[drgonzonm]

google a number value equal to ten to hundredth power.

Those of us of the slide rule generation and five place logs learned engineering calculations are seldom better than three significant figures.  If you invest in oil, mining or gold stocks, be careful of estimates. The numbers usually significantly worse than the calculations generated by spice and other programs.

HBP, this thread was started by KT88...jfk, someone who has been trained stocastic and non-stocastic statistics. My comments were addressed mainly to him, I agree with you more than you realize. 

HBP, your statement regarding data on 12au7s is not unexpected, I am surprised that you found as many tubes that were that similar. 

[HotBluePlates]

google a number value equal to ten to hundredth power. ...

I know what a "google" is, and why a search company chose the name. Your sentence structure was incomprehensible, hence my reply.

[mresistor]

Well ... ya learn something new every day....  googol.....  (HPB I didn't understand what he said either)

[shooter]

The vacuum amount and gas type, are they a longevity thing only, or also a characteristic part of the tube? 
thanks

[HotBluePlates]

The vacuum amount ... are they a longevity thing only, or ...

Mostly a "production capability" thing.

It takes time and equipment to draw a very hard (meaning "closer to absolute") vacuum in a tube. A harder vacuum also implies that the glass envelope of the tube may need to be thicker/stronger.

For tubes where cost was no object (certain military systems which had to be "absolutely no fail"), harder glass formulation and harder vacuum was part of the construction formula. But so were a lot of other improvement, along with very significant de-rating below the tube's true capabilities so every sample would be absolutely guaranteed to meet the published specs over time and under severe conditions.

But that's no different than building something where 1" diameter wood dowel is sufficient but the item is built with 1" diameter titanium rod...

The ... gas type, are they a longevity thing only, or also a characteristic part of the tube? ...

Relatively few tubes (intentionally) have gas inside, and when they do it's an integral part of the tube design and characteristics. Mercury vapor tubes come to mind, as do voltage regulator tubes. You know these tubes from the pink or purple glow inside the envelope between plate & cathode.

I had a gassy tube (should have been vacuum, but had some type of gas inside) which had a nice pink glow between the plate & cathode. It was a 6AU6 which is not supposed to be gas-filled, so the moment I saw that it went in the garbage (of course, the amp didn't work with the gassy tube either).

[drgonzonm]

high vacuum, please define. 10 torr 3 torr?

thicker glass for high vacuum?  not so sure, after all at sea level looking at 14.7 psi average difference between atmo and vacuum.  Material selection to counter vibration and to address temperature extremes; definitely.

[HotBluePlates]

thicker glass for high vacuum?  not so sure, after all at sea level looking at 14.7 psi average difference between atmo and vacuum.  Material selection to counter vibration and to address temperature extremes; definitely.

Read Vacuum Tube Valley #5 if you want info on tubes with up-rated glass.

The vacuum is a non-issue since we almost never have a spec for it. It is mentioned under "Inside a Tube" and the reality is that gettering treatments are used at least partially to offset imperfect vacuum in manufacture (as well as other effects during the tube's life). Glass thickness is probably mostly about impact and temperature.

Since you really don't care about these details but like to bring them up to play stump-the-chump, I consider your last post trolling. You have been warned.

[drgonzonm]

Not in the mood to play stump the chump.  Just too lazy to research the vacuum info.  HBP, you are correct there is no spec on vacuum. From the brief quotes from RCA, there is a wide range of vacuums desired before getter action. 

I disagree that vacuum is non issue, while data is hard to find, it is out there, from a 1962 RCA book on tubes. 

Rca_1962_eletronic_tube_design.
While a pressure in finished tubes in the region of 10e-5 to 10e-7 mm Hg is expected, this degree of vacuum is attained in present receiving-tubes only by the use of getters.

The range required on trolley-processed tubes may be from 10e-5 to 2.5x10e-1 mm Hg (or 0.01 to 250 microns).

A thermnionic vacuum tube requires that its pressure be reduced for most applications to a range of 10e-6 to 10e-7 mm Hg for stable operation and good life.. Getters are used to assist the exhaust system. Typical pressures in exhausted tubes prior to action by a getter are 10e-1 mm Hg for a type 807 (6L6), 10e-4  for a type 6146 …. And 5x10e-7 mm Hg for large power tubes. 

My vacuum experience, back 40-45 years ago, is obtaining high vacuums, is a matter of time, and in business, time is money.
When a company is producing 1000 tubes/hr, being able to use getters to reduce pressure by orders of magnitude means less time spent in the vacuum process, as HBP has elegantly stated.   

[shooter]

The vacuum is a non-issue

Thanks, what I suspected.  It's hard to *purge* my old life, in MR we used a turbo-molecular pump to suck every molecule we could out of the liquid helium chamber so there was *~~zero~~* thermal conduction.  Kinda cool, you'd start out hearing a constant *scream* from the sensor, by day 3 maybe a *beep* an hour as another molecule got sucked out.

[PRR]

It is just not possible to get "every" gas atom out by sucking. Before you get there, it isn't really a "gas" any more. The atoms are so sparse that they hardly ever bump into each other. There is no trend to head for the exit. You are on the infinitely long tail of a random distribution curve.

Getting free electron flow is harder than getting "zero" thermal conduction (as hard as that may be).

The getter splash is a much bigger "exit", an inch big instead of a 1/8 inch stem. It is also "sticky", whereas an atom can bounce back from the stem as easily as bounce in.

Commercially, it also means gettering goes on for days and years without tying-up costly pumps and trolleys. Gets the time consuming part of the job out of the factory and into the warehouse.

And of course no matter how you suck at first, in-use the metals keep leaking absorbed gas. Your good vacuum would be spoiled in a month or the first over-heat. Getters maintain a good vacuum over time. As only microscopic amounts of getter are needed, most tubes are over-gettered, and we know they stay clean for decades. You hardly ever see a whisp of brown unless a seal is cracked.