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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 bull****, and bull****, we all can agree, is something to be avoided. Right? Have a nice day. -Henry |
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