...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. :D 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 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.

[Old Tele man]

...the Child-Langmuir 3/2's Law has an invariant exponent of 3/2; real-world vacuum tubes, however, only follow that exponent over the middle portions of their "S-shaped" conduction curves, as I mentioned earlier.

...maybe a separate posting on the effects of ODD- versus EVEN-harmonics upon fundamental tone summations should be separately initiated?

[Joe Bee]

Duh, I don't know what made me do it, but I made a quick implementation of a Fourier series to plot out the power spectrum of the x^3/2 nonlinearity and it's reconstruction from Fourier components. Units are linear, not the common logarithmic dB scale, so there are a LOT of amazingly high harmonics. If I didn't do it wrong that is.

Steve, say something!

[Steve Conner]

Yes, you are right, there is no such thing as a 3/2 harmonic! The medication must be wearing off. :eek:

I've experimented a lot with trying to get soft low-order clipping out of solid-state devices. Here are some things that I found to work well:

A small MOSFET or JFET with its drain connected to its gate

A high voltage diode from a microwave oven

Both of these actually have a much softer knee than the grid-cathode "diode" of a tube! I compared them against 12AX7s and 12AU7s. So when a tube is driven into grid current, it generates a lot of high-order harmonics. It's the other end, when the grid is driven negative into cutoff, that has the soft characteristic.

My conclusion is that many people's favourite tube tones probably contain a lot of seriously hard clipping, and the low order harmonics of the tube's linear region have little to do with it. In other words, I propose that dirty blues and rock tones are basically PWM square waves like you would get from a synth, and the only really important parameter is the duty cycle and how it varies with the degree of overdrive.

I used the MOSFET clipper in an amp design, and it sounds rather, well, soft, dark and mushy compared to overdriven tube crunch.

My gut feeling has always been that you could make an amp out of JFETs, MOSFETs and BJTs that couldn't be told apart from, say, a '59 Bassman, in a blind test, even though the harmonics generated before hard clipping set in would be quite different. AFAIK, Craig Anderton used to do this at lectures: he would bring a tube guitar amp and a solid-state one, play through both and challenge the audience to tell them apart. They always failed.

Even so, if I wanted to clone a '59 Bassman I'd still use tubes :P

[MattT]

...with current passing from cathode (abbreviation K or C) to plate/anode (abbreviation P or A).
OTM has forgotten more tube theory than I'll ever know...but...isn't it electrons that pass from cathode to anode? While current actually goes from anode to cathode?

I know it seems like semantics but I can easily visualize and explain how a vacuum tube works when I think in terms of electron flow...but I can't when it comes to current flow.

[Steve Conner]

Well, current is made of electrons that flow from negative to positive! When we think of so-called "Conventional" current, flowing from positive to negative, that's just a convenient fiction.

[MattT]

I realize that Steve...that's sorta the point. When you think of it one way vs. another...it makes a difference.

To put it another way...try to explain how a vacuum tube works using 'conventional current' and not using electron flow. It's a lot harder...for me anyways.

[Old Tele man]

OTM has forgotten more tube theory than I'll ever know...but...isn't it electrons that pass from cathode to anode? While current actually goes from anode to cathode?

I know it seems like semantics but I can easily visualize and explain how a vacuum tube works when I think in terms of electron flow...but I can't when it comes to current flow....oops! my USN schooling is "showing"...USN schools taught electron flow (ie: negative-to-positive movement), whereas most other schools tend to teach current flow.

...so, obviously, I was referring to "electron" current flow (wink,wink)!

[MattT]

...that's just a convenient fiction.
I think it's extremely inconvenient! It downright sucks!:p

[Steve Conner]

Well, that's the point I was trying to make! You can't explain how a vacuum tube works with conventional current, because conventional current doesn't exist.

[MattT]

Well, that's the point I was trying to make!
Oh, sorry...I didn't realize you were trying to make a point that I had just made one post earlier.

[Old Tele man]

My gut feeling has always been that you could make an amp out of JFETs, MOSFETs and BJTs that couldn't be told apart from, say, a '59 Bassman, in a blind test, even though the harmonics generated before hard clipping set in would be quite different....like this:
http://home.comcast.net/~elmccaul/AMPS/SS_6V6_0.JPG

...from an unknown British electronics magazine many years ago...anybody remember seeing it?

[Steve Conner]

Well, I'd never seen that before, but it's the kind of thing I was thinking of... From the look of the typeface, the magazine was Electronics World, or Electronics & Wireless World, or whatever it was called at the time.

[Old Tele man]

...continue on to TRIODES?

[Joe Bee]

I am not sure if it is really as easy as that. Over at runoffgroove.com, there is a bunch of people trying to replicated classic valve circuits (mostly preamps) with JFETs, and they seem to have a lot of trouble biasing the devices correctly. Apparently FETs drift wildly with temperature, and there are huge variations between devices of the same type.
My guess that FETs were never meant to be used in the linear region, so no manufacturer ever bothered to optimize them for this purpose.

Furthermore, while I agree that most guitar sounds are wildly clipped, this does not mean that subtle nonlinearlities don't play a role too. I dont see why the power amp, which usually has a lot of clean headroom these days, could play such a big role in shaping the sound. Think about it this way: If you look at the waveform of a cello, a singer or whatever, it will probably look more like a distorted square wave than a clean sine. Still if you play it back throug an old tube radio or a modern SS HiFi, you will hear a difference. By your logic this difference should be swamped by the THD already present in the original signal.

I think Steve is a heretic and should burn at the stake! :D

[Hermanni]

...continue on to TRIODES?

Yes please

[Old Tele man]

...using the concept of "equivalent Plate voltage" the fundamental Child-Langmuir 3/2's Law (which was originally for planar DIODES) was empirically extented to include TRIODES by simply 'equating' a "scaled/reduced" combination of control-grid voltage and plate voltage to what its DIODE equivalent voltage would be:

Vp(diode) = (Vg + Vp/mu)

...here, the TRIODEs control grid voltage (Vg) is a negative voltage (called bias voltage) which exactly equals (and therefore cancels) the 'effective' plate voltage (Vp/mu), which is done by 'scaling/reducing' the plate voltage by the tubes Amplification Factor (AF = dVp/dVg)...and AF is abbreciated as "mu" which is the ratio of change in plate voltage (dVp = output) over the change in control-grid (dVg = input). Thus, the C-L equation for TRIODES becomes:

Ip = G*(Vg + Vp/mu)^(3/2)

...with the voltage within the parenthesis (...) being called the "equivalent diode voltage."

...also, notice that G is still Perveance, but now has a slightly lower value due to the presence and location of the added control-grid element (often abbreviated as g1).