[Patrick Turner]

Henry Pasternack wrote:

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.

In a thermionic diode the anode voltage determines the current flow.
The effect of the anode electrostatic field upon the space charge of electrons is no
different
to what occurs in the triode, but a triode has a GRID, and so you have TWO
things which JOINTLY conrol electron flow in the triode, and this interation
involves a simple shunt or summing electrostatic NFB effect which does not exist in a
diode.
A triode can be used as a diode if the grid voltage is kept fixed; the Ra curves
of a triode at fixed value for Eg-k = 0.0V, ie, grid is tied to cathode are little
different to the Ra curves
of a diode. But where you have the grid controlling the Ia with interaction with Ea
there is, IMHO, a NFB effect.


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 non-inverting opamp used with NFB taken to its inverting input
can be considered a unit witth low Rout. But its low Rout because of the NFB.
if you remove the NFB by ground the inverting FB input port
then the gain goes sky high and the Rout is high, and bandwidth very poor as the NFB
is no longer connected.
The opamp becomes like a pentode with little NFB.



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.

Its not as simple as that Henry.
if a screen is placed in a diode, then it becomes a triode, and thre Ia can be controlled
by the screen
which works as a grid which draws input current and has a low gm and low µ and gives the
Ra a high value.
There is little NFB because the anode has such a small effect on the space charge.

The position of the screen electrode is such that its distance between cathode and anode
is MUCH
further away from the cathode than a normal control grid.

There are some beam tetrodes and pentodes where the g1 is tied to the cathode
or kept at a fixed voltage slightly negative and all the control of the the
anode voltage is by the g2 screen, and some such tubes can be very linear
and there is enough linearizing NFB within even though Ra seems rather high for such a
triode.
The µ of such tubes is usually very low.

The use of the g2 as a control grid is evident with UL operation where the screen
accpts a % of the anode signal which is in fact an injection of local NFB
normal triode connection with screen strapped to anode is merely where ALL
the anode voltage is fed back into the tube which is a large amount of applied
shunt NFB but employed in an electostatic voltage divider and where the effective or
virtual
control point is the summed ecct of the anode and grid 1 voltages.
Such summing effects just don't happen in diodes.




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.

The applied NFB in a triode is applied via a 3/2 rule, so the NFB mechanism isn't
linear where a current change occurs in the triode.
But it becomes VERY linear when voltage change occurs between anode and cathode
but WITHOUT any current change; ie, where the load line is horizontal.



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.

We are not waving hands.
We are having a technical discussion.



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.

A diode has no amplification and no gain.
Its just a non-linear resistance.

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.

The diode has no forward gain. Current flows due to one single effcect,
anode voltage is raised by some external active device and current flows.
Solid state diodes are no different, except that their on resistance curve is
very much more abrupt and of lower resistance than a thermionic diode.

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.

Its not a problem to show there are two interacting fields of control in a triode.



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.

With no change in Va -k, there is no voltage gain and no NFB applied.
The triode NFB is purely a voltage caused phenomena .
There is current gain and is simply gm x Eg applied.



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 is no need for fictitious screens to be considered.

There are TWO voltage fields which sum together to control Ia.
As RL at the anode becomes lower, the nfb becomes lower, but with a CCS
connected NFB is at a maximum applied amount, and thus maximally
linearizes the tube.


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.

Just connect the screen to anode and you have a triode because the anode voltage is
allowed
to work against the operation of the grid1, so gain, Ra and thd reduces.



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.

Nothing hard to understand about a virtual controlling field in a triode.
Grid goes +10V, anode goes -200V.

The effects of the two voltage changes sum together according to the
distances between cathode and grid and cathode and anode.

The triode operates with a virtual input similar to the virtual
input of an inverting opamp with its non-inverting input taken to 0V,
and fitted with a two resistor shunt FB network.

But the arms of the network in a triode are electrostatic fields, not resistances.


One of the points made against the triode feedback model is that there is no
effect on the input impedance seen at the grid.

Well in fact there is, and its the Miller effect.
If the input source signal resistance is many meg-ohms, then the miller effect
has considerable input Z effect at audio F.


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.

Shunt FB normally lowers Rin, while series FB such as the case of a cathode follower
will raise Rin.

But triodes in AF circuits have very high Rin up to 20kHz regardless
of the NFB because the arms of the electrostatic shunt FB network are
very high Z reactances.






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.

The argument in favour of triode NFB CANNOT be used for resistors etc.



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?

I don't think you quite have it right yet.

Patrick Turner.



Have a nice day.

-Henry