Yes, this is the physical explanation... but of the Early effect... Note the question is about the physical explanation of the Early voltage...

I agree with Dr. Nikolai

But, where is an answer to my question (Ib or Vbe as a constant parameter) ?

I think, the physical background was clear from the beginning.

Dear Lutz,

"The physical background was clear from the beginning"... but this is the background of the Early effect... not of the Early voltage... but they are different things...

I am not a specialist on the Early effect and it is difficult for me to take an attitude on your question... I was just impressed how such a simple and clear trick (Early voltage) could be explained in such an abstract way, e.g.:

"Tangents to the characteristics at large voltages extrapolate backward to intercept the voltage axis at a voltage called the Early voltage."

"If you look at the load line of collector current vs collector voltage of a BJT, it has a slope. If you extrapolate that slope back to the X axis, the intercept is the Early voltage."

IMO the idea is extremely simple and material (physical) - the high (but finite) differential resistance of the transistor in the active region of its output characteristic is presented by the IV curve of a humble resistor-type current source (sink). It consists of a constant voltage source (with Early voltage) and constant ohmic resistor with resistance equivalent to the transistor differential resistance in this region...

Rather, over the last few days, I have been thinking very intensely on our discussion about the cause of the low output resistance of the emitter follower... and definitely already have a view on the matter...

Cyril, thank you for your answer. However, I am afraid I was not able to make my doubts clear to you.

Of course. the output charactrristics Ic=f(Vce) has a slope. And this slope can be modelled as mentioned using such a ficticious term like Early voltage.

This can be found in all relevant textbooks.

HOWEVER, THERE ARE TWO OPTIONS - AND YOUDID NOT MENTION IF YOU WANT TO KEEP IB OR VBE CONSTANT.

Only this was my original question from the beginning.

In my first post I have presented some examples (references) for the two diffrent ways to define the quantity Early voltage.

Wh is it necessary to state if we keep Ib or Vbe constant ?

BECAUSE IN BOTH CASES WE GET DIFFERENT VALUES.

This is the core of my question

There should be ONE definition - but which one ??

To me, If the Early voltage is a physical parameter modelling the Early effect then it must be independent of Ib and Vbe

Erik - we have two possible sets of functions Ic=f(Vce). One set with Ib and another with Vbe as a parametr. And in both sets we observe DIFFERENT SLOPES. Do you agree?

When modelling/describing these slopes we make use of an ARTIFICIAL quantity called EARLY VOLTAGE.

Because of the different slopes we get different values for this describing quantity.

Question to you (my main question, up to now not answered):

Which set is to be used to find this Early voltage for a specific transistor?

Here are two hypotethical teachers trying to explain to their students what the Early voltage is:

Teacher A: "As you can see, the BJT output characteristic has a slope. Extrapolate that slope back to the X axis. The interception point is the Early voltage."

Teacher B: "The BJT output characteristic has a slope determining the differential resistance in this region. You can think of it as of a characteristic of an imperfect current source consisting of two elements in series - a constant voltage source with Early voltage and constant ohmic resistor with resistance equal to the differential resistance."

Who do you think will be more successful?

Exactly, Nikolai!

Erik, I am not able to answer - because you speak about the “output characteristic“ . But you completely ignore the fact that there are TWO possible set of curves - as I have mentioned several times.

Moreover, what is your answer to my question?

When we speak about output characteristics of the BJT we always must indicate if Vbe or Ib is held constant. BECAUSE BOTH SETS OF FUNCTIONS HAVE DIFFERENT SLOPES.

Hence, also the corresponding output resistances are DIFFERENT !

I repeat again: THIS IS THE CERNEL OF THE QUESTION.

Nikolai, please go back to my initial question.

I have given some references as an example for DIFFERENT explanations which can be found in the literature.

I am really surprised that - up to now - nobody in this discussion is able to realize this discreapency. Even worse,it seems nobody understands my question. Sometimes, the existence of two different sets of output characteristics is completely ignored!!

Cyril, regarding both teachers A an B, I think teacher B needs inputs from teacher A (value of Early voltage as well as the diff. resistance).

Hence, the model of teacher B does not compete with the method of teacher A. That means we cannot compare both approaches.

B is helpless without A.

B alone makes no sense at all because it even needs the definitions of A.

The presentations of A are clear and logical - the artificial model of B does not help at all, it confuses the students .

This is the link:

https://www.researchgate.net/post/How_is_the_Early_voltage_defined

Maybe I should begin thinking on this question too...

Cyril, thank You for providing the link.

Nikolai, please look in particular to the start (question) and my contributions No. 7 and No. 12.

Cyril, in your first contribution (initial question) you have explained the derivation of the Early voltage based on a diagram with VBE as a parameter.

What does this mean?

Was this already an answer to my basic question (Ib or Vbe as a parameter)?