...vacuum tube THEORY?

[Old Tele man]

...any people here interested in some "basic" vacuum tube THEORY?

[Daver]

I'm always interested in vacuum tube knowledge. Basic is good too. I never learned anything about tubes back in school, so I don't know what I've missed. What have you got for us? Class is now in session.
Dave

[hasserl]

Hey OTM, whatcha got?

[Enzo]

The tutorial chapters in the front of the RCA book are pretty concise, yet fairly thorough. An older copy of Radio AMateurs Handbook has similar material.

[Old Tele man]

...in the beginning.

...in the beginning there was Thomas Edison and the LIGHT bulb.

...when he noticed current flow toward a plate placed inside a lightbulb, the "Edison Effect" was coined.

...all vacuum tubes are descendents of the light bulb...regardless of how "bright" or "dim" they look (poor humor joke).

...Fleming sticks a flat plate inside an evacuated lightbulb and invents the "Fleming Valve" or diode...a name derived from "DI" meaning two and "ode" meaning elements, hence a two element device, the filament (source of HEAT)/cathode (source of electrons) and plate/anode ("catcher" of electrons).

...the diode is a unidirectional device (as are ALL vacuum tubes), with current passing from cathode (abbreviation K or C) to plate/anode (abbreviation P or A).

..."How much" current is determined by the Child-Langmuir 3/2's Law:

Ip = G*Vp^(3/2)

where:
Ip = Plate current, amps
Vp = Plate potential, volts
G = Tube coefficient Perveance, amps-per-volt^(3/2)

...although, theoretically based, this equation is fundamentally correct, especially for DIODES and "diode-equivalent" models of TRODES, TETRODES and PENTODES (to be covered later).

...what good is this DIODE equation? Well, once you've determined the Perveance (G) value for a given DIODE, you can determine the diode rectifiers PLATE VOLTAGE drop, the minimum plate voltage (Vp) necessary for the diode to conduct a given plate current (Ip)...and THAT enables you to estimate power supply "sag" at full power output.

[Sock Puppet]

http://www.pmillett.com/tecnical_books_online.htm

Many a fine book on this.

S.

[Old Tele man]

http://www.pmillett.com/tecnical_books_online.htm

Many a fine book on this.

S.

...yep, and I have most of those listed as well as have donated to Pete's outstanding repository of vacuum tube knowledge.

...key word: "basic" secondary word: "theory"

[Hermanni]

I've got a question. How can i determine the Perveance (G)?

[bob p]

http://www.pmillett.com/tecnical_books_online.htm

Many a fine book on this.

S.

Its a Gold Mine!

(I drew at least one of the corrected McIntosh schematics.)

[Old Tele man]

I've got a question. How can i determine the Perveance (G)?

...for diodes, it's a simple backsolving problem:

Ip = G*(V)^(3/2)

G = Ip/(V)^(3/2)

...for example, for the RCA "...5U4GB has a plate voltage drop of 44V per plate at a plate current of 225 mA." [page 95 of RCA Receiving Tube Manual, RC-26, 5/68], so it's perveanace value is 0.00077 amps-per-volt^(3/2) or "S" for Siemans:

G = 0.225A/(44^(3/2)) = 0.000771 ~ 0.00077 A/V^(3/2)

...and, the 5V3A has a plate voltage drop of 42V per plate at a plate current of 350 mA per plate, so its perveance value is,

G = 0.350A/(42^(3/2)) = 0.001286 ~ 0.00129 A/V^(3/2)

...when Ip and Vp aren't explicitly given, you can get these numbers from the published Eb-Ib curve; simply read the plate voltage (Vp) value off the curve that corresponds with the diodes "rated" or "maximum" current (Ip) value.

...as an example, the '58 GZ34 Philips data sheet lists Ip max of 250mA but no Vp value, however the "diode-line" chart [ 7R05949, dated 6.6.1958 A] shows Vp = 16Vdc at Ip = 250mA, so it's perveance value is:

G = 0.250A/(16^(3/2)) = 0.003906 ~ 0.0039 A/V^(3/2)

...but, be aware of different Perveance values from different manufacturers! For instance, the GE 5AR4/GZ34 (GE: ET-T1547, 11/59) lists Ip = 225mA and Vp = 17Vdc, thus it has a lower G value:

G = 0.225A/(17^(3/2)) = 0.003210 ~ 0.0032 A/V^(3/2)

[Hermanni]

...for diodes, it's a simple backsolving problem:

Ip = G*(V)^(3/2)

G = Ip/(V)^(3/2)

...for example, for the RCA "...5U4GB has a plate voltage drop of 44V per plate at a plate current of 225 mA." [page 95 of RCA Receiving Tube Manual, RC-26, 5/68], so it's perveanace value is 0.00077 amps-per-volt^(3/2) or "S" for Siemans:

G = 0.225A/(44^(3/2)) = 0.000771 ~ 0.00077 A/V^(3/2)

...and, the 5V3A has a plate voltage drop of 42V per plate at a plate current of 350 mA per plate, so its perveance value is,

G = 0.350A/(42^(3/2)) = 0.001286 ~ 0.00129 A/V^(3/2)

...when Ip and Vp aren't explicitly given, you can get these numbers from the published Eb-Ib curve; simply read the plate voltage (Vp) value off the curve that corresponds with the diodes "rated" or "maximum" current (Ip) value.

Thanks.

Ok, so V = (3/2)root (Ip/G)

I hope there will be more vacuum tube theory coming up.

[Old Tele man]

...here's an interesting way to visualize the "relationship" between current and voltage:

Ip = G*Vp^(3/2)

Ip/G = Vp^(3/2)

(Ip/G)^(1/3) = Vp^(1/2)

...thus, plate current (Ip) is CUBIC-root function of the SQUARE-root of plate voltage (Vp)...and since G has units of AMPS-per-VOLT^(3/2), this last equation is actually comparing VOLTS^(1/2) to VOLTS^(1/2)...where (Ip/G)^(1/3) reduces to an "equivalent" diode plate voltage [ ie: Vp(eq.diode) ], hence:

Vp(eq.diode) = (Ip/G)^(1/3)

...and this concept of "equivalent diode voltage" is the foundation of the "explaination" of how TRIODES operate.

[Steve Conner]

I always thought this was a possible explanation for how tubes get their "mojo", too.

They're the only electronic device with nonlinearities that follow a three-halves power law. MOSFETs and JFETs have square-law nonlinearities, and bipolars are exponential.

So, with some unpleasant math:

http://en.wikipedia.org/wiki/De_Moivre's_formula

you may be able to prove that tubes generate more "phat" low-order harmonics than any other device. Or maybe not, I've never tried.

[Old Tele man]

They're the only electronic device with nonlinearities that follow a three-halves power law. MOSFETs and JFETs have square-law nonlinearities, and bipolars are exponential.

...to be really honest, I wish that were 100% true, but unfortunately, it's not, darn it.

...while the "theory" is exactly 3/2's power, the reality is that tubes vary QUITE a bit, from about 5/2-power down near cutoff, where the current doesn't cleanly 'stop' but rather 'trickles down,' up to about 2-power approaching saturation, where space charge depletion comes into effect. It's really only over the "middle" (quasi-straight) portion of the conduction curves that the 3/2's-power law predominates. That's why there are so many "different" SPICE simulations, they're all trying to accommodate the non-3/2's power "edge/fringe" effects.

...all that being admitted, the 3/2's-Law *is* however valid over the normal operating range--the linear(?) "middle" portion--so that, as long as we're not operating Class-C (beyond cutoff) nor intentionally trying to make squarewaves (purposely 'overdriven' for signal clipping, ie: control grid drawing current), the 3/2's law is valid.

...this "rounding" of transistion into cutoff and saturation is what makes vacuum tubes different from the "hard/sudden" transistions of solid state devices.

[Joe Bee]

That's a clever twist, bringing up de Moivre's formula here. Checking with a ruler on the Steinberger paddle guitar that I always keep handy in my office, 3/2 the fundamental frequency corresponds to a perfect fifth, a rather musical interval. OK I _could_ have known this, but it is better to make sure, right?

I am sure that tube hifi tries to stick in the "linear" or "3/2" region of the operating curve, so maybe the warmth and alleged plesantness of tubes comes from this?

However, I am seriously confused now. I was brought up with the belief that all distortion can be expressed as a Fourier series of harmonics, and there is no such thing as a 3/2th harmonic, right? So presumably it would take a complex harmonic spectrum to describe this interval in terms of integer multiples of the fundamental, not just some 2nd and 3rd order. Does this mean we need to rethink the notion of higher order harmonics being harsh and unmusical?


Tele man, I guess I am struggeling to stay on topic here, but I have a brief comment regarding the "rounding" vs "harsh cutoff" issue. I don't think this is a fundamental property of tubes / BJTs, FETs etc., but rather of the circuits they are used in. Since silicon is cheap and plentiful, it tends to be used in Op-Amp configurations, with practically infinite open loop gain and obscene amounts of feedback. This is what causes the "first linear, then sharp cut-off" behavior. Tubes on the other hand are so expensive that you need to use all the gain you can get from one, so you have to live with all the nonlinearities, which include a soft cut-off as a sort of consolation gift.