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Testing emission without risk

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DF96, I have several textbooks on vacuum tubes that use dozens of pages liberally sprinkled with math that explain what I've explained here in one page. So, simplification is essential. If I wrote a Ph.D exposition for you, it would not help the other members of the forum one bit, and probably not your good self either. And I haven't got the time.

As it happens, I did my undergrad course, in Electronic Engineering and subsequently a thesis on robot diagnosis of printed circuit assembly faults, and a 2nd thesis on switchmode (multi-phase Class-D) power amplification somewhat over 40 years ago. We were taught grey body theory, cavity radiators, thermal emissivity, etc in 1st year - its bread and butter stuff for an E.E. Electronics generates waste heat, and we have to get rid of it in a controlled temperature manner. For the same reason I know quite a bit about convection - I know how to accurately estimate exiting air temperature in rack-mounted equipment, for example. As you will realise, I have passed official retirement age, but I am still doing consultancy work.

It IS common for emissivity to rise with temperature. But, in this thread, it doesn't really matter whether its' common to many materials or not. Oxide coatings of cathodes are known to show emissivity rising with temperature - known by me and the authors of papers I have consulted anyway. Oxide cathodes are near white (in the thermodynamic sense as well as visually) at low temperatures and that's a fact.

You asked a very valid question, and I have answered it. Rather than just comment on what might be well known or not well known, if you are a physicist, have a go at a theoretical study and see if you can refute it. Or add to it. If you do, I'll be very greatfull, as then we'll both learn something.

Your expression "emission moving into the wavelength region where the surface has higher emissivity" is just a long way of saying "emissivity changes with temperature" as far as I am concerned - becaue we know that the radiation energy moves to shorter wavelengths as temperature increases. There's not two effects, it's just the one and the same effect.

Keit
 
Your expression "emission moving into the wavelength region where the surface has higher emissivity" is just a long way of saying "emissivity changes with temperature" as far as I am concerned - becaue we know that the radiation energy moves to shorter wavelengths as temperature increases. There's not two effects, it's just the one and the same effect.
OK, now I know why I was confused - you are conflating two different effects: emissivity change with temperature (at constant wavelength), and emissivity change with wavelength (at constant temperature). When someone talks of emissivity changing with temperature I naturally assume that they are speaking of the former, not the latter.

A very rough analogy would be a claim that a receiver has more gain when tuned in to a signal. In reality the receiver gain does not change, but the spectrum of the signal more closely matches the passband of the receiver. In physics such distinctions matter. Having done postgrad research in both physics and EE departments I am aware of the difference in modes of thinking which can occur.

I was puzzled because I could not think of a mechanism which would make emissivity vary much with temperature, but change with wavelength is obvious. It may be that the authors of the books/papers you have read made the same mistake.

I am not asking for a PhD thesis (I already have one of my own on Class E PA). If you want us to check your ideas (which I think is why you posted here?) then you should not be surprised if we press you on details.
 
DF96, you are making a distinction that has relevance to coloured bodies (a coloured body is analogous to your tuned radio receiver). We are talking about grey bodies. Per Plank Law - with these, a change of temperature MUST be accompanied by a change in the peak wavelength. The books don't need to make a distinction in this context - indeed emissivity is by standard definition a constant that goes in the Stefan-Boltzmann equation known to all engineers (and hopefully, most physicists), and that equation simply has no accounting for coloured bodies. And neither do I need to make a distinction.

There is a thing called spectral emissivity - emissivity measured at a specified wavelength - which is of importance in testing vacuum tube designs in the factory, because the glass used in tube envelopes pretty much blocks infrared radiation, leaving only the visible, which is at the red end of the spectrum. They measure the intensity of the red light to get a rough verification that the cathode temperature is correct. It's not relevant to this discussion. If it was, I would have used the term spectral emissivity.

No argument with your view my request for a check on an idea implies an invitation to press for details (in this case why would there be a corelation between electron emissivity and thermal emissivity), but that isn't what you are doing. What you are doing looking for semantic flaws at best, and trying to cover up or excuse your unfamiliarity with the topic at worst.

You asked a quite relavent question, and I answered it. If you had said it had been a long time since you studied grey body theory, and asked for a definition of emissivity, I would have simply given it.

Nothing you've written since my answer invalidates my answer. That, of course does not mean my answer is not invalid because of some other reason not discovered by me and not discussed by on this forum.

Now, can we move on, and find what that/those undiscussed reason(s) is/are? I wouldn't be all that surprised or upset if there is some reason. As I said before, over my lifetime I've learnt that nearly every time I've had what seemd a good idea, it turned out that someone else thought of it before, and/or there is a good reason why it's not in use. Or would you like to measure some tubes yourself? A power supply or two, a couple of suitable pots, and a couple of DVM's is all you need.

Keit
 
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What about effects of the electron emission itself causing cathode cooling. The hottest electrons are the ones to "boil" off (thermal velocity). I have seen articles on energy conversion, where e- emitting surfaces (in a diode) were used to convert thermal energy directly to electrical energy.

When a large tube transmitter is keyed, one can even see the final tube filaments darken (inside section) during key down. (Assuming the B+ xfmr is separate from the filament xfmr. to avoid voltage drop effects.)

There would also be a confounding effect from using voltage drive for the filament illumination. A colder filament would draw more filament current and heat up some to compensate. Various time constants would come into play for a key down condition. This might be useable for determining electron emission efficiency, just key the B+ or grid1, and watch the effect on filament current. This would not necessarily have to be at or near limiting cathode current, so could be non-destructive also. Possibly could be enhanced using a bridge circuit (comparing filament currents), with two similar tubes, one of them keyed for plate current and the other not.

One can see a drop in cathode emission readily on a curve tracer. Old tubes just won't reach the high currents that the new ones will (for the same curve tracer settings). Lowering the filament voltage will cause the curves to shrink down as well (reduced plate current). And conversely, bringing the filament voltage up further can increase the emission for old worn tubes.

One has to be careful though in comparing tubes on the curve tracer between different manufacturers, because some manufacturers tubes just require more g2 voltage (for a pentode) to get the same curves. Some error in cloning the tubes I presume.
 
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What really would be useful, is some means of measuring cathode emission efficiency while the tube is in actual operation (say in an amplifier). Then some readout could be given of the tube's quality. Time to service limit, etc.

Runner up might be a power on test performed by a uP.

Could maybe square wave modify the bias voltages and monitor (synchronously) the filament current responses. Or, conversely, maybe square wave modify the filament voltages, and synchronously monitor the operating currents. For a fully differential amplifier setup, one might be able to do these tests at a sub-sonic rate during operation using a quiet sine wave modulation.

One caveot: Modifying the operating "currents" themselves directly, might not show an effect, since the same cathode current may cause the same cathode cooling effect.
 
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Keit said:
Your expression "emission moving into the wavelength region where the surface has higher emissivity" is just a long way of saying "emissivity changes with temperature" as far as I am concerned - becaue we know that the radiation energy moves to shorter wavelengths as temperature increases. There's not two effects, it's just the one and the same effect.
Keit said:
DF96, you are making a distinction that has relevance to coloured bodies (a coloured body is analogous to your tuned radio receiver). We are talking about grey bodies. Per Plank Law - with these, a change of temperature MUST be accompanied by a change in the peak wavelength. The books don't need to make a distinction in this context - indeed emissivity is by standard definition a constant that goes in the Stefan-Boltzmann equation known to all engineers (and hopefully, most physicists), and that equation simply has no accounting for coloured bodies. And neither do I need to make a distinction.
These two statements appear to contradict each other. The first says that emissivity depends on wavelength (i.e. the cathode surface is not a grey body) which gives rise to an apparent change in emissivity with temperature; the second says that it does not (i.e. the cathode surface is a grey body).

What you are doing looking for semantic flaws at best, and trying to cover up or excuse your unfamiliarity with the topic at worst.
I am looking for an explanation from someone who claims to understand things better than I do. A change in emissivity with temperature seems to lie at the heart of your idea, yet you seem to continue to conflate this temperature-dependence with wavelength-dependence - yet from a grey body! However, as I seem to be unable to achieve clarity I will drop it. A pity, as I was interested in your findings.
 
Reply for Smoking-Amp:-

There are two opposing effects I didn't mention: 1) electron emission cooling, which is often visually noticeable in directly heated tubes, very noticeable in tungsten filament tubes, and 2) joule (i-squared-R) heating in the emissive layer electrical resistance of oxide coated cathodes. The oxide coating is a semiconductor and the resistance surprisingly high, reducing gm below what the tube electron geometry and cathode temperature should give.

As I tested by measuring the ratio of two heater currents, both with grids and anode left open circuit, there is no electron cooling and no emission current heating.

Your 3rd paragraph is a litlle unclear - I assume it is a proposal for how to measure electron cooling, and for tungsten filament transmitter tubes is quite vaild. But not vaild for oxice-coated cathode receiving tubes, due to the joule heating comfounding the test.

When doing an emission test at lower or higher heater voltages, results can be affected by a number of phenomena. I have several tubes that test just a little low at normal voltage but are no worse at 80% voltage. I have a couple that fail at 120% voltage. It depends on what the cause of low emission is. A straight emission test can pass, even if the cathode is weak, if the tube is quite gassy. Of course if you know the tube is gassy, you should reject it for that reason. By accurately plotting emssion current over the range of anode voltage in the schottly region, you can easily pick gassy tubes, but that is also a good way to ruin usuable tubes, even wth pulse testing.

Re some tubes needing a different sceen voltage or taking a different screen current: Tubes that are supposed to be pentodes are often beam tetrodes, and vice versa. A noted example is the 3V4 battery output "pentode". When originally designed by RCA tube engineers, they chose a pentode structure. Most, but not all, manufacturers' datasheets describe it as a pentode. And every one of them used a beam tetrode structure. Another example is the KT88. As design by BGE, it's a beam tetrode. but some European and Chinese made KT88's are pentodes.

Re emission testing of filament response with square wave filament energisation: This is an old idea, mentioned in Wagener's "Oxide Coated Cathodes Vol 2" published in English in 1951. It avoids inaccuracy in starderd emsision testing directly heated tubes, especially power tubes and rectifiers intended for series heater chains and therefore having qite high filament voltage ratings. It gives no practical benefit for indirectly heated tubes.

Re testing emission while the tube is in operation: This is actually theorectically possible! A tube with relatively low emission has a less dense electron cloud around the cathode. Recall that only a portion of electrons in the cloud (known as the "virtual cathode") get accelerated towards and into the screen grid and anode. Most just buzz around near the cathode, contullay returing to the cathode.

This "virtual cathode" electron cloud, as it comprises electrons continually exchanging themsleves with their brothers in returning and arising out of the cathode, is thus effectively one plate of a capacitor connected to the cathode. The other plate of the capacitor is the grid.

I've measured the grid-cathode capacitance of receing tubes over a range of heater voltages with a Q-meter method, which lets you measure changes down to 0.01 pF or better. Unfornuately that's the order of the change. Tiny. And of course the grid-cathode capcitance is acutely sensitive to grid bias.

So, a circuit could be devised to monitor the grid-cathode capacitance using a frequency different to the circuit's functional frequency, and calculate a compensation for grid voltage. Doesn't sound easy though!
 
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DF96 said "These two statements appear to contradict each other. The first says that emissivity depends on wavelength (i.e. the cathode surface is not a grey body) which gives rise to an apparent change in emissivity with temperature; the second says that it does not (i.e. the cathode surface is a grey body)."

There is no conflict. DF96 simply does not understand the terminology of thermal physics. He should go look up the subject in his physics books.

A grey body, or a white body, does not emit all wavelengths at equal ENERGY, it has equal EMISSIVITY at all wavelengths.

For any given temperature, a white or grey body emits energy most concentated around a certain wavelength. That wavelength depends on the temperature, and can be calculated by suitable evaluation of Plank's Law to derive Wein's displacement Law.

Plank's Law describes the response curve of emitted energy of a black (perfect emitter) body. A grey body emits on the exact same curve, reduced in amplitude at all wavelengths by the emissivity value, which for all surfaces must lie between zero (no emission at all) and unity (an emitter that emits 100% of what is theorectically possible.

A coloured body is an emitter that departs from the Plank Law curve shape.

We think of the Sun's light as "white". Laymen may think that means all visible wavelengths are at equall intensity. But they are not, even though the Sun is an almost perfect black body emitter with a black body temperature about 5800 K.
 
Keit said:
A grey body, or a white body, does not emit all wavelengths at equal ENERGY, it has equal EMISSIVITY at all wavelengths.
This is precisely my point, yet you seem unable to grasp the consequences of it. If apparent emissivity changes markedly with temperature, as you claim, then this either means some significant change in the surface (e.g. a phase transition - which nobody has mentioned thus far) or the surface is not really grey but coloured so what is actually being seen is a variation with wavelength which favours higher temperatures as the emitted spectrum shifts. As an engineer you may wish to conflate these two effects together, but as a physicist I must maintain their distinction.

Anyway, I said I will drop it so reluctantly I will do just that.
 
There is NO phase change in cathode material. It's an approximate 50:50 molar mix of barium oxide and strontium oxide in the same micro-crystal phase from the day the tube is activated in the factory, until the glass envelope is broken (these oxide are not stable in air).

You are now being totally silly. You yourself nominated a mechanism by which a substance can display a higher emissivity as temperature is increased, without departing from being a grey body. And there are other ways - including indeed a phase transition, though this does not happen in tube cathodes.

Go and do what I suggested - go and read up a good text book on the subject. Failing that, read the following carefully and ponder it.

A material such as a mix of barium and strontium oxide, and a multitude of other substances, including most metals (see note), shows an emissivity of value e1 at temperature T1, and a higher emissivity e2 at a higher temperature T2. At temperature T1 the substance is not coloured - that is the emissivity is the same value for all wavelengths. And at temperature T2 the emissivity, while it is a higher value, is STILL the same for all wavelengths. In other words, the substance is not coloured at T1 and not coloured at T2 either. And generally not coloured at any temperature in between. It's grey all the time. It's just that the TOTAL emission over ALL wavelengths has increased by a perecentage beyond what would be expected from the Stefan-Boltzmann law with constant emissivity. The S-B Law says that energy emission is proportional to the 4th power of temperature multiplied by the emissivity.

As I said, typical cathode coatings show emissivity smoothly increasing from about 0.1 at room temperature to about 0.3 at operating temperature. That's a fact, and has nothing to do with being coloured.

Note 1: With mill finish metals such as nickel, used for many vacuum tube parts, the increase in emissivity with temperature is only slight. But it does occur. And, no, nickel is not coloured, not visually, and not in the thermal physics sense at infrared.
 
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Keit said:
You are now being totally silly.
Thank you for your kind remarks.

You yourself nominated a mechanism by which a substance can display a higher emissivity as temperature is increased, without departing from being a grey body.
I did not. A surface with cavities will be coloured. I believe you suggested cavities as a possible mechanism?

As I said, typical cathode coatings show emissivity smoothly increasing from about 0.1 at room temperature to about 0.3 at operating temperature. That's a fact, and has nothing to do with being coloured.
In that case, your postulated cavity explanation cannot be true.
 
I said that cathode coatings become porous and that increases thermal emissivity (ie at any temperature). I never said that porosity or cavities causes emissivity to become temperature dependent though. In fact they can but need not.

But in your post yesterday 11:37 AM, you said "I guess surface effects could play a role, as cavity-like surface features would have a greater effect as peak emission goes up in frequency with temperature." Which is actually correct!

So, it's a mechanism YOU suggested, not me.

But no matter, random cavities, pores, whatever, do not in themselves make a surface coloured, nor take away any colour. Optically polished alauminium has no colour, nor polished aluminium nor aluminium with a tactile rough surface.

You can make a surface coloured by ruling a grating into it with micometer spacing, or some other periodic indentation, eg a dot pattern, but this has no relevance to cathodes.

Incidentally, it says in Wagener (see 1951 ref cited earlier) that the pore size in cathode coating relevent to recieving tubes is of the order 1 to 10 um. At the temperatures relavent to this thread, the longest significant wavelength is around 0.6 um. So, porosity/cavities, which YOU suggested as a possible mechanism, is entirely plausible, but cannot be the full story.
 
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In my last paragraph, my 1st para was meant to read as follows:-

I said that cathode coatings become porous and that increases thermal emissivity (ie at any temperature). I never said that porosity or cavities causes emissivity to become temperature dependent though alignment with changed wavelengths. In fact they can but need not.

In the last sentence of the 2nd para, it should read "Which is actually correct, but there is more to it than you realise!"
 
Further to SmokingAmp's comment that a test for emission with the tube in circuit and in use would be nice:-

If the application can tolerate brief interrruptions, another way suggests itself. For almost the whole period of the vacuum tube being the primary active device (ie before the transistor), factory tube design engineers never figured out how to measure the cathode temperature accurately. And that is a key parameter - a little low and the tube life is shortened. A little high and its still shortened, but for different reasons.

In theory cathode temperature can be inferred by measuring the retarding field current (ie with the anode negative) but variations in cathode coatings, heater wire guage, etc, prevented it from being accurate.

But in June 1954, NEC Japan engineer S Ikehara published in J. App. Phys. a method involving using the tube to generate harmonics from a sinewave added to a small negative anode voltage, plus manipulation of teh grid voltages, and claimed it was accurate. He presented lab measurements to support his idea, but tested only a handfull of tubes.

If the Ikehara method is indeed accurate, indeed if it merely just gives a different result, you could compare the apparent cathode temperature with that determined by testing with DC, and infer a "cathode health" figure of merit.

Another possiblity is using a computer model to calculate the cathode temperature accurately from measurement of the heater voltage/current curve and use this to calibrate the DC retarding field test. Not difficult now (I've used such accurate computer modelling of vacuum tubes myself), but there were no computers available to tube engineers back in the tube days. PC's and microprocessors were then a few decades in the future.
 
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You said (post 14)
Keit said:
A); As cathode matetial is depleted (essentially, turned into gases, some of which coat other electrodes, and some which are absorbed by the gettering on the glass), the cathode coating, which is slightly rough to begin with, is left porus. You may remember from high school science that rough surfaces have greater thermal emissivity than do smooth surfaces. Porus surfaces have even greater thermal emissivity due to -in effect - they comprising lots of little "cavity radiators".

So cause (a) causes an increase in thermal emissivity, naturally more noticeable when temperature is low. This temperature-dependent change is enhanced by the change to shorter wavelengths of significant energy in black-body/grey-body radiation as temperature rises.
You said (post 33)
I said that cathode coatings become porous and that increases thermal emissivity (ie at any temperature). I never said that porosity or cavities causes emissivity to become temperature dependent though alignment with changed wavelengths. In fact they can but need not.
These appear to conflict.

But in your post yesterday 11:37 AM, you said "I guess surface effects could play a role, as cavity-like surface features would have a greater effect as peak emission goes up in frequency with temperature." Which is actually correct!

So, it's a mechanism YOU suggested, not me.
You appear to propose this mechanism in post 14 (quoted above).

But no matter, random cavities, pores, whatever, do not in themselves make a surface coloured, nor take away any colour. Optically polished alauminium has no colour, nor polished aluminium nor aluminium with a tactile rough surface.
Cavities/pores etc. will make a surface coloured (although not necessarily in the visible spectrum). This is because the effect of the cavity depends on the relationship between its size and the wavelength. A very small cavity may be merely a scatterer (although even that may be wavelength-dependent - which is why the sky is blue). A large cavity increases absoption and emissivity. Hence a surface with cavities is likely to have greater emissivity at smaller wavelengths.

You can make a surface coloured by ruling a grating into it with micometer spacing, or some other periodic indentation, eg a dot pattern, but this has no relevance to cathodes.
Colour due to periodic structures is a separate issue; this can work even when the structures themselves are small compared with a wavelength, as it is the periodicity which is relevant not the feature size.

In the last sentence of the 2nd para, it should read "Which is actually correct, but there is more to it than you realise!"
I am sure that there is more to it than I realise, but I am struggling to learn from someone who seems to feel the need to insult me from time to time. Can we concentrate on the physics from now on?
 
Regarding the method at hand of varying the filament current and measuring resistance. I take it that this (indirect) measurement of thermal emissivity is expected to predict the cathode wear, or decline, in electron emission of the tube. Do we have any data to support some predictable relationship here?

For the capacitance measurement approach, I imagine the evaporation of cathode material onto the grid would further complicate matters, although this might just be transferring dielectric from on location to another in the "capacitor".

Measuring sub pico-Farad capacitances sounds like it would have numerous confounding factors, like dielectric evaporating off the tube socket lead wires or humidity.

How about a measurement where the negative voltage on the grid/plate is varied, and the grid current gets measured at several points?

Reaching for more desperate measures, maybe a weak axial magnetic field along the cathode axis could be varied until neg. or zero bias (both grid and plate at low V) grid current is cut off at some value. This assumes that the size of the electron cloud is related to thermal electron velocity, and that emission is having some effect on that. Or sweep the bias V for a fixed magnetic field, and measure grid current. (An axial B field has been tested and does vary actual tube parameters like Rp in the normal operating region. I think this leaves Mu alone, so gm must vary as well. Baxial => higher Rp and lower gm)
 
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DF96 - By all means concentrate on the physics - but bring in a new aspect, rather than just trying to defend with semantics a position that has no validity.

You claim to be a physicist. So please go away and read a good text on thermal radiation, the Stefan-Botzmann Law, Plank's Law, Wein's Displacement Law, and understand the meaning of emissivity and spectral emissivity. If you haven't learnt from me, that's fine, learn from books instead.

The increase in thermal emissivity with temperature in grey bodies does not require a colour change, visible or otherwise, and that's the sum, total, and end of it.


Nothing you have written invalidates in the slightlest way the answer I originally gave (even supposing there is a colour change in the emissive surface), so go away a find something that does.

How about measuring a few tubes yourself. There's nothing like a good play in the Lab to straighten out one's thinking. Or are you just an armchair debater?
 
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Response to SmokingAmp 3:01 AM:-

1. "Regarding the method at hand..." In the post I made starting this thread I mentioned that I had tested a number of tubes I have on hand for emission using the standard way of testing emission given in the Radiotron Designer's Handbook and elsewhere. By this means I identified which tubes had good emission, and which tubes had poor emission, and to what degree. Some of my tubes are recently purchased NOS, some were taken from scrapped equipment and are up to 70 years old. I then measured the heater current at 25% and 100% rated voltage, and computed the ratio. The ratio was consistently higher in low emission tubes that were not excessively gassy. But I only tested one type - RF pentodes. I will purchase more tubes on ebay and other sources and test more types, such as power tetrodes, which I don't currently have in sufficient numbers for statistical confidence.

2. Evaporation of cathode material should not be a problem, as the coating is very thin, in the range 15 to 50 um. This sensibly neglible compared to the grid-cathode spacing. Socket lead wires would be a problem. Humidity I expect would not be - heat from the tube will lower humidity in the vicinity of the socket. To measure such tiny capacitance changes requires the use of the Q-meter method or some other form of resonance test. That requires a stable inductance and/or an accurate variable capacitance - both not insurmountable, but definitely issues to be addressed.

3. Measuring grid current at several points: This make it possible to distinguish between tubes that are gassy from good tubes and tubes that have grid emission from contamination with cathode material. I can't see that it has any merit in assessing cathode emission or in assessing the tube any any way other than grid contamination of tube gassy-ness. Only minute quantities of cathode material transferred to the grid are needed to make quite a difference in grid current.

4. Weak axial magnetic fields. Hmmm. I'l have to think about that one. Note that emitted electron velocity is not correlated with emission. To understand why, imagine a cathode with an excessive number of dead spots or excessive porosity. Or even a directly tube with DC fed filament, these sometimes have one half the filament good, and one half low emission, due to the emission current aiding the heating current on the postive filament half, and cancelling in the positive half. So one half runs a high temperature, the other low temperature. In such cases the electron mean velocity is normal, but there are fewer electrons. That will still reduce the capacitance, as capacitance "plate" has less effective area, and the series resistance will be greater, lowering the Q.

All in all, it seems to me you CAN have an in-circuit & in-service emission or cathode health test. But it will certainly cost more that just simply replacing tubes on a schedule, as some recording studios and radio stations used to do. Or just keeping the equipment powered up 24x7 as TV stations and phone companies have always done. Without switch-on surges every day, you get very few failures. The in-circuit in-service tester will be more complicated than the rest of the (tube) equipment!

I never liked the idea of cluttering up tube-based equipment with smarty-pants semiconductors anyway. Rectifier diodes are about as much as I'll tolerate.

Semiconductors from reputable US, UK, and Eurpean manufactuers are MUCH more reliable than tubes. But if you mix semis with tubes, the semis become the failure points.

Keit
 
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Not sure if this helps anyone here, RCA has a book on the design and construction of VT's. In reality it's a series of lectures on the physics and the applied techniques for mfg of them. worth a read, helps if you have a physics background and good math skills. Link here to PDF.
http://www.tubebooks.org/Books/Atwood/RCA 1940 Vacuum Tube Design.pdf

If you guys are familiar with or already know of this, then disregard.
 
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