Collector current of an NPN common emitter circuit

[Jony130]

Hi Jony,
As i understand, you are trying to find Vbe of a transistor by solving the equation using iterative method. I thought that Vbe for a trans is always constant regardless of β value.

No Vbe is not a constant. The Vbe varies with Ib current.

I measure Vbe Vs Ib for BC337-40 for Vcc = 10V

RB = 680kΩ....Vbe = 0.614V....Ib = 13.8µA

RB = 470kΩ....Vbe = 0.616V....Ib = 20µA

RB = 220kΩ....Vbe = 0.624V....Ib = 42.61µA

RB = 100kΩ....Vbe = 0.639V....Ib = 93.61µA

RB = 50kΩ......Vbe = 0.659V....Ib = 187µA

RB = 10kΩ......Vbe = 0.719V....Ib = 928µA

RB = 5kΩ........Vbe = 0.748V....Ib = 1.85mA

RB = 2kΩ........Vbe = 0.787V....Ib = 4.6mA

RB = 1kΩ........Vbe = 0.819V....Ib = 9.18mA

RB = 500Ω......Vbe = 0.856V....Ib = 18.29mA

RB = 200Ω......Vbe = 0.989V....Ib = 45mA

As you can see the base current change 45mA/13.8μA = 3260 times. But Vbe change only by 375mV. This very small change in Vbe compared with the huge changes in the base current can be ignored in some cases. And this is why we use Vbe= 0.6...0.7V in hand calculations.

Jony, i don't see the second method that you mentioned. Can you show the other method to figure out Vbe?

The first method is to simply assume that the Vbe is in range between 0.6V...0.7V.
And next find the base current
Ib = (Vcc - Vbe)/Rb and Ic = β * Ib (current control method)
And the second method (voltage control method) is to use Shockley equation (Ic=Is*(e^(Vbe/VT)-1)) and iterative method to solve for Ib, Vbe and Ic.

 

[hanhan]

Oh, thanks for the info.

As you can see the base current change 45mA/13.8μA = 3260 times. But Vbe change only by 375mV. This very small change in Vbe compared with the huge changes in the base current can be ignored in some cases. And this is why we use Vbe= 0.6...0.7V in hand calculations.

Yeah, this was confusing me.

The first method is to simply assume that the Vbe is in range between 0.6V...0.7V.
And next find the base current
Ib = (Vcc - Vbe)/Rb and Ic = β * Ib (current control method)

Does this mean that we also can't find exactly the value of Ic?

 

[MrAl]

You need to get out more.

https://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=895330&queryText=lambert+w

Hello there,

Well actually i think they should get out more. Ive done this before year 2000 im sure, and that's the date of publication. And i cant believe it took them until then to figure it out.

 

[MrAl]

Hello Winterstone,


I'll try to answer your question since you seem so intent on this answer.

The car pedal is not the same as the equation we are looking at. The equation we have looked at has clear inputs and outputs and there's no integration required. It's a simple formula.

Eric used the data sheet and that seemed like a good idea. So what is wrong with that? Clearly they put that graph(s) into the data sheet so that we could see them right? If you dont agree, then show me what you use that graph for, or tell my why it was a mistake for them to put that data sheet graph into the data sheet.

But because you asked this of the equation i then thought that i would ask you if you dont or cant use it for that then what would you use that formula for? Certainly it is not a wasteful formula is it?

So simply show me how you would use this formula and what you would use it for.

 

[Jony130]

Does this mean that we also can't find exactly the value of Ic?

Yes, you're right.

 

[The Electrician]

Hello there,

Well actually i think they should get out more. Ive done this before year 2000 im sure, and that's the date of publication.

Why should they get out more? Did you publish something before 2000 that they overlooked?

And i cant believe it took them until then to figure it out.

What makes you think that is the earliest paper on the subject? It was just the first one that came up with a search.

 

[MrAl]

Hello,

I wont argue over this, but im sure i've used it circa 1980, but i think it was originally written before the 1900's, at least the w function anyway. What i am surprised about is that it took them until 2000 to publish this. If you look at a write up of the function you'll see it screams "Diode"

I appreciate the link anyway.

 

[Winterstone]

Hello Winterstone,
I'll try to answer your question since you seem so intent on this answer.

Thank you. To me, it is good engineering practice to have a fair interplay between question and answers. This helps to solve problems and avoids misunderstandings.

The car pedal is not the same as the equation we are looking at. The equation we have looked at has clear inputs and outputs and there's no integration required. It's a simple formula.

Yes - I agree. The BJT does not act like a car (surprise?). However, in the technical world the BJT is not the only device that can be controlled.
And because you wanted me to explain the difference between either to "control" a quantity or to "determine" its value I have used a simple mechanical example to explain the difference.
And from your reply I can derive that you still are not clearly aware of the difference, are you?

Eric used the data sheet and that seemed like a good idea. So what is wrong with that? Clearly they put that graph(s) into the data sheet so that we could see them right? If you dont agree, then show me what you use that graph for, or tell my why it was a mistake for them to put that data sheet graph into the data sheet.

I do not understand this comment. Please, read again my replies. I cannot remember that I have used the terms "wrong" or "mistake" in connection with the usage of Shockley`s formula or the corresponding graph in the data sheet.
I simply have mentioned that it cannot be used to calculate a "good" value (lets say with an error of 10...20 %) because of large technological uncertainties.
And - if you remember your own comments - you are not very far from me (see your reply#19)

But because you asked this of the equation i then thought that i would ask you if you dont or cant use it for that then what would you use that formula for? Certainly it is not a wasteful formula is it?
So simply show me how you would use this formula and what you would use it for.

Is it really necessary to give you an answer to this question?
You are asking how and where this formula is used? Well, here is my answer:

Shockley`s famous formula describes how the current through a pn junction is determined (determined!) by the three quantities Vbe, Vt and Is.
And, obviously, if not all of these quantities are known (with sufficient accuracy) you cannot determine the exact value of Ic - however you clearly can see how the current Ic can be externally controlled by the voltage Vbe. To "control" something means to be able to change/modify the value (perhaps without knowing the absolute values; see the example with the car).

And this knowledge (how to control based on Shockley) is very important because of the following:

1.) It clearly shows how we can apply negative feedback (by feeding back a stabilizing voltage to the emitter node in order to influence Vbe)

2.) More than that the formula contains the most important property of the BJT: It`s ability to amplify!
The transconductance which describes the relationship between input (voltage) and output (current) is identical to the slope of the graph from Shockley´s formula.
______________________

I am sure, most of these information is not new for you - however, perhaps some parts are interesting or helpful for some beginners.

Winterstone

 

[MrAl]

Thank you. To me, it is good engineering practice to have a fair interplay between question and answers. This helps to solve problems and avoids misunderstandings.


Yes - I agree. The BJT does not act like a car (surprise?). However, in the technical world the BJT is not the only device that can be controlled.
And because you wanted me to explain the difference between either to "control" a quantity or to "determine" its value I have used a simple mechanical example to explain the difference.
And from your reply I can derive that you still are not clearly aware of the difference, are you?


I do not understand this comment. Please, read again my replies. I cannot remember that I have used the terms "wrong" or "mistake" in connection with the usage of Shockley`s formula or the corresponding graph in the data sheet.
I simply have mentioned that it cannot be used to calculate a "good" value (lets say with an error of 10...20 %) because of large technological uncertainties.
And - if you remember your own comments - you are not very far from me (see your reply#19)


Is it really necessary to give you an answer to this question?
You are asking how and where this formula is used? Well, here is my answer:

Shockley`s famous formula describes how the current through a pn junction is determined (determined!) by the three quantities Vbe, Vt and Is.
And, obviously, if not all of these quantities are known (with sufficient accuracy) you cannot determine the exact value of Ic - however you clearly can see how the current Ic can be externally controlled by the voltage Vbe. To "control" something means to be able to change/modify the value (perhaps without knowing the absolute values; see the example with the car).

And this knowledge (how to control based on Shockley) is very important because of the following:

1.) It clearly shows how we can apply negative feedback (by feeding back a stabilizing voltage to the emitter node in order to influence Vbe)

2.) More than that the formula contains the most important property of the BJT: It`s ability to amplify!
The transconductance which describes the relationship between input (voltage) and output (current) is identical to the slope of the graph from Shockley´s formula.
______________________

I am sure, most of these information is not new for you - however, perhaps some parts are interesting or helpful for some beginners.

Winterstone

Hello Winterstone,

Ok so what are you saying here...are you saying that we can 'determine' the collector current with Vbe but we can not 'control' it, or are you saying that we can 'control' the collector current with Vbe but we can not 'determine' it (using Shockey's equation)?

 

[Winterstone]

Hello Winterstone,

Ok so what are you saying here...are you saying that we can 'determine' the collector current with Vbe but we can not 'control' it, or are you saying that we can 'control' the collector current with Vbe but we can not 'determine' it (using Shockey's equation)?

Hello MrAl,

To answer this question I simply repeat the corresponding part of my former reply:

"Shockley`s famous formula describes how the current through a pn junction is determined by the three quantities Vbe, Vt and Is.
And, obviously, if not all of these quantities are known (with sufficient accuracy) you cannot determine the exact value of Ic - however you clearly can see how the current Ic can be externally controlled by the voltage Vbe. To "control" something means to be able to change/modify the value (perhaps without knowing the absolute values; see the example with the car)."

By the way - that`s not a result of my own investigations or "brainstorming" but common knowledge as documented in all textbooks.
And - as I have already mentioned - because we cannot fix (determine) the Ic value to the desired value (due to technological problems causing very large uncertainties/tolerances) we always provide DC feedback.
This feedback stabilizes the Ic value against tolerances as well as deviations (temperature) from its target value.

(I hope you have no problems with the last sentence, because it didn`t exactly fit to your question. You know the background of this remark? Eric did criticize my attempt to answer more than was asked.
He is afraid I could set new criteria).

Regards

Winterstone

 

[MrAl]

Hello again,


So you are basically saying that we cant do anything with Shockley's formula then because we can never know the variables exactly.

So you are saying that we can not 'determine' the Ic with Shockley's formula because we dont know Is exactly?

I am trying hard to understand what it is exactly you are saying here so i ask a question.

 

[The Electrician]

Hello,

I wont argue over this, but im sure i've used it circa 1980, but i think it was originally written before the 1900's, at least the w function anyway. What i am surprised about is that it took them until 2000 to publish this. If you look at a write up of the function you'll see it screams "Diode"

I appreciate the link anyway.

I'm sorry you feel that we're arguing; I'm trying to discuss, not argue.

This is the second time you've said "What i am surprised about is that it took them until 2000 to publish this." Implicit in that statement is the assumption that the referenced paper is the earliest on the subject. Why do you make that assumption?

If you were using the function circa 1980, you must have read about it somewhere. That means you were paying attention to the literature then. If you were still reading the technical literature nowadays, you would have been aware that the referenced paper had been published 13 years ago. But, you apparently haven't been keeping up for at least the last 13 years. You seemed surprised that someone other than yourself was using it to solve circuits involving diodes and resistors. That's what I meant when I said "you haven't been getting out enough".

Lambert himself derived the function around 1758, but it wasn't named the "Lambert W" function until 1993, so there will be no papers in the technical literature before 1993 referring to the "Lambert W". If you were using it circa 1980, you weren't calling it the "Lambert W".

Where did you first read about it?

 

[MrAl]

Hello again,

Ok thanks for clarifying. I was so long ago now that i dont remember, but i was probably given the idea from the chief engineer. We're talking some 32 or 33 years ago. But it really doesnt matter that much as i dont read every technical article under the sun. There's so much to cover these days i am lucky if i read my own bank statement

These days the only time i read anything is when someone brings up a subject (like this) about something interesting that i used to use or was interested in in the past.

As i am sure you know, knowledge often comes far sooner than the publication, and history shows us that people credited with first discoveries are sometimes not the very first to discover something or use something in a particular way that had never been done before.

So do you know if anyone published anything sooner than that? I ask because if you look at the writeup you will seem immediately that it most likely could be used for a diode. It's actually hard to miss, so that's why i was surprised. But if you know of a publication that came out sooner than that about using it at least for a diode that would be interesting too. If not, it could be because computer models sort of trump the method anyway, as computer programs for circuits started getting real intense that didnt need this particular function. I just found it interesting that's all, as a side method for a particular kind of circuit containing the exponential.
So if you now of another publication that uses it for a diode you could post that and i'll take a look.

I didnt mean to imply that we *were* arguing (yet) but that i didnt want to get into a heated debate about when it was published, when the first one was, how much i get out, etc., but if you have more info i'd be happy to read it. But now that you mention it i should be taking more trips to the library these days
We rely on the web too much i think and the web doesnt have everything yet.

 

[Winterstone]

Hello MrAl, here comes my answer.

So you are basically saying that we cant do anything with Shockley's formula then because we can never know the variables exactly.

No, that´s NOT what I am saying. Please read again the end of my reply#48 - I repeat again:

1.) The formula shows that we can control Ic via Vbe. With other words: From the formula we can derive the information that we can apply
negative voltage feedback (by feeding back a stabilizing voltage to the emitter node in order to influence Vbe)

2.) More than that, the formula reveals the most important property of the BJT: It`s ability to amplify!
The transconductance g which describes the relationship between input (voltage) and output (current) is identical to the slope of the graph from Shockley´s formula.

So you are saying that we can not 'determine' the Ic with Shockley's formula because we dont know Is exactly?

Yes, that`s correct (as mentioned already several times in this and a related foregoing thread).

 

[MrAl]

Hello MrAl, here comes my answer.


No, that´s NOT what I am saying. Please read again the end of my reply#48 - I repeat again:

1.) The formula shows that we can control Ic via Vbe. With other words: From the formula we can derive the information that we can apply
negative voltage feedback (by feeding back a stabilizing voltage to the emitter node in order to influence Vbe)

2.) More than that, the formula reveals the most important property of the BJT: It`s ability to amplify!
The transconductance g which describes the relationship between input (voltage) and output (current) is identical to the slope of the graph from Shockley´s formula.


Yes, that`s correct (as mentioned already several times in this and a related foregoing thread).

Hello again,

Well i ask because people have already done this. The results are not perfect, but they are still usable. And since Vbe does not depend on the emitter resistor being there or not we still see it working to some degree without an emitter resistor. So i am not sure what degree of accuracy you want to say is the criterion for 'works' or 'doesnt work'.

My only point was that it was not any better than using Beta. But you seem to be dismissing it entirely for 'determining' the Ic.

It's unfortunate that Ratchit is not here to reply because he has always shown himself to be a strong advocate of the voltage control method.

 

[Winterstone]

MrAl, Hello again

Well i ask because people have already done this. The results are not perfect, but they are still usable. And since Vbe does not depend on the emitter resistor being there or not we still see it working to some degree without an emitter resistor. So i am not sure what degree of accuracy you want to say is the criterion for 'works' or 'doesnt work'.

There are, of course, people who "have done it". People have done a lot of things. But - the question is if it makes sense or not. And I doubt, if the results "are really "usable".
Do you consider the temperature effects which even can destroy the transistor? I never have seen an amplifier stage in common emitter configuration without any dc feedback, did you?
If you don`t believe me - here are some statements to be found in the "electronic bible" (H&H, The Art of Electronics):

* "The grounded emitter amplifier should be avoided - eccept in circuits with overall negative feedback";
* "The grounded emitter amplifier is difficult to bias. It might be tempting just to apply a voltage that gives the right quiescent current. That won´t work because of the temperature dependence of Vbe.
* "Such unstable biasing is useless."

My only point was that it was not any better than using Beta. But you seem to be dismissing it entirely for 'determining' the Ic.

Sorry - I don`t understand what you mean because you always speak about "it". What is better than what?

It's unfortunate that Ratchit is not here to reply because he has always shown himself to be a strong advocate of the voltage control method.

I think, now we come to the "core" of the problem - and I am not sure if you aren`t mixing up two different things: (1) The physical truth and (2) the technical method.

1.) At first, there is the question, if the current Ic of a BJT is PHYSICALLY controlled by the voltage Vbe or by the base current Ib. Only one single answer is possible because the transistor physics cannot depend on external circuitry. I know, that two different explanations can be found in textbooks - however, only one can be correct. I think, the people who are "advocates" of voltage control (Ratch and myself) have some good arguments, see for example the link Ratch has given elsewhere (I think, a very useful link, in particular post#10):

https://cr4.globalspec.com/thread/68055/voltage-vs-current

If you are interested, I can give you a reference from Berkeley University explaining why the BJT is physically voltage controlled.
But - this question has nothing to do with the METHOD how the transistor is biased.

2.) There are two different methods a BJT can be biased: Voltage driven or current driven (not "controlled"). What means "current driven"? We use a large resistor Rb and a relatively large dc voltage to realize a voltage divider between Rb and the dc resistance Rbe of the B-E path. In our engineering community it is a common agreement to call this method "current driven", in spite of the fact that it is not really a current source.
The current Ib is primarily determined by the resistor Rb - that`s all. And, of course, there is a useful relationship Ic=B*Ib. But this formula does not mean that Ib controls Ic. It`s just a fixed relation.
However, the current Ic still is controlled by the voltage, which is developed across the B-E path.

 

[Jony130]

Sorry - I don`t understand what you mean because you always speak about "it". What is better than what?

We have a two equation that we can use to determine the Ic. First equations is
Ic = Hfe *Ib and the second one is Ic = Is*(e^(Vbe/Vt) - 1).
And I think that MrAl want to compare this two equation from engineering point of view.
Which of this two equations gives "better" result in determining Ic current.

 

[Winterstone]

We have a two equation that we can use to determine the Ic. First equations is
Ic = Hfe *Ib and the second one is Ic = Is*(e^(Vbe/Vt) - 1).
And I think that MrAl want to compare this two equation from engineering point of view.
Which of this two equations gives "better" result in determining Ic current.

Jony, when you speak about "better results in determining" - do you mean pure calculation with pencil and paper or do you mean "to realize" in a practical circuit?
In the first case, it depends, of course, on the knowledge of the corresponding parameters Hfe or Is, respectively.
Normally, both are unknown for a certain unit. So - what do you really mean?

W.

 

[Jony130]

We have been given this circuit and 2n2222 datasheets

RB = 510kΩ; Rc = 1KΩ

And our task is to find Ib and Ic current. Next we build this circuit and we check our calculation on the bench.

 

[Winterstone]

We have been given this circuit and 2n2222 datasheets
RB = 510kΩ; Rc = 1KΩ
And our task is to find Ib and Ic current. Next we build this circuit and we check our calculation on the bench.

Is this a question to me?
Well, that`s basic.
Assuming Vbe=0.65 volts the base current is Ib=18.3 µA.
If you have a reasonable value for B you can calculate Ic=B*Ib.
Without some knowledge about B you have a relatively large uncertainty (typically up to 500%)
Another (small) uncertainty stems from Vbe=0.65 V which also is an assumption only.