Electron Velocity In Tubes

[Nowhere-Man]

As I am currently very busy trying to fix up my boat before Winter sets in, I'm only doing my radio project work in small fits and starts. Actual repair work will resume as Winter closes in. Therefore, after a day doing some very dirty work in an engine room, I'm back to late nights doing radio theory. As always I use books from the early sixties and these have a bias towards American circuit design.

This is really a very short and uneventful post that may only interest a small number of people. Even so, the question itself is interesting.

I was interested to discover that the actual velocity of the flow of electrons from cathode to anode on, say, a triode, is 0.001 Microsecond. This becomes a factor when signals start to go beyond 1 Megahertz. Actually I was having a few issues digesting this data as, for some reason. my brain felt like it was being pulled through a rack. Here is what I was pondering:

If a signal of 1000 Kilohertz is directed to the grid of a triode and if the electron velocity is 0.001 Microsecond, then the electron flow is 1000/1 cycles. That is, the electron flow is much faster than the signal and, at this stage, there is no problem.

If a signal at 100 Megahertz is applied to the grid of a triode. the cycle is now 10/1. The difference between speed of the signal and the velocity of the electron flow is reduced.

At 500 Megahertz, electron velocity now takes half the speed of one alternating cycle.

I forget what the specific figure was but even at around 300 Megahertz, electron velocity becomes an issue. The faster the dsignal on the grid, the more the gap between flow and signal speed decreases.

Thus, Klystrons came into being as well as Magnetrons.

Here is the question:

As I know very little about semiconductors, does anybody know how electron velocity in a semiconductor compares to a tube? For example, I forgot to say that at very high signal speed a tube tends to become unstable due to capacitances generated between electrodes. So, if the velocity of electron flow in a triode is 0.001 Microsecond, how does a transistor compare? Are they less efficient or more efficient?

My guess is in modern technology by now, they probably found ways to use equivalents of klystrons.

Please forgive this post is by chance there are any maths errors. I'll recheck my figures later to be sure I did get the ratios correct at the given frequencies.

[ppppenguin]

You ar quite correct. Electron velocity in valves sets the ultimate limit to upper operating frequency. Hence high frequency valves have smaller electrode structures. In fact the actual transit time isn't a fundamental limit - radio waves travel through the atmosphere for many times their wavelength without losing their shape. The trick of klystrons etc is to ensure that the waves travel coherently through the device, despite the deveice being longer than a wavelength.

Transistors start off with the advantage of being small so the distances the carriers have to move is small too. Not sure how fast the carriers (remember you can have electrons and holes as carriers) actually move but again the smaller the device that higher the frequency it can do. The transistors in a modern PCU or memory chip are truly minute, down to a few 10s of nanometres, and so can switch very fast.

All of this causes a conflict if you want high power (large device) and high frequency (small device) at the same time. A lot of effort has gone into resolving this.

The important term in semiconductors is CARRIER MOBILITY. It's higher in specialist materials such as Gallium Arsenide than in ordinary silicon. This article isn't bad but you'll find it very hard going: https://en.wikipedia.org/wiki/Electron_mobility Google carrier mobility and you might find something a bit easier to follow.

It's worth knowing that the electrons in a conductor such as copper move very slowly indeed, snails pace gives you some idea. But think of it like a set of billiard balls bumping into each other. Each ball may not move far or fast but the shove you put in at one end of the line can appear at the other pretty quickly.

[Nick]

Not sure about your numbers and can't sleep  , so here are my numbers: (I originally wrote this for another forum...)


You can use simple maths than that to show what's going on. What follows is an ideal-case solution, ignoring some of the losses that occur in a real valve...

The anode heats up due to it being bombarded with electrons from the cathode. If we know the number of electrons arriving and the energy they carry, we can work out the incident energy in the electron stream and thus how much power the anode has to dissipate.

The energy gained by an electron moving though a potential difference is E = QV, where Q is the charge on the electron and V is the potential difference. If the electron starts at rest (from the cathode), E is just the kinetic energy of the electron.
For any electron, Q = 1.6e-19 Coulombs (this is a constant)

NB: The definition of an Ampere is the passage of 1 Coulomb per second past a point (about 6.25e18 electrons)

So, as an example, lets look at the Ia vs. Va graph for an ECC83C http://en.wikipedia.org/wiki/File:Triode...istic1.png. At Vg = 0 (fully conducting) we can read off that Ia = 5mA at Va = 225V. Assume Vk = 0.

Thus, in our example, the energy per electron, E, = QV = 1.6e-19 * 225 = 3.6e-17 Joules

...and the number of electrons per second, N, for a given Ia = total current/charge per electron = Ia / Q = 5e-3 / 1.6e-19 = 3.125e16 electrons/sec going from the cathode to the anode.

The total energy per second of the electrons impacting the anode is therefore the number of electrons per second x their energy which = N * E or Ia / Q * Q * Va. The "Q"s cancel out leaving us with the anode power dissipation being Ia * Va (as expected) or 5e-3 * 225 = 1.125 Watts.

The anode therefore heats up - there can be no heat loss though convection (we are in an vacuum) so conduction via the anode connection and black-body radiation (infra-red) are the only ways.

As an aside, given the kinetic energy of each electron from the E = QV equation above, we can determine how fast they are going. 
Using the general-case kinetic energy equation E = 0.5 * m * v * v, we re-arrange to get v = sqrroot(2E/m).

The mass of an electron, m, is = 9.1e-31 Kg and we have E from the equations above (3.6e-17 J) so v = 8.9e6 metres per second (about 20 million mph ). The speed of light, c, is about 3e8 metres per second, so our electrons are doing about 0.03 c. If we say (guess) that the cathode->anode gap is about 5mm, then each electron takes approximately 560pS to make the trip... some things in valves happen quite quickly...

Ho, hum...

Edit: Just noticed that my example is outside the SOA in the datasheet - the maths is still valid, though  

[ppppenguin]

Nick, I like your derivation from first principles. Note that this applies to electrons in free space. If you try to apply it to a current in a conductor I don't think it will give a sensible answer as that's not how current flows in a conductor.

[Terry]

I remember a very effective demo at college of electron flow in a conductor.

Two 12" rulers with a column of ha'pennies between them - I'd use 2p coins these days. Then, shove ha'penny style, place another coin over the table edge and fire it into the column.

As one goes in, another one fires out of the other end ...

Simply, innit?

[Nick]

As one goes in, another one fires out of the other end ...

Newton's Cradle...

[Terry]

As one goes in, another one fires out of the other end ...

Newton's Cradle...

Err ... we were simulating electron flow in a length of wire which, in itself, is useless as an oscillator (unlike Newton's Cradle ...)

[Nick]

As one goes in, another one fires out of the other end ...

Newton's Cradle...

Err ... we were simulating electron flow in a length of wire which, in itself, is useless as an oscillator (unlike Newton's Cradle ...)

Cross purposes, maybe. Newton's Cradle is designed to demonstrate the law of conservation of momentum - the fact that the end ball(s) swing out to repeat the process is incidental - it was never intended to be an oscillator - its all about the transfer & conservation of momentum.

The effect is identical in every way to that you described with the row of coins: cf. https://en.wikipedia.org/wiki/Newton%27s...his_effect

Electron == steel ball == coin. As long as they are in straight line, touching & have the same mass, it works.

The truth is that it's a very simplistic explanation of how current travels through a conductor - at an atomic level its just a tad more complex... (and not a lot to do with the transfer of momentum!)

[Nowhere-Man]

It's been noted that tubes conduct through free electrons which is indeed a factor of interest. This is perhaps the major big difference between transistors and tubes. As everybody here is aware, electron flow in semiconductors involves an electron jumping from atom to atom. It's not a cloud of free electrons as is the case in a tube (produced by heating a filament). This in itself poses many questions. For example:

In a tube, the alternating voltage on the grid, either speeds on or retards the electron flow. During the negative cycle, the cathode to anode flow will be retarded in velocity but speeded on positive cycles. Sometimes there is a fixed DC bias on the grid so current will always flow and sometimes the tube will be biased to cut-off. In the latter case, only positive cycles will have any effect. At any rate, electron velocity in a normal tube should be 0.001 Microsecond (so not a big problem when the cycles are at Kilohertz frequency.

I'm rambling a bit in the second paragraph but I wanted to point out that tubes need more voltage or power if you like than transistors. I noted a very simple point mentioned in a text book that tubes always lose more power coming in than they deliver coming out. Part of the power loss is thought to be due to the electrons that lag during negative grid cycles.

So, it's already been pointed out above that one way semi conductors can reduce the loss of velocity is the size of the transistor itself. So, anyone know what is the electron speed capacity of PNP AF117, for example? Do you think they are more efficient than tubes on high frequency?

I downloaded an article on Klystrons out of curiosity. It more or less said the Klystron takes advantage of electron velocity by causing the retarded or advanced electrons to bunch in cavities (hence "buncher"). The corresponding flow of electrons then amplifies the signal. I've never seen Klystron but am led to believe they're pretty big and seemingly expensive.

As an update today I put the potentiometer on the GEC radio and tested the resistance on the grid of the Double Diode Triode. This was because the weather was too poor for working on boats (and maybe also because I fell off my boat yesterday and am bruised somewhat). It now has a working switch and all is fine. I confess sometimes I have to force myself to do something on rainy days but I'm content the day's not been wasted. Ohms between neutral and live now also reads fine.

I am basically very lazy by nature and often enjoy delving into theory till the early hours of the morning. Then I watch a DVD.