What determines a vacuum tube's perveance?

[EinsteinKreuz]

So books on VT electronics are quite hard to come by these days and many electronics textbooks don't mention thermionic valves whatsoever. I managed to find a very good vintage book : Vacuum tube and semiconductor electronics(Millman, 1958).

It describes the triode plate current characteristic curve as defined by the equation:

$$I_{A} = g_{m} = \sqrt{V_{G} + \frac {V_{A}{\mu}^{3}$$Where μ is the amplification factor and g_m is the transconductance.

But another book defines I_A = f(V_A,V_G) and expands it into a taylor series. Now first question is: Are the amplification factor and transconductance constant characteristics of the tube and if not, what are the independent variables which they depend on and how can they be calculated?

Also, is the first equation an aproximation? Because in another book it shows the triode current curves plotted against anode voltage for both negative grid voltages and one for positive grid voltage and when the grid is positive the curve has an inverted parabolic shape whereas when V_G < 0 the curves are almost linear.

So in a nutshell, what's the best fit mathematical model of the triode anode current if you know the grid voltage function V_G(t) and the voltage applied to the anode?

 

[Baluncore]

All VTs are different. There is no single best approximation equation. Triodes are very rarely operated at fixed anode voltage. The characteristics of a VT change as it ages.

If you post the tube number and the available curves of the triode you intend to use, we may be able to help you.

Why do you need the approximation? Will you model a circuit with spice or use it in a numerical model?
See the PSpice model; http://www.duncanamps.com/spicevalvesgt.html
google 'spice triode model'

Have you got a copy of “Radiotron Designers Handbook”. Langford Smith. 4'th Edn. 1952. There are .pdf copies available.

Take a look at the MIT Radiation Laboratory Series. Series index is V28. .pdf are available from; http://www.jlab.org/ir//MITSeries.html

 

[tech99]

So books on VT electronics are quite hard to come by these days and many electronics textbooks don't mention thermionic valves whatsoever. I managed to find a very good vintage book : https://www.amazon.com/dp/125832282X/?tag=pfamazon01-20

It describes the triode plate current characteristic curve as defined by the equation:

$$I_{A} = g_{m} = \sqrt{V_{G} + \frac {V_{A}{\mu}^{3}$$Where μ is the amplification factor and g_m is the transconductance.

But another book defines I_A = f(V_A,V_G) and expands it into a taylor series. Now first question is: Are the amplification factor and transconductance constant characteristics of the tube and if not, what are the independent variables which they depend on and how can they be calculated?

Also, is the first equation an aproximation? Because in another book it shows the triode current curves plotted against anode voltage for both negative grid voltages and one for positive grid voltage and when the grid is positive the curve has an inverted parabolic shape whereas when V_G < 0 the curves are almost linear.

So in a nutshell, what's the best fit mathematical model of the triode anode current if you know the grid voltage function V_G(t) and the voltage applied to the anode?

There are useful formulas in Radio Engineers' Handbook, by Terman, one of which I will try to write for you:-
Ip = k(Eg+Ep/mu)^3/2. In this formula, k is a constant called the perveance - the ability of the device to pass current. The plate voltage is divided by mu, the amplification factor, as its influence on current is less than the grid by this factor. The tube constants depend on the geometry and on the electrode voltages. mu tends to be rather constant as voltages are altered, but Gm does not. The manufacturer usually gives standard operating voltages.
If going from negative to positive grid, there is no sudden change in the curvature of the mutual characteristic, but grid current will flow, so the grid circuit must have low resistance. If the grid positive voltage approaches Ep, then it suddenly robs the plate of electrons, and the Ep/Ip characteristic then saturates, or flat tops.

 

[Old Tele man]

There is an excellent RCA in-house-published book, ELECTRON TUBE DESIGN, 1962, with information on what affects/determines a vacuum tube's "perveance." See specifically pages 753-760:

http://www.tubebooks.org/Books/Atwood/RCA 1962 Electron Tube Design.pdf