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In Reply to: RE: The mind blowing "untouched" NFB of triode plates to grid. posted by kurt s on October 26, 2009 at 22:19:19
but it is brilliant.
Thank you.
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
Newsgroups: rec.audio.tubes
From: "Henry Pasternack"
Date: Fri, 22 Sep 2006 16:06:35 -0400
Local: Fri, Sep 22 2006 4:06 pm
Subject: Diodes, triodes, and negative feedback
I noticed that the triode negative feedback argument is still going on. I'm a
bit surprised because I don't think the issue is really all that complicated.
Somewhat complicated, yes, but not beyond resolution.
The answer to the question, "Does a triode have internal negative feedback?",
is, "Yes, if you want it to, no if you don't." But I'll admit my bias and state
from the start that I don't see much use to the triode feedback viewpoint.
I'll explain what I mean. Negative feedback is a model. The system operates
the same regardless of the model. You can imagine an operational amplifier
with its inverting input connected to its output through a voltage divider. You
can model the system in terms of its forward and reverse transfer functions
and use the feedback equation to come up with the answer. Or you can just
solve for the response as a single system of equations, and never bother to
consider negative feedback. The amplifier doesn't care. It's up to you, the
designer, to decide what form of analysis you find most convenient at the time.
It's true that if you open and close the feedback loop, certain predictable
changes occur. The gain, bandwidth, transient response, and input/output
impedances change. You can say that the existence of these changes
"proves" that feedback is at work. But this is circular reasoning. You could
just as easily explain the difference by noting how the connection from
output to input connection modifies the signal input voltage.
With respect to triodes, you can model the internal behavior different ways.
The traditional model views the cathode as an electron emitter where the
probability of emission depends on the cathode temperature and the
electric field at the cathode surface. It assumes the electrons come out
with zero kinetic energy. The plate-cathode voltage establishes a boundary
condition and the subsequent density, distribution, and velocity of electrons
within the tube falls out from the solution of a relatively simple differential
equation.
The effect of the grid-cathode potential is to augment the plate-to-cathode
electric field, modifyinng the boundary conditions of the differential equation
and shifting the current-vs-voltage curve left or right according to the grid
voltage. The plate resistance is simply the slope of this curve, and the
effects of both plate and grid potentials are purely in the "forward" path.
Taking the other position, you could view both the plate and the grid as inputs.
Their voltages each produce an electric field at the cathode surface which,
summed together, determine the space charge density around the cathode.
The space change density, in turn, determines the plate current and, in
conjunction with the plate resistor, this creates a signal voltage at the plate.
The signal voltage "feeds back" to the cathode electric field, modulating the
space charge density and therefore the resulting current flow.
The second model is pretty complicated, and there are some serious
objectsions to be made to it. I'll get to that, but first I want to talk about
diodes and triodes.
It's been stated on this forum that diodes, unlike triodes, have no internal
negative feedback. Isn't this is a paradoxical claim? The grid in a triode
biases the space charge density, but It doesn't fundamentally change how the
tube operates. Indeed, if you connect the triode's grid to its cathode, the
E-field component due to the grid is zero and the tube behaves for all intents
and purposes, exactly like a diode. If a triode has internal negative feedback,
then by the exact same argument, so must a diode. This is an extremely
important point to understand.
If you have an operational amplifier in the classic non-inverting configuration
and you connect the input to ground, the negative feedback is still in control
and the amplifier's output impedance stays the same. But grounding the
non-inverting input takes that input out of the picture. Mathematically, it's
as though it no longer exists. The three-terminal op-amp has turned into a
two-terminal op-amp yet the negative feedback is unaffected. This is how a
regulated power supply works, incidentally.
The NFB argument says that the low output impedance of the triode is due
to the negative feedback between the plate and cathode, which, if we were to
put a screen grid into the tube, could be taken away, thereby significantly
raising the output impedance. Now, the plate curves of the diode and the
triode (with Vg=0) are exactly the same. You could put a screen grid in the
diode, apply a fixed potential, and greatly increase its plate resistance, just
like a triode. Overall, if you are comfortable saying that a triode is a pentode
without a screen grid, then you should be equally comfortable saying that a
diode is is a pentode without a screen grid or a control grid. Either they both
have feedback, or they don't.
Why is this important? One of the claims I have read on this newsgroup recently
is that the plate resistance of a diode is just an "ordinary" non-linear resistance
and has nothing to do with negative feedback. The mechanism that produces the
3/2 power plate curve is exactly the same for the diode as it is for the triode. The
Child-Langmuir law applies to both and the derivation is the same. If the plate
resistance of a diode is just an "ordinary" resistance, then so is the plate
resistance of a triode. The control grid is a complication, but it has no bearing
on this mechanism.
To understand whether or not a triode has negative feedback, we'd like to boil
the problem down to its barest essentials so that the underlying principles
are exposed clearly and without confusion. That's why it helps to show that
the control grid is irrelevant to the question. It's hard to visualize negative
feedback in a diode (or a resistor, for that matter, but more on that later)
because a simpler, open-loop model is just cleaner and more intuitive. When
you add a control grid in there, things get more complicated and it becomes
tempting to start waving hands. We'd like to avoid that.
Getting back to op-amps, it's very easy to separate out the forward path and
the reverse path. The forward path is everything inside the little triangle,
between the two input leads and the one output lead. The reverse path is the
external network connecting the output terminal to the inverting input terminal.
Being able to separate these two paths so cleanly makes it much easier to
visualize how the operational amplifier operates as a feedback circuit.
In the proposed diode NFB model, there is an inconvenient blurring between
the forward and reverse paths. The plate-cathode potential has two functions.
First, it establishes the electric field at the surface of the cathode, which in
turn modulates the space charge density. Second, the very same field
sweeps electrons out of the electron cloud and accelerates them to the
plate, establishing plate current. The first of these two functions may be
called feedback. The other determines the forward gain. To show that the
tube has negative feedback, you have to separate these two paths out, but
it's not such an easy thing to do. This is a problem for the feedback model.
There are two ways that tube feedback modelers have solved this problem.
The first is propose connecting the plate to a fixed DC potential. This lets
the tube keep conducting but eliminates any E-field feedback from the plate.
Fixing the plate potential raises the gain (transconductance) as predicted by
feedback theory. This is the essence of an argument that one member of
this forum put forth as "proof" of triode NFB.
But there is a glaring hole in this argument. There is absolutlely nothing
that external observation can prove conclusively about the internal operation
of the tube. There could just as easily be a nonlinear resistor inside the tube,
or little elves with voltmeters and a rheostat controlling the electron flow in
real time. All you can determine from external observations are the external
properties of the tube, and while these may suggest the action of negative
feedback, they do not by any means prove it.
The other, perhaps more convincing way that feedback modelers have tried
to prove their point is by postulating the existence of a fictitious screen grid
inside the tube. The screen grid takes away the feedback due to the varying
plate E-field while allowing the plate voltage to vary. With this fictitious screen
grid in place, the tube has higher gain, like a pentode.
There are several rebuttals to this argument. The simpler one is that the
fictitious screen grid is, indeed, a fiction. The triode is not a tetrode. It
should suffice to model the tube without the artifice of the fictitious grid.
Indeed, there is there is a perfectly good model that doesn't depend on
this complication. But the real problem with the fictitious grid argument
is that it pulls itself up by its own bootstraps. It says, a triode has NFB,
and a pentode is a triode with the NFB taken away by the screen. So
if we take a pentode and remove the screen, the feedback comes back
and this proves the triode has NFB. This is a brilliant example of circular
reasoning.
The triode NFB argument depends on another fiction, the "virtual grid", which
is the internal control point related to the electric field strength at the cathode
and space charge density. The model says the actual input to the tube is
this "virtual grid", which is related to but distinct from the external grid and
plate connections. This is an extremely awkward model because it relies
on an abstraction of the tube that is quite removed from its actual use in-circuit.
Contrast this with the op-amp where the input, output, and feedback connections
are quite clear and in the open.
One of the points made against the triode feedback model is that there is no
effect on the input impedance seen at the grid. In response, it's been noted
that even with conventional shunt feedback applied to the cathode, there is no
effect in the tube's input impedance. This isn't true. Shunt cathode feedback
definitely raises the input impedance seen at the grid. It's just that the tube's
input impedance is already so high and swamped by the bias resistor that we
don't notice the difference.
I mentioned resistors earlier, and I'd like to get back to that. Others have
pointed out that you can use the same kind of argument for triode NFB to
show that there is negative feedback in resistors, or automobiles, or electric
motors. It's actually kind of fun to derive the formula for a voltage divider in
terms of negative feedback, or even transmission line reflection coefficients.
Consider a resistor as a cylinder of material with a metallic cathode
bonded to one end and a metallic anode bonded to the other end. If you
apply a positive potential between the anode and the cathode, an electric
field will be established between the electrodes and electrons will begin to
drift inside the cylinder, creating a current flow. If the power supply has
significant output resistance, the supply voltage will drop, reducing the
electric field within the body of the resistor and modulating the current. In
other words, negative feedback. Or is it feedback?
The difference between the diode feedback model and the resistor feedback
model is that in the resistor you don't have the additional complication of
the space space charge density. But the principle is the same. In either
case, the current flow that results from the application of an external
voltage is set by an equilibrium that develops within the device. You can
find zillions of similar examples in nature and engineering.
Parachutists are grateful for the negative feedback of air resistance that
reduces the "gain" of gravity accelerating them to the ground. Airplane
designers take pains to eliminate this feedback, maximizing the "gain" of
their engines by installing aerodynamic screens on the aircraft. Yes,
feedback is everywhere. And nowhere. It all depends on your point of
view.
Whether or not you choose to think of tube operation in terms of feedback
is your choice. It causes no harm to anyone. But you should be careful
to avoid insisting on the presence of feedback. Feedback is only as good
as the value it brings to engineering analysis. In practical terms, when it
comes to triodes the value isn't that great. I don't believe it gives us any
greater insight than we get from the standard models. In particular, as we
move from coarse generalities to much finer levels of detail, it remains to be
shown that feedback helps to predict the second- and third-order nonlinear
behavior of the tube.
It's been said, and I agree, the tube doesn't give a damn how you model it,
but goes about its business in blissful ignorance. Triode negative feedback
is a great conversation starter, but there is a risk, in invoking negative feedback,
of making things more confusing than they have to be. Out of confusion comes
bullshit, and bullshit, we all can agree, is something to be avoided.
Right?
Have a nice day.
-Henry
where I take the "white box" or "clear box" testing paradigm and Henry takes the "black box" approach. But will yield same results where I am curious about the physics known inside and designed inside (but obviously don't know enough to be any expert there) to Henry's "so what how it does it, it just does it, take the simple external model."
Correct me if I am wrong.
-kurt
Thanks for the reply, but I don't think you really got the point of my long article. (IMHO it's a brilliant essay, but I never expected anyone to read or understand it, not then, not now -- though I would be delighted if they did.)
Here is a synopsis for the attention challenged: All the common triode circuit models are just abstractions of the tube that have no real bearing on the actual internal structure or operation. The internal NFB model is one such abstraction that does away with the series (Thevenin) or parallel (Norton) plate resistor and replaces it with an active control structure. It's no closer to the reality of how the tube works than the models it replaces. Furthermore, it gives no additional insight into externally observable behavior of the tube and its use in practical problems complicates circuit analysis. The model is based on circular logic and awkward assumptions. Finally, the underlying approach applied to other problems leads to feedback appearing in all kinds of devices where we don't normally think of it existing, like diodes, resistors, electric motors, and parachutes.
I'm not actually that committed to the argument, not like I was three years ago, but I couldn't resist Tre's invitation to dredge up a few thousand words of archived historical drivel.
-Henry
I do understand all your points and maybe I am not conveying this understanding at all to you. And your essay was brilliant, Henry, and I mean that. I know I was certainly only one of the few who understood but pondered it over and said little about it for there are lingering doubts about what is knowable and what is important to know. Ya know?
To access the POTENTIAL of its internal actions always requires external devices to complete the circuit that shows what that device is doing. If you don't have any way to predict what's inside as in Black Box.
For the parachute, it is in a NFB situation when the application is showing the device's POTENTIAL. If it were used above the moon, it would never exhibit its POTENTIAL for any application, just as the feather and hammer simultaneous drop hides the properties inherent to a drop in atmosphere. External atmosphere differentiates the feather and the hammer and shows it's otherwise hidden basic property against wind resistance. Seeing it only on the moon would all make us think they were the same.
You have to apply the device to see what the device's internal characteristics are. That can be done by black box analysis. Or if we do another analysis outside its normal application and peered inside instead to "measure" what's going on in there - the White Box case would tell us and predict to us what it will do in atmosphere and no atmosphere before we even begin applying it. Let's see: Broad light fabric attached to weight and we know F=ma and Force up will equal Force down. In resistive atmosphere Force up is real and we might even know it by calculation beforehand. In a vacuum Force up = 0 and nothing is even there to open it. So all forces are straight down to a parabolic descent.
I see it as a viewpoint of believing you can predict the outcome of distortion in pentodes with varying plate loads without plate curves, but more basic physics that concludes calculable plate curves. And then do for structure analysis for triodes as well. And someone has written a computer program that will take triode structures and predict the plate curves from that and some other pre-known properties about the metals and coatings and what the heater is expected to see, etc., etc. And then we have insight into what triode curves are based on and what pentode curves are based on. No need to build the circuit to predict the basic outcome.
An analogy is High Frequency Structure Simulator software, or HFSS. It allows you to draw a metal and dielectric full structure of however complicated you can get to in practical terms (hint, simplest geometries only, please). Then you can run the calculations and see what the EM fields do when sourced at one end through various frequency sweeps or just one point. This has helped many designers make some weird microwave accessories to better perfection, such as couplers. You now have a White Box to add into another application surrounding it and predict its basic performance, such as return loss, insertion loss, coupled loss, etc. Very helpful to add to further powerful microwave simulators of full circuits. But the circuits are only good as the designed couplers and those are based on known physical modeling and then making them as close as the model. So again, we see beforehand what kind of "in circuit" "NFB" will take place as we vary the circuit. Seeing it in action after the fact and modeling only after the build and measurement of the device and ignoring the structure simulator is a valid course of action and viewpoint on how you want to see that Black Box model. Just ignore the insides that do have loops and feedback all in there and how it became optimized by a more fundamental physical model. Or know that it was only this good because it "Clear Box" peered inside and did do that modeling work for a more precise design and a more predictable Black Box output spec.
So this "new wave" is going on now. It's not enough to design a resistor by over processing with spirals as it will increase costs beyond the competitors and diminish performance. It can be designed and built by more stringent first pass controls and predictions from physical structural models. And then it really does matter that you know exactly how much NFB the device will cause in the circuit and what that is "internally" the "internal NFB" is, for lack of a better term.
Now we need to differentiate those terms, like maybe the expected resistance, inductance, and capacitance along with what distortions are in it from nonlinear dielectrics in use from the device itself and what it will expect to do in a normal simulator of a full circuit it's used in.
This is why I cannot dismiss the internals in knowledge and its own internal circuit that might have that wrongful by a tad "internal NFB" when placed in the circuit that shows what its properties are when applied for its intended use.
There is just a new lower level of simulation that's happening, and has happened for many years actually. Parts need optimization by computer, too.
Or am I still way off base here? I don't think so. Maybe I am not understood what I am trying to say. NFB requires more than one part and it needs stimulus, too. A device with "internal NFB" is assumed that the property of that poor term will come out in the circuit (environment) it was intended to be in.
-kurt
Interesting points, Kurt. This discussion has probably gotten too esoteric to be of interest to most readers, so I'll try not to go on too long.
I agree that "white box" models based on direct internal testing or knowledge of device physics can help us do more accurate simulations and hopefully create better designs.
I'm a bit hung up on whether the "triode internal NFB" model is really a white box model, or if it's just another black box model based on externally observable behavior that doesn't really tell us anything useful about how the triode works internally.
The paper that was discussed on r.a.t., as I recall, wasn't derived from the physics equations (i.e., Child-Langmuir). I do know if you crack open a genuine triode and go looking for that hidden screen grid to do white box testing, you won't find it.
So, let's not pretend the triode has a fictitious internally connected screen grid. Instead, let's treat it as a test probe that we use, in fact or in a thought experiment, to disconnect the hypothetical feedback loop inside the tube. I can't claim that this is really all that different from opening up a feedback amplifier and using a test probe to short out an internal feedback node for just the same purpose. Except, of course, in the case of the amplifier the internal feedback node is a tangible internal structure, whereas in the triode it's harder to visualize. But to a mathematician, I suppose, it's clear enough.
Getting back to the introduction to my long essay, I can't argue that there is no way to model internal NFB in the triode. I just don't see what you gain from it versus, say, more detailed physics-based models. I know that internal negative feedback is a good way to model grid-plate capacitance, for instance, but I've never seen a practical problem where the kind of feedback model we're talking about here made the solution easier.
I know that Mark Kelly, whom I respect as a math genius with a strong interest in triode modeling, looked at this question and came away unimpressed. Though I've had some strenuous arguments, notably with one fellow from Australia, nobody's ever framed it in such a way that I said to myself, "Holy moly, now I see da light!"
In the end, I'm waiting for people to take this triode internal NFB thing and start solving problems with it that nobody's been able to solve by conventional methods. Or taking previously hard problems and making them simple. That will convince me.
-Henry
After reading thourgh lots of the triode-has-internal-FB writings it seems for the most part to be a 'proof' that the pentode is bad.
cheers,
Douglas
Friend, I would not hurt thee for the world...but thou art standing where I am about to shoot.
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