A simple transistor question

[magic]

With a BJT and the emitter tied to ground, the base is (with a perfect transistor) 0.7v. If a resistor is on the emitter to ground, then that changes the base voltage which changes the base current, which changes the collector current because beta changes, etc... Now I'm confused.

If I understand correctly, you refer to the case of a series connection of: a voltage source, base resistor, NPN, emitter resistor, ground.
That's one of the legitimate uses of β, which is to say, the result will vary between transistor types.

If Ib is the base current,
Vsupply = Ib·Rb + Vbe + Ie·Re = Ib·Rb + Vbe + Ib·(β+1)·Re

Knowing the values of resistors, Vbe and β+1 it's easy to get Ib and all the rest from there.
To be strict, Vbe is the logarithm of Ie times some constant, but you can take 0.7V and it's likely close enough.

[Sredni]

Leon O. Chua, Charles A. Desoer, Ernest S. Kuh
Linear and Nonlinear Circuits
1987, McGraw Hill

I would call this THE bible of circuit theory.
p. 50 : section 1.2: The nonlinear resistor
the first example is the ideal diode.

I don't have this book handy, sorry.  Are you saying that the motivation for analyzing it as a "resistor" comes from this reference then?

You can find the first 15 pages of the second chapter on the website of Berkeley University.
https://inst.eecs.berkeley.edu/~ee100/fa08/lectures/EE100supplementary_notes_3.pdf
(if your google-fu assists you, there is even the whole second chapter online - at another uni. I link this from Berkeley because that's where Chua, Desoer and Kuh taught.)

And no, it's not only that book, even if it is one of the most authoritative textbooks in circuit theory. You can find examples of diodes as nonlinear resistors in Smith & Alley's "Electrical Circuits" book, and here and there in lectures and recitations. One example: https://6002.catsoop.org/_static/S20/s20notes/Recitation11.pdf where it says explicitly that a "[d]iode is another common example of a two-terminal nonlinear resistor."
It's everywhere. Well, maybe not on Forrest Mim's notebooks (I haven't checked) but I believe any university level textbook of circuit theory should carry this simple notion.
Unless... unless all new books have been Upgrayedd already (I am pretty sure the process is under way).

You can find the notion - in a way or the other - also in commercial EE sites. Here's Cadence:
https://resources.pcb.cadence.com/blog/2019-what-is-linear-and-nonlinear-resistance
it shows a diode as an example of nonlinear resistance. Gives the correct definition, even though it successively focus on the differential resistance (which is linear, by the way!).

[TimFox]

Your original post involved confusion in a novice student.
I submit that he will be further confused if you call the diode a resistor:  he already mis-applied Ohm's law in his sketch.
A diode, by definition, is a two-terminal device.

[rfeecs]

Leon O. Chua, Charles A. Desoer, Ernest S. Kuh
Linear and Nonlinear Circuits
1987, McGraw Hill

I would call this THE bible of circuit theory.
p. 50 : section 1.2: The nonlinear resistor
the first example is the ideal diode.

My "bible" was it's predecessor, so I guess it's the "old testament":

Charles A. Desoer, Ernest S. Kuh
Basic Circuit Theory
1969, McGraw Hill

I bought a used copy from the local university bookstore when I was in high school.  I decided one summer to read it from cover to cover.  I got maybe half way through. 

The section on the nonlinear resistor is very similar.  Some sentences are identical.  There is also a definition of "voltage controlled" (current is a single valued function of voltage) and "current controlled" (voltage is a single valued function of current) in that section.

[TimFox]

That distinction is important, since some device functions are not monotonic, and the inverse function is multi-valued.

[magic]

Their definition of a nonlinear resistor seems to admit devices capable of conducting any current that can be expressed with a rational number when biased with irrational voltage and arbitrary irrational current when biased with a rational voltage, so it is a fairly general notion indeed.

However, they state very explicitly right at the beginning of 1.1 that Ohm's law is the linear correlation of current and voltage and that it applies to what they call linear resistors, i.e. ordinary resistors that respect Ohm's law. None of that justifies your student's talk about "Ohm's law" with regard to PN junctions.

TL;DR, but I very much doubt that there is a single place in the whole chapter where they actually bother to divide the instantaneous voltage by the instantaneous current of a nonlinear resistor. Because it makes no sense to do so.

Even  if they do, they certainly don't call the resulting ratio "resistance" - that word only appears in reference to the constant R in Ohm's law for linear resistors.


Long story short, they use the term "nonlinear resistor" to refer to things that aren't real resistors, but they don't mean it to imply that all those devices suddenly have typical resistor properties and can be analyzed as resistors. It's just a silly name that they came up with.

[bdunham7]

Even  if they do, they certainly don't call the resulting ratio "resistance" - that word only appears in reference to the constant R in Ohm's law for linear resistors.

Well, tunnel diodes are said to have 'negative resistance', but the meaning of that is clearly dV/dI, not that V/I is negative at any point.  I suppose a photo diode could actually have a negative V/I, but...

i think the term 'dynamic resistance' as used with zeners would be a reasonable term to distinguish dV/dI from ohmic resistance.

[TimFox]

Yes, the tunnel diode is a good example of "negative resistance", where the slope of the I-V curve is negative (opposite from that of a resistor) over a limited region.
It is also an example of a non-monotonic curve of current (dependent variable) vs. voltage (independent variable), which has other implications.
These "incremental" or "dynamic" resistances (derivatives) are useful in small-signal analysis, for example using the negative conductance of the tunnel diode to cancel the positive conductance (loss) of a resonant circuit to make an oscillator.  Negative resistances (including tunnel diodes, op-amp circuits, and vacuum-tube transitron circuits) all need external power to function properly.

[aneevuser]

This is not the first time I have witnessed the closing of potentially very interesting question out of the ignorance of those who voted to close them, and asking why a question was closed is like being appointed defense attorney in a witch trial :-)

Well, I'm not surprised by this: StackExchange is fundamentally broken-by-design. It seems to work on the principle that a question has an "answer", and those involved seem ignorant of the fact that most of the value provided by asking a question is the back-and-forth discussion that a good question generates - often when I ask a question, I'm aware that I don't really know what I don't know well enough to formulate a good question, but I expect the following discussion and explanation to clarify it. SE doesn't allow that - discussion is deleted, answers remain.

I suspect that the model just about works for its original purpose ("what setting do I use to make the compiler optimize for X architecture?" or similar software questions); it fails miserably in a more general context. All IMHO, of course.

[aneevuser]

Being nonlinear, the device resistance is a function of the current - or the voltage (I am still an agnostic). And I am not talking of the differential resistance, but to full blown resistance computed as the ratio of the voltage across the diode and the current flowing through it. It all depends on how this student has been exposed to the concept in class: not all the world is alike.

If I understand this correctly, you would consider all two-terminal devices (or indeed anything physical that you could put a voltage across - a piece of wood?) as a resistor?

If so, that seems to generalise the word "resistor" to meaningless.

[aneevuser]

How do you think I set the collector current in my two examples? By choosing VEB? No - I programmed IE by choosing a resistor of value (VEE-0.7V)/IE (this is by modeling the input diode as a vertical line at 0.7V).

I don't see how this relates to my question about controlling a BJT by setting the base current.

[T3sl4co1l]

Even  if they do, they certainly don't call the resulting ratio "resistance" - that word only appears in reference to the constant R in Ohm's law for linear resistors.

Well, tunnel diodes are said to have 'negative resistance', but the meaning of that is clearly dV/dI, not that V/I is negative at any point.  I suppose a photo diode could actually have a negative V/I, but...

i think the term 'dynamic resistance' as used with zeners would be a reasonable term to distinguish dV/dI from ohmic resistance.

I use "average resistance" to mean instantaneous V/I.  I think this is a fairly common use.  And yeah, a power source is often defined as negative current (sourcing), while loads are sinking (whose definition? SPICE for example: take a positive voltage source wired to a resistor, V1[i] will be negative, R1[i] will be positive), so an illuminated photodiode is an example of a diode with negative average resistance, over at least some portion of its curve.

Also, another instance: "marginal" in economics is synonymous with "incremental".

Tim

[Sredni]

How do you think I set the collector current in my two examples? By choosing VEB? No - I programmed IE by choosing a resistor of value (VEE-0.7V)/IE (this is by modeling the input diode as a vertical line at 0.7V).

I don't see how this relates to my question about controlling a BJT by setting the base current.

We were talking about current control vs voltage control. The common base configuration is probably the best in showing how you can consider the transistor as a current controlled device: you pump a big current IE in, you get an essentially identical big current IC out, with a little leakage as base current.
And what you set, when you design the circuit, is the current.

As to how a small base current can induce a much bigger current in the emitter and collector, you can find an explanation in Streetman or even in Hu. I believe I posted a link to a SE answer where I give several references.
But we can explain it with the Stormtrooper analogy:

Let's say we put a single electron in base, and this electron is in the form of a rebel alliance soldier with a target on his back. The emitter is filled with stormtroopers who see the lone rebel and start shooting at him - the 'light bullets' are the holes. Stormtroopers being stormtroopers, they will mostly miss their target - let's say they have an accuracy of (1-alpha): out of 100 shots only one will be on target - all the others will hit the collector's wall.
One rebel in base will result, on average, in 99 holes in the collector wall.

A small incursion of rebel soldiers in base (let's say 0.1 mA) will result in a large flow of light bullets coming from the emitter - almost all missing their targets - and a giant number of holes in the collector's wall (let's say beta times? 10 mA).

[Sredni]

Being nonlinear, the device resistance is a function of the current - or the voltage (I am still an agnostic). And I am not talking of the differential resistance, but to full blown resistance computed as the ratio of the voltage across the diode and the current flowing through it. It all depends on how this student has been exposed to the concept in class: not all the world is alike.

If I understand this correctly, you would consider all two-terminal devices (or indeed anything physical that you could put a voltage across - a piece of wood?) as a resistor?

Well, if you burn it and turn the charcoal into a fine powder, add a little bit of binder (for example clay) and put a terminal here and there - that's a carbon resistor.

If so, that seems to generalise the word "resistor" to meaningless.

Has anyone here ever heard of the 'tetrahedron of state'? Of effort and flow variables? Of constitutive relations?
In circuit theory we have two main quantities: electric charge q and magnetic flux phi. Their time derivatives are current and voltage. These are two fundamental relations that come out of Maxwell's equations

i = dq/dt      v = dphi/dt

(If you prefer seeing it the other way around, the time integrals of current and voltage are electric charge and magnetic flux.)

How many relationships can we find between these four variables (q, i, phi, v) ? Apart from the derivative and integral ones, we have four possibility

v    vs    i      ---> resistance
v   vs   q      ---> capacitance
phi   vs    i       ---> inductance
phi   vs   q      ---> memristance

A resistor (or, if you prefer, a generalized resistor) is a two terminal device whose constitutive relation is between the values of voltage and current.
An inductor's constitutive relation is between magnetic flux and current (or, if you prefer between voltage and the derivative of current)
A capacitor's constitutive relation is between voltage and charge (or, if you prefer, between voltage derivative and current)
A memristor's constitutive relation is between magnetic flux and electric charge (or, if you prefer, between the integral of voltage and the integral of current)

I hope you won't ask me now: "but a capacitor has voltage and current too, so why is not a capacitor a resistor as well"? Or, "what about a SQUID"?

The relationship between the variables is in general a nonlinear and time-variant one. In the case of the resistor it is also called 'generalized Ohm's law'. Some shorten it to just Ohm's law. In high school they only know about the 'ungeneralized' Ohm's law, the linear one, and they think that resistors can only be linear.

[TimFox]

"Ungeneralized Ohm's Law" seems to be just that the current is an arbitrary function of the voltage, and vice-versa.
In physics, for linear conductors, we use the vector relation J = s E, where the current density J and the electric field (voltage gradient) E are vectors.  For an isotropic linear conductor, s is a scalar, but for anisotropic conductors it is a tensor.
(I have no problem with the well-worked-out theory of non-linear components, but I thought this thread was about teaching transistors to novices.)

[aneevuser]

How do you think I set the collector current in my two examples? By choosing VEB? No - I programmed IE by choosing a resistor of value (VEE-0.7V)/IE (this is by modeling the input diode as a vertical line at 0.7V).

I don't see how this relates to my question about controlling a BJT by setting the base current.

We were talking about current control vs voltage control. The common base configuration is probably the best in showing how you can consider the transistor as a current controlled device: you pump a big current IE in, you get an essentially identical big current IC out, with a little leakage as base current.
And what you set, when you design the circuit, is the current.

Short of time to engage fully, but..

1) "considering" the transistor as a current controlled device doesn't mean that it is indeed such a one - I prefer to consider "current control" as a mere observation of the correlation of two currents, which is then promoted to a (non-existent, IMHO) causal relationship. Nothing in this thread so far has changed my mind (but being the most open-minded of open-minded individuals, I'm happy to be persuaded otherwise, by sensible arguments)

2) in your calculation of base current, the base current was computed using V_{BE} i.e. the base current was the dependent variable, and V_{BE} was one of the independent variables. Surely when we talk about controlling a quantity, we want to consider it as one of the independent variables in our experiment. Unless I'm confused, your own argument is promoting voltage control, no?

As to how a small base current can induce a much bigger current in the emitter and collector, you can find an explanation in Streetman

I have Streetman, but not Hu. I don't recall Streetman promoting current control much, but I will take a look - haven't looked at it properly for a long time.

But we can explain it with the Stormtrooper analogy:

Let's say we put a single electron in base, and this electron is in the form of a rebel alliance soldier with a target on his back. The emitter is filled with stormtroopers who see the lone rebel and start shooting at him - the 'light bullets' are the holes...

I'm rather more interested in the physical principles of current control than analogies, TBH.

And one point has occurred to me: isn't it the case that recombination in the base (which leads to base current) is something that transistor designers seek to minimise via base thickness and doping? - i.e. they seek to eliminate the very mechanism by which you claim the transistor is controlled? That looks like something of a logical problem in the argument of those who promote current control.

Anyway, au revoir. I have a Queen to celebrate!

[aneevuser]

It's amusing that Shockley wrote that in both the vacuum tube and the bipolar transistor, "one current is controlled by another":

I took a brief look at that paper - the current control comment seems to appear only at the end, when he is making an analogy with tube behaviour. He doesn't go on to discuss it more fully, so it looks like something of a throwaway comment. I'll look at it again when I've got more time though.

[Kleinstein]

For the DC case one can use both ways (voltage control and current control) to understand the transistor. They both work about equally well, maybe the current control a little more for the beginners and the voltage control if you need to include details like the early effect. Still both ways work OK.

It gets a litte different in the AC / time dependent case, especially turning off a transistor in emitter configuration from saturation. One can directly turn off the base current externally or even reverse the direction, but the collector current does not instantly follow the base current. It is only when the base votlage goes down to near zero that the collector current stops. To understand, model the transient or AC behavior the base - emitter votlage becomes the more important parameter. The base current sees complications from internal capacitance and storred minority carriers.

[rfeecs]

And one point has occurred to me: isn't it the case that recombination in the base (which leads to base current) is something that transistor designers seek to minimise via base thickness and doping? - i.e. they seek to eliminate the very mechanism by which you claim the transistor is controlled? That looks like something of a logical problem in the argument of those who promote current control.

For a modern transistor (since the 1960s), recombination in the base is not a major contributor to base current.  If it was totally eliminated, you would still have base current.

The base current is (almost entirely) the current flowing from the base into the emitter.


I'm not sure anyone is promoting current control.  I, for one, am simply saying that you can't prove it is one way or the other, and that it doesn't really matter.

[aneevuser]

And one point has occurred to me: isn't it the case that recombination in the base (which leads to base current) is something that transistor designers seek to minimise via base thickness and doping? - i.e. they seek to eliminate the very mechanism by which you claim the transistor is controlled? That looks like something of a logical problem in the argument of those who promote current control.

For a modern transistor (since the 1960s), recombination in the base is not a major contributor to base current.  If it was totally eliminated, you would still have base current.

The base current is (almost entirely) the current flowing from the base into the emitter.

You are of course correct here: I was mentally lumping the two causes of emitter current into one, when I made my comment. However, it is still the case, is it not, that in, say, a PNP device, the electron component of emitter current (I think they call it injection current? - need to check) is deliberately made as small as possible by doping, so I think my point here isn't entirely undermined - we don't want base current, if possible.

But I wasn't aware of your second comment about recombination current being so insignificant, so I have learnt something useful anyway. I'll have to go and look up the figures.

I'm not sure anyone is promoting current control.  I, for one, am simply saying that you can't prove it is one way or the other,

Well, maybe...

and that it doesn't really matter.

Most of the time, it doesn't. But people do argue about it a lot, don't they?

Anyway, since Mr Sredni has said that Streetman talks about the current control POV, I am recusing myself from this discussion to go and read it. I may return as a turncoat and try to convince you all that BJTs are indeed current controlled.

[Zero999]

I thought that nearly all of the base current flows through the emitter, until the transistor approaches the saturation region, when a significant amount starts to flow into the collector, as the base-collector junction diode forms a Baker clamp.

[Sredni]

1) "considering" the transistor as a current controlled device doesn't mean that it is indeed such a one

I am on the same page as rfeecs, here. I do not claim that BJT are solely current controlled. I claim that you can either see them as current controlled or voltage controlled. Or charge controlled, for that matter. The idea that they are 'fundamentally' voltage controlled is the result of a double... bias: first the way solid state physics is all about energy levels, and therefore potentials; and then the fact the 99% of the sources we use in our daily life are best approximated as voltage sources.

I do not see cause-effect in physical relations. Just relations. If you can bring in the time, in a way or the other, we could discuss cause and effect.

2) in your calculation of base current, the base current was computed using V_{BE} i.e. the base current was the dependent variable, and V_{BE} was one of the independent variables.

Actually I considered VBE as a constant. I used the approximation of the input diode as a vertical line at 0.7V. The current does not depend, by definition, on VBE because 0.7V is associated with ALL possible values of (positive) current.
This of course does not 'prove' current control (I am an agnostic: to me both voltage and current control are equally valid), but it shows that in this application it's easier to consider the transistor as current controlled.

isn't it the case that recombination in the base (which leads to base current) is something that transistor designers seek to minimise via base thickness and doping? - i.e. they seek to eliminate the very mechanism by which you claim the transistor is controlled? That looks like something of a logical problem in the argument of those who promote current control.

In the stormtrooper analogy, you don't want too many rebels in base. They would either shield the collector walls with their bodies or even go get them 'troopers in the emitter if they are too many.
But you still need a few to attract the stormtroopers' fire, otherwise you won't get any holes in the opposite wall.

No rebels in base, no flood of laser-fire.

Anyway, au revoir. I have a Queen to celebrate!

Whatever it takes to get those pints down, right? 

[Kleinstein]

How the current is divided between IB1 and IB2 depends on the purity of the matrials. In both cases there is recombination:  either in the base or in the emitter (including the contact). Due to the doping levels only rather few holes are send to the emitter. However the high doping level usually also comes with a shorter life-time and the emitter is usually large and thus more volume ( though planar transistors have rather small emitters).

[TimFox]

"Actually I considered VBE as a constant. I used the approximation of the input diode as a vertical line at 0.7V. The current does not depend, by definition, on VBE because 0.7V is associated with ALL possible values of (positive) current.
This of course does not 'prove' current control (I am an agnostic: to me both voltage and current control are equally valid), but it shows that in this application it's easier to consider the transistor as current controlled."

With this assumption, of course the current is independent of V_BE, since you don't allow it to vary.
I do not agree with this logic to disprove that the current depends on V_BE.

[Sredni]

It was never my intention to disprove that the current depends on VBE.
My point is that voltage and current are concomitant, so neither is the cause of the other.
I was replying to an objection that in order to design a transistor circuit one need to set VBE to a certain value. Nope, if it fits me better, i can set the current to a certain value (and that is what I did).

Given the exponential dependence of I from VBE, there is too much sensitivity on the value of VBE to be able to set it to a desired value in practice. I seem to recall you said something similar in a post of yours in the first page. I said something similar in this answer on SE a few years earlier ( https://electronics.stackexchange.com/questions/252791/why-is-a-bjt-considered-current-controlled ).

I am not setting VBE: I am setting IE and let VBE to be whatever value happens to be on the exponential curve for a value of VBE close enough to the 0.7V I assumed.