Collector current of an NPN common emitter circuit

[MrAl]

Hello again,


Oblivion:
Yes that sums it up nicely, thank you for that very informative post.
We are looking at methods more than circuits themselves and trying to
determine what might be better, if any, and also hoping for more
contributions like Claude's to add to the pile of methods and maybe
one will stand out more than another in the end. I wont guess yet
until we see more and look at this more carefully.

Claude:
I will be interested to see your analysis when you get to posting it,
but take your time, a better analysis is always nicer than one posted
in haste I dont mind waiting, and i might post a little on this
myself at some point using the other methods then we can compare.

Thanks again to both of you for the really nice posts!

 

[Winterstone]

Transistor Maths
As for a formula that can be used to calculate a transistor general parameters without knowing Hfe/β, I don't think such a thing exists. As amplifying devices, β is the most important factor, this is the gain of the transistor, it's the reason for having a transistor. To suggest that the β of a transistor can be canceled out or ignored in such an equation is quite preposterous. It's like trying not to use the capacity of a capacitor, or the resistance of a resistor in a circuit calculation.

Hello ()blivion,

I just have read your contribution and like to add a comment ?

I have some doubts if beta really is "the most important factor" and that beta would be "the gain of the transistor" and that this is the "reason for having a transistor".
Regarding the gain properties I think the transconductance g=delta_Ic/delta_Vbe is the relevant parameter (remember the basic expression gain=g*Rc).
Regarding the role of the base current Ib and the factor beta I like to direct your attention to the enclosed document from Berkeley University (summary of chapter 8).
It would be interesting to hear what you think about the statements in this text regarding the importance of Ib and beta.

Thank you
regards

Winterstone


Quote:"To suggest that the β of a transistor can be canceled out or ignored in such an equation is quite preposterous"

May I point to the fact that in post#16 I have designed a circuit in common emitter configuration - including the bias resistors.
And in this calculation, I intentionally have ignored the so-called current gain value.
For my opinion, the results (deviation between desired and actual collector current) are not too bad (4...8% deviation).
In this context I remind you on the principle and the consequences of negative feedback: To reduce the influence of the active parameters and its uncertainties.

 

[Claude Abraham]

Now there is a dispute regarding the "importance" of Ib/beta. The Berkely reference is misleading and sophomoric. This book excerpt treats base current as a mere residue from "applying Vbe". Nobody applied Vbe to a bjt, it would be destroyed. Vbe is the energy per unit charge lost crossing the junction, Vbe does not drive anything. Ib is necessary to initiate bjt action as is Ie.
Also, what is Ib good for? First we must learn what Ib consists of, how it is formed. Ib has 3 important components, transport, injection, and displacement. The Berkley reference correctly identifies the injection component as consisting of holes from base to emitter when b-e junction influenced by external E field source. Buit they call this Ib component an annoyance. My beef is that Vbe is every bit as much an annoyance as is Ib. An ideal p-n junction when forward biased exhibits a non-zero current with zero voltage drop.

The b-e junction of a bjt is a forward biased p-n jcn, so how can Ib be an annoyance. A perfect p-n junction would result in Ib and Ie non-zero with zero Vbe. Treating Vbe as the driver, and Ib as an undesirable "side effect" is pure nonsense. Superbeta or supergain bjt parts have been around for decades, i.e. beta values around 5,000 or so. How is it done? The base region is doped with a very sparse density of acceptor ions during fabrication. By injecting dense donor population into emitter, and sparse acceptor population into base, low Ib is achieved. So we have had the ability to reduce Ib to a fraction on the order Ie/5000. Why then, do we intentionally produce bjt parts with beta 100-500? Ib is intentionally allowed to be 10 to 100 times greater than what we can achieve if we minimize it.

The answer is that base region hole density is what prevents collector base punch through and leakage current. Early Ge devices had atrocious c-b leakage esp at high temp. Ge devices were rated no more than 100 deg C junction temp. Designers had to keep in mind the high leakage. Also, punch-through is catastrophic. If one is amplifying a signal or switching power loads, when the device is intended to be off, the c-b junction must block the Vcb w/ minimal leakage current. Punch through results in the load being placed across Vcc w/ no control. Usually this is a disaster.

So injecting way more acceptors into the base, resulting in more Ib than otherwise would exist, is not an annoying side effect at all. High voltage bjt parts, like MPSA42 at 300 volts Vce, require wide base region heavily doped with acceptor ions. A 100V part requires moderate base doping, while a 20V part uses light base doping. Superbeta parts have a Vce breakdowm of 4-5 volts. The leakage is so high that servo circuits are employed to force Vcb to near zero. These are used in op amp inputs.

Ib is not an annoyance or side effect at all. Having higher than minimum acceptor doping in the base improves the bjt leakage current, Vce break down voltage capability. In addition to providing these needed features, an emitter follower benefits from Ib another way. In an EF, the load is connected to the emitter, whose current Ie is the sum of Ic and Ib. The source driving the base must output Ib, so it is desirable that Ib be as small as can be to not load that source. But the Ib value does power the load. Ib here is not wasted, it does useful work. For common base and common emitter, high Ib/low beta provides high Vce and low leakage assuring against c-b punch through.

Beta and Ib are very important, it just happens that beta is hard to control. So we employ clever methods to neutralize effects of beta variation like emitter degen and/or global NF. I will wxpound if needed. To sum it up, those who claim that beta/Ib are mere annoyances, or residues, are low information light weight hackers who have no understanding of semicon physics. We have bjt parts w/ beta=5,000. If Ib is useless undesirable side-effect, why does the semicon OEM make parts w/ beta=50, 100, 250, etc. when they already know how to get beta=5,000. If Ib is useless every bjt would be designed as superbeta.

Reducing Ib incurs other performance tradeoffs that are downright ugly. BR.

 

[Winterstone]

Hello Claude Abraham,

I must confess, I can agree to (nearly) all what is included in your reply.
There are only three sequences I do not understand:

1.) Nobody applied Vbe to a bjt, it would be destroyed.
(What does this mean ?)

2.) An ideal p-n junction when forward biased exhibits a non-zero current with zero voltage drop.
(Zero voltage drop? What then means „forward biased“?)

3.) The source driving the base must output Ib, so it is desirable that Ib be as small as can be to not load that source. But the Ib value does power the load. Ib here is not wasted, it does useful work.
(...power the load? Useful work?)

However, that`s not too important.
To me, more important is that, for my opinion, you didn`t touch at all the main question „Vbe vs. Ib control“. And I still think it is worth to be discussed.

It is neither my intention nor my job to defend the Berkeley text (although I think you are a bit too harsh using expressions like “pure nonsense“ or “low information light weight hackers„).
However - as far as I`ve understood the background of the Berkeley text - I think the main objective was the question „Vbe vs. Ib control“.
And, in this context, I think that it is not „pure nonsense“ to state that the base current Ib is „an undesirable but unavoidable sideeffect of the application of VBE“.
Note: This statement directly follows the claim that Vbe „uniquely determines the collector current“.
Therefore, I understand the term „unavoidable“ to mean: With respect to other performance parameters.

I think, in your contribution you have provided a very good explanation why we have BJT`s with moderate beta values (rather than super-beta-transistors).
With other words: You have shown why it is desirable to have a BJT technology that allows a certain amount of base current.
And for my understanding this is nothing else than a demonstration of a general principle in electronics we have to live with:

Every design is a trade-off between conflicting requirements. Improvement on one side of the device or circuit is paid for with a worsening of some other parameters.

Thus, I think there are good reasons (leakage, breakdown - as explained by you) to have a design that causes/allows a certain amount of base current Ib - but the current itself is not the final goal.
Am I wrong? Do you know what I mean ?

To sum it up: I agree with you that there are good reasons to have BJT`s with moderate beta values (although super-beta designs are possible).
However, does this mean that the BJT is current-controlled? I don`t think so.

You certainly will remember a discussion on the same subject we had in this forum some time ago (one year or more?).
To make my position clear again:
Vbe uniquely controls the collector current Ic through the transconductance g which is the slope of the Ic=f(Vbe) characteristic. Of course, Vbe can also be caused by a large resistor Rb and a relatively large DC voltage (non-ideal „current source“). In this case, we have a voltage divider between Rb and the finite DC resistance of the B-E path. But this does NOT imply that Ic is physically current-controlled.

W.

 

[MrAl]

Hello again Winterstone,


I see what you did in post #16. It looked like you did not calculate the values at first because you never showed the Shockley equation and the results using that equation. Instead, you used a different method and came up with possibly reasonable values for the bias circuit.

That's ok i guess, but what confused me is you quote the Shockley equation and then you use a different method to arrive at the bias solution. If you quote the Shockley equation then you should show how you used that equation.

So you dont want to actually use the Shockley equation then?

 

[Winterstone]

That's ok i guess, but what confused me is you quote the Shockley equation and then you use a different method to arrive at the bias solution. If you quote the Shockley equation then you should show how you used that equation.
So you dont want to actually use the Shockley equation then?

MrAl, I answer your question as follows (I repeat again and again):

*The Shockley equation shows that the collector current Ic can be controlled by the voltage Vbe. That is an important fact that is exploited for biasing each BJT. Thus, of course I have used it in this sense.
At the same time one can see that there are two other parameters (VT and Is) that determine the actual value of this current.

*From this it follows - and that is common knowledge - that it is not wise to bias the BJT with a fixed voltage Vbe (for example using a voltage divider directly across the B-E path).
As a consequence, a certain amount of negative DC feedback is applied (using resistor Re).
It was the intention of my calculation in post#16 to show that in this case the sensitivity of the resulting Ic to uncertainties/deviations of unknown parameters is considerably reduced.

*However, that`s no surprise because this sensitivity reduction is one of the big advantages of negative feedback in general.
(In analogy to the above described usage of Shockley´s equation we also bias an opamp using negative dc feedback - without regard to the open-loop gain and frequency response. However, this approach applies to the task of dc biasing only - dynamic stability must be ensured separately).

W.

Remark: I forgot to mention that Shockley`s equation, of course, is the key to determine/calculate the gain of an amplifier.
This is because the slope of this function Ic=f(Vbe) gives the transconductance g (g=Ic/Vt), which is used in the gain formulas.
(sometimes the inverse expression 1/g is interpreted as an internal small-signal resistance re=1/g, but - in reality - it is NOT a resistance).

 

[MrAl]

Hello again Winterestone,


Ok that's fine, but you still have not shown any example where you USE the Shockley equation for anything at all. I'd like to see how you use the Shockley equation next because you have quoted that and after all that is what part of my goal was for this thread. Do you understand this now? It will not help to keep repeating the same thing again because you've told me a lot of times now about negative feedback, the transconductance, how it is not wise to bias it a certain way, and other things. So you do not have to tell me this again ok? For example, show HOW the Shockley equation makes a good bias circuit possible or something like that.

All i wanted was for you to show how you use the Shockley equation with an example, even if you dont really want to use the circuit i posted with the emitter resistor and other bias resistors. I think it would be fine if you wanted to choose the resistors yourself, or even another bias circuit really. Do whatever you think is best, but include the Shockley equation and if possible how it helps and what values you think we should use for Is and so forth. We were using VT as a constant 0.0257 but if you want to use 0.026 for short that's ok too. We are looking at the common emitter circuit so it would be best to stick with that though, with any resistors you choose.

So the main idea now is to show the Shockley equation and all of the values for the variables in that equation.

 

[Winterstone]

Hello again Winterestone,

Ok that's fine, but you still have not shown any example where you USE the Shockley equation for anything at all. I'd like to see how you use the Shockley equation next because you have quoted that and after all that is what part of my goal was for this thread. Do you understand this now? .

No, I don`t.

Please. would you tell me why I should show you "any example" where I am going to "USE the Shockley equation for anything at all" ?
May be that you would like "to see how I use the Shockley equation". But I cannot fulfill your desire, because it cannot be used directly. This I have explained several times to you.

May I kindly ask you the following question: Is there any reply or contribution from me which contains or announces my intention to do this what you want me to do?
Please, give an answer to the above question.

Just the opposite is true! At least four times in this thread I have said that this equation can NOT be used to fix any Ic value.
This equation is only an indication that I can CONTROL the Ic value (that means: to change/modify the value) but not to fix it at a specific value.
Is this so hard to understand?

By the way: If I remember well, it was YOU who first introduced the Shockley equation into this thread.
I really don`t understand the contents and the background of your question.l

 

[()blivion]

1.) Nobody applied Vbe to a bjt, it would be destroyed.
(What does this mean ?)

Audioguru explained this in post #6

If you apply 0.65V [V[SUB]be[/SUB]] to the base-emitter of a transistor then some transistors will have a high base and collector current and maybe will burn out but other transistors will have a low base and collector current because each transistor is different even if they have the same part number. Also, a transistor conducts more when it is warm and conducts less when it is cool.

As for statements directed at me.

I have some doubts if beta really is "the most important factor" and that beta would be "the gain of the transistor" and that this is the "reason for having a transistor". Regarding the gain properties I think the transconductance g=delta_Ic/delta_Vbe is the relevant parameter (remember the basic expression gain=g*Rc).

I will concede that some circuits have no need to use β directly. However, everything I have read says that a transistors transconductance is derived from beta/β/H[SUB]fe[/SUB]. In the words of Wikipedia...

By controlling the number of electrons that can leave the base, the number of electrons entering the collector can be controlled. Collector current is approximately β (common-emitter current gain) times the base current. [...] Also, as the base–emitter voltage (V[SUB]be[/SUB]) is increased the base–emitter current [I[SUB]be[/SUB]] and hence the collector–emitter current (I[SUB]ce[/SUB]) increase exponentially according to the Shockley diode model and the Ebers-Moll model.

It would be interesting to hear what you[()blivion] think about the statements in [the berkeley] text regarding the importance of Ib and beta.

The specific words you are calling out in that paper are more than likely an inexact placeholder for the sake of simplicity, and not intended to be taken so literally. It is convenient to say "apply Vbe" in that document, even if that is not actually what they mean.

If the above proves false, then I would have to agree with Claude, audioguru, MrAl, Eric, and all same minded people. To say that one "applies Vbe" is just plain false, in most cases that would either destroy the transistor or not turn it on. In any case you can't design with this as your underlying transistor control mechanism. You need to work around it.

I have designed a circuit in common emitter configuration - including the bias resistors. And in this calculation, I intentionally have ignored the so-called current gain value.

I can't speak for MrAl, but from what I read he seems to doubt that you have in fact done exactly what you claim hear. I believe his position is that it just appears to you that you have ignored the current gain value. Again, I really can't speak for him.

As for my own opinion...

Even if you have come up with an equation that does not involve β, it does not mean you have an equation that can parameterize a transistor without ever using β. One can of course design a circuit that minimizes the effects of a parts variables. But that is not the same as designing a formula that can express a parts functions without those same variables. These things are totally different concepts.

In other words...

The success of negative feedback designs does not prove your argument for neglecting β altogether. The design was made specifically to allow one to neglect β. This says nothing about the transistors internal functionality or it's analysis that supports your claims through. If it proves anything, it proves that β is more significant.

Crutschow put it this way in post #17, which is essentially what I am saying...

You can ignore β in your calculations but that doesn't mean it[β] has no effect on the bias point.

Please. would you tell me why I should show you "any example" where I am going to "USE the Shockley equation for anything at all" ?

Winterstone... I think MrAl is simply asking you to show your work. Shockley equation or not.

If what you have actually done is created/used a mathematical equation for voltage controlling a transistor that does not involve beta/β... then you should be able to provide this equation and an example solution (or two or three) for any circuits. It's as simple as that.

You can say "I did it a new way" all you want... but we can say lots of things if we don't have to show proof. I can tell you I have found the answer to 408/12 through some new exciting way. Then I can give you the answer to 408/12, which is 34, and claim because this true it proves my point. But if all I show you is "408/12=34", you can't know that I didn't just use a calculator. One need to show your work for anyone to be able to believe one actually did it the way they claim.

As far as I see, you are the one making the extrordinary claims, therfore The burden of proof lies with you.

 

[MrAl]

Hello again,

Oblivion:
That's pretty much it, except this time i was asking Winterstone (again) to show how and what he would use the Shockley equation for. He states that the Shockley equation does SOMETHING, like prove something, but he seems to not want to show an example. I dont understand why this is so. Is it that we can not ask a question like this? I dont see why not, it's just a question that anyone might ask of anyone else knowledgeable in the field.

Winterstone:
As i said above, this is just a question that anyone might ask anyone else that is knowledgeable in the field. You stated that the Shockley equation did SOMETHING or proved something or somehow made something better, so i asked that you show WHAT it is that the Shockley equation could do for us. If you say it can not computer the Ic that's fine, but you did say it can control, so i'd like to see what it will control for us in a circuit of your choosing. That's not too much to ask is it?

Perhaps Ratchit can add to this thread also as he likes the voltage control method most.

 

[Winterstone]

Hi ()blivion,

it is not easy to answer your reply because you are going to mix several things (post`s from audioguru, MrAl, chrutschov, yourself). Nevertheless, I will try it.
For my opinion, there is a basic question behind all the other subjects (formulas, circuits, claims,..): BJT voltage- or current-controlled?
It is not the first time that this question is discussed in this forum and that`s not surprising because some books say "voltage" and some others "current".
I wiil come to this point later (at the end of this reply).

Here are my comments

I will concede that some circuits have no need to use β directly. However, everything I have read says that a transistors transconductance is derived from beta/β/H[SUB]fe[/SUB]. In the words of Wikipedia...

Do you blindly trust Wikipedia?
Do you know what "transconductance" means? Output current-to-input voltage ratio. Where is beta? Who told you that the transconductance is derived from beta?

The specific words you are calling out in that paper are more than likely an inexact placeholder for the sake of simplicity, and not intended to be taken so literally. It is convenient to say "apply Vbe" in that document, even if that is not actually what they mean.

Ahh - I see. You are going to interpret the text and you know what they mean.
Why didn`t you comment the sentences about the role of the base current and the claim that Ic "uniquely" is determined by the voltage Vbe?

I can't speak for MrAl, but from what I read he seems to doubt that you have in fact done exactly what you claim hear. I believe his position is that it just appears to you that you have ignored the current gain value. Again, I really can't speak for him.
[/URL]

Do YOU understand the meaning of this part of your reply? It just "appears" that I have ignored the current gain value?
In post#16 I have calculated a resistive voltage divider. It is not a hard job to proof if I have done this for an unloaded or a loaded divider chain (loaded by Ib).

Even if you have come up with an equation that does not involve β, it does not mean you have an equation that can parameterize a transistor without ever using β.

I am afraid, you didn`t understand the purpose of my example. What I have done is simply an approximate calculation - without using the parameter beta. It was my intention to show that - in contrast to your claims regarding beta ("most inportant", "gain of the transistor") - a design with good results is possible if dc feedback is applied. At the same time I have mentioned that any rough guess regarding beta would improve the exactness of the design (calculation of a loaded base divider). Didn`t you understand this approach?

Winterstone... I think MrAl is simply asking you to show your work. Shockley equation or not.

...."to show your work? In contrary: Several times he has asked me to show how I would use Shockley`s equation to establish a certain collector current.
And several times I have answered that I cannot do this, because of two reasons: (1) Missing parameters Vt and Is, and (2) bad/unrealistic design because of missing DC feedback.
I am really not motivated to insert numbers into a formula if this makes absolutely no sense.
It seems, up to now he didn`t understand the difference between "to control" and "to determine". Can YOU accept the different meanings? I have explained it several times in the thread and I never got a comment on this.

If what you have actually done is created/used a mathematical equation for voltage controlling a transistor that does not involve beta/β... then you should be able to provide this equation and an example solution (or two or three) for any circuits. It's as simple as that.

Which equation do you want me to provide? How to calculate a voltage divider? Are you joking? There is no secret equation. I have done a simple calculation that can be found in each beginners textbook and I was of the opinion that I discuss with people who know basic calculations.

As far as I see, you are the one making the extrordinary claims, therfore The burden of proof lies with you.

OK ()blivion, I will follow your recommendation to proof WHAT? What do want me to proof? The exactness of my complicated calculation of a resistive voltage divider?
What are my "extraordinary claims"? Please be specific - otherwise I cannot follow you. Please excuse my sarcasm, but I really don`t know what you are asking for.

Perhaps you are referring to the question "BJT voltage or current controlled". Indeed, that`s a basic question. However, it is not "my extraordinary claim" that the BJT, of course, is voltage controlled (in contrary to your knowledge source Wikipedia). I will summarize my point of view in a separate answer soon.
Regards
W.

 

[MrAl]

Hello again Winterstone,


Perhaps you missed this post:

Winterstone:
As i said above, this is just a question that anyone might ask anyone else that is knowledgeable in the field. You stated that the Shockley equation did SOMETHING or proved something or somehow made something better, so i asked that you show WHAT it is that the Shockley equation could do for us. If you say it can not to compute the Ic that's fine, but you did say it can control, so i'd like to see what it will control for us in a circuit of your choosing. That's not too much to ask is it?

So i am not asking the following:
1. Calculate Ic
2. Use a circuit that does not contain an emitter resistor
3. Use anyone else's circuit but your own

I also quoted values for VT previously. If you knew how to use the Shockley equation then you should know how to find Is somewhere, or else the equation is useless to anybody anywhere any time.

I just wanted to see how you would use it, that's all. Use it for anything at all that you care to show.

 

[Winterstone]

If you knew how to use the Shockley equation then you should know how to find Is somewhere, or else the equation is useless to anybody anywhere any time.

I just wanted to see how you would use it, that's all. Use it for anything at all that you care to show.

MrAl, I don`t remember how often in this thread I have stated already that

* this equation shows that the BJT can and must be controlled with a VOLTAGE (in contrast to some other people who think the BJT is current-controlled),
* the SLOPE of the corresponding characteristic Ic=f(Vbe) leads to the most important parameter in designing BJT amplifiers: Transconductance g.

For my opinion, both properties are of major importance, are they not?
What else do you want me to do? To insert numbers (Vbe, VT, Is) in a given formula?

W.

 

[MrAl]

Hi there Winterstone,


Thanks for the nice reply there.

I was hoping you could show some work so that we could take it farther, to investigate what we can use for Is and the emission constant and whatever else comes up here.

We hear and read so very much on the web about how we use Beta in an equation like:
Ic=Beta*Ib

and we often see a flood of calculations that follow. But we rarely see this Shockley equation except when someone happens to mention it, and then we almost never see any calculation examples to go with it. Examples really hit home for many people, including myself, so we like to see examples and talk about them further if something comes up that we dont quite understand.

If you still dont want to show any information like this well that's ok i guess, but then i'll have to search on the web to find something useful.

But just to quote the equation on the other site which played a large part in my motivation to start this thread, it read as:
Ic=Is*(e^(Vbe/VT)-1)

and the poster went on and on to say how good it was, and Ratchit seemed to agree as he was the one who linked to it, and you seemed to like it too so that seems to be the point of the discussion right now. So i guess we have to come up with some reasonable values for Is (and later the emission coefficient) and that would get us on our way i think.

As i said though, if you really feel strongly that you dont want to do this for any reason then dont worry about it too much anymore and then i will search the internet for more information and hope i can find some useful stuff there.

My end goal is to compare the different equations.

 

[Winterstone]

I was hoping you could show some work so that we could take it farther, to investigate what we can use for Is and the emission constant and whatever else comes up here.

But we rarely see this Shockley equation except when someone happens to mention it, and then we almost never see any calculation examples to go with it.

So i guess we have to come up with some reasonable values for Is (and later the emission coefficient) and that would get us on our way i think.

Hello MrAl,

your reply contains - for my opinion - a mixture of two items.

1.) I cannot help you in finding a reasonable value for Is - you must ask the BJT manufacturer. Of course, I could start a search in books and internet sites - but do you really expect this from me?

2.) However, as far as the second point is concerned - usage of Shockley`s equation - I can give you some more information (in addition to that I gave you already earlier):

(a) You certainly know the tanh characteristic of the transistor-based differential amplifier. This has been derived based on Shockley`s equation and using the relation exp(x)=sh(x)+ch(x).
May I add a comment? Several times in the past (in other threads) I have asked the "current-control" defenders how they would explain this characteristic based on the current-control principle.
Surprisingly, I never got an answer!

(b) Here is another example that works only for the voltage-control principle using Shockley`s equation: The famous Barry Gilbert (by the way: of course on the "voltage-control side")
has invented the principle of translinear loops, which leads to the very promising signal processing methods in the "log domain".

These are two examples, where Shockley`s equation must be used because that is the only way to solve the particular problem.
I hope I could help you.
Regards
W.

PS: I have started a new thread about BJT current control and I expect comments/corrections/critics from forum members in favour of BJT current-control.

 

[Claude Abraham]

Hello MrAl,

your reply contains - for my opinion - a mixture of two items.

1.) I cannot help you in finding a reasonable value for Is - you must ask the BJT manufacturer. Of course, I could start a search in books and internet sites - but do you really expect this from me?

2.) However, as far as the second point is concerned - usage of Shockley`s equation - I can give you some more information (in addition to that I gave you already earlier):

(a) You certainly know the tanh characteristic of the transistor-based differential amplifier. This has been derived based on Shockley`s equation and using the relation exp(x)=sh(x)+ch(x).
May I add a comment? Several times in the past (in other threads) I have asked the "current-control" defenders how they would explain this characteristic based on the current-control principle.
Surprisingly, I never got an answer!

(b) Here is another example that works only for the voltage-control principle using Shockley`s equation: The famous Barry Gilbert (by the way: of course on the "voltage-control side")
has invented the principle of translinear loops, which leads to the very promising signal processing methods in the "log domain".

These are two examples, where Shockley`s equation must be used because that is the only way to solve the particular problem.
I hope I could help you.
Regards
W.

PS: I have started a new thread about BJT current control and I expect comments/corrections/critics from forum members in favour of BJT current-control.

I can answer. Regarding the "tanh" characteristic of the emitter coupled pair, aka "diff amp", remember how it is configured. The emitters are joined with some degenerating emitter R. The emitters are driven by either a large emitter resistor to Vcc or ground, or by a CCS (constant current source). The large Re and/or the CCS have large impedance value. The input impedance to the diff amp, either base input, is the already large Z multiplied by beta, which makes it even larger.

These diff amps often appear at an op amp front end. Analyzing it as connected requires that we apply a voltage source to the input, not CCS. Because of the very high input Z, a CCS is ineffective. If an op amp input has 100 nA of input bias current with 1.0 volts, that would be an equivalent Zin of 10 Mohm. Also, with diff amps, the signal voltage source is not connected directly across b-e, but rather, the source hot lead drives the base input, with the output feedback driving the other base input.

"Digital Integrated Electronics" text, used in unis around the world, by Taub & Schilling, covers this diff amp. A diff amp can be ground referenced, i.e. no large Re nor CCS in emitter, but emitters (npn) tied straight to ground. In that reference text, the gain of the diff amp stage is computed solely in terms of "hfe" (beta). Tonight I will post the chapter and page. Diff amps can be described with beta, but for an op amp input, we generally drive them from a voltage source, except for photodiodes, which are current sources. For a PD transimpedance amp, the input is the CCS of the PD, the feedback resistance is the transresistance, and the output voltage is the current in times the transimpedance.

In this case the "tanh" function has little significance. The PD current is much larger than the input bias current. All PD current is supplied by op amp output through Rfb (feedback R). The accuracy is limited by the ratio of PD current to Ibias. Hence a very large beta value, superbeta, works very well on the diff amp front end. Here, beta is what matters most. Offset voltage due to Vbe mismatches usually is not a problem since PD shunt R value is larger than the Rfb value. Again, "tanh" is pretty much academic here.

But for voltage input voltage output amplifier applications, with negative feedback, the input and output are both CVS (constant voltage sources), and the feedback is also "voltage feedback" (vfb). It makes more sense to compute the diff amp stage in terms of transconductance, then view the second stage (voltage gain stage) as transimpedance. The CVS at the input is translated into a current by the diff amp transconductance (tanh). This current undergoes "voltage gain" at the 2nd stage, but it's really a transimpedance stage, outputting a voltage. This voltage drives an emitter follower output or compound pair (Cziklai).

So for voltage in voltage out amps with voltage feedback, I use the "tanh" computational method. But some amp designs, not much these days, used diff amps in the 2nd stage ("voltage gain" stage which is really trans-Z). Here we don't use the tanh function of hfe instead. The 1st stage (diff amp) output is a current source. The 2nd stage base terminal of the bjt receives a current source as its input, hence its collector current is defined as Ic2 = hfe2*Ib2. The "2" denoted 2nd stage bjt parameters.

Also, you mentioned that "gm*Rc" defines gain. Remember that passive parts, like a transformer, can provide voltage gain, or current gain, but not both in unison since power cannot increase. The beauty of active devices such as bjt/FET, is that they provide both current gain and voltage gain in unison, i.e. power gain >> 1. I found a computational sheet at home late last night which I will post after work. The hfe value is the upper limit for stage current gain. The gm value is that for stage transconductance. A bjt amplifies both I & V. It's not just 1 or the other.

The hfe value enters into voltage/transconductance gain as well. To compute, ic = gm*r_pi, we need to know r_pi. R_pi is the b-e junction equivalent resistance for small signals. R_pi = vbe/ib. To compute r_pi we must divide hfe by gm, r_pi = hfe/gm. Since r_pi = vbe/ib, we affirm that hfe/gm is given as (ic/ib)/(ic/vbe) = vbe/ib.

So to compute voltage gain of a single amp stage, we must compute Ic to get gm = Ic/Vt. Then we need r_pi to determine fraction of input voltage across r_pi (b-e junction), this value is vbe small signal, or "v_pi" in some texts. Then we multiply "vbe" or "v_pi" by gm to get ic. Multiplying ic by Rc' gives vout. But we cannot compute vbe w/o knowledge of hfe, esp. if Re is large. See what I mean? The parameters are so related and interactive/interdependent, that current gain hfe influences stage voltage gain.

Also, hfe influences loading down of signal source by amp stage input. A higher beta device not only gives us more stage current gain, but higher stage voltage gain as well. More later.

 

[()blivion]

At the end of the day, this thread, and the answers to all the problems in it boil down to two things...

1) Ignoring practical concerns, when you apply a voltage (V[SUB]be[/SUB]) to the gate of a BJT , it develops a current (I[SUB]be[/SUB]) through it. If you apply a current (I[SUB]be[/SUB]) through the base of a BJT, it will develop a voltage (V[SUB]be[/SUB]) across it. This is basic Ohm's law. From this, we can clearly know that there is really no such thing as "voltage control" or "current control" as they simply break down into each other in the end anyway. They are the same thing, and since they are, then obviously there can be no such thing as one being better than the other.

2) For all practical intent and purposes, the gain of a transistor can be derived from Ic=H[SUB]FE[/SUB]*Ib. This is well known and well established so it can be trusted. Now modifying Ebers–Moll model to be I[SUB]C[/SUB]=I[SUB]ES[/SUB]*(e^(V[SUB]BE[/SUB]/V[SUB]T[/SUB])-1) may work, it may even work well. However, this STILL involves parameters that are just as unit specific as H[SUB]FE[/SUB], namely V[SUB]be[/SUB]. If that wasn't enough, by using an irrational number, exponentiation, and a lot of approximations, I[SUB]C[/SUB]=I[SUB]ES[/SUB]*(e^(V[SUB]BE[/SUB]/V[SUB]T[/SUB])-1) becomes far more clunky, obscure, and imprecise than Ic=H[SUB]FE[/SUB]*Ib. For these clear reasons I[SUB]C[/SUB]=I[SUB]ES[/SUB]*(e^(V[SUB]BE[/SUB]/V[SUB]T[/SUB])-1) should be avoided in favor of simplicity, accuracy, and ease of use of Ic=H[SUB]FE[/SUB]*Ib.

 

[Winterstone]

Hello Claude Abraham,

I don`t know if your reply is an answer to my post or to MrAl`s last post. Nevertheless, thank you.

The forum member MrAl has asked for some examples where Shockley`s equation plays a role or is used, respectively. And I gave him two additional examples. That`s all!
Were anything wrong with that?

However, I must confess that I don`t know how to reply to your "lesson". I suppose, I can agree to everything - except the last to paragraphs.
I could not find out what you are going to tell me with that (somewhat confusing) collection of formulas (ic = gm*r_pi ??).

"So to compute voltage gain of a single amp stage, we must compute Ic to get gm = Ic/Vt."

For my opinion - and according to my experience - the design of an amplifier stage starts with the selection of a suitable collector current Ic.
Thus, it is not necessary to "compute Ic". Otherwise, if it is not known it can be simply measured

But we cannot compute vbe w/o knowledge of hfe, esp. if Re is large
Why do you want to compute the small signal value of vbe ? And from where you will get hfe?
What is the purpose of these parts of your reply?

Regards
W.

 

[Winterstone]

At the end of the day, this thread, and the answers to all the problems in it boil down to two things...

1) Ignoring practical concerns, when you apply a voltage (V[SUB]be[/SUB]) to the gate of a BJT , it develops a current (I[SUB]be[/SUB]) through it. If you apply a current (I[SUB]be[/SUB]) through the base of a BJT, it will develop a voltage (V[SUB]be[/SUB]) across it. This is basic Ohm's law. From this, we can clearly know that there is really no such thing as "voltage control" or "current control" as they simply break down into each other in the end anyway. They are the same thing, and since they are, then obviously there can be no such thing as one being better than the other.

I am afraid, you did not get the point. It is NOT the question if one or another principle is "better" or not.
The question is simply: What is the physical truth? And there can be only one answer.
More than that, don`t you think that a current can exist only if there is a driving voltage?
"They are the same thing?". Interesting statement.

I kindly ask you to reply to the new thread I have opened "BJT - current controlled?").

Regards
W.

 

[Claude Abraham]

computational details

I've attached a 4 page calculation sheet I just generated for a generic bjt single stage amp. This was done to demonstrate the interactive nature of bjt parameters. The relations between Ic, hfe, gm, etc., is detailed in this analysis. Feel free to comment or ask for clarity. Best regards.