Collector current of an NPN common emitter circuit

[Winterstone]

Anyway, for those who would like to see an emitter resistor in the circuit i've included that in this next circuit. The values are:
..........................
If you would like to throw a few calculations for this circuit in, we can take a look.

Hello to all.
Just for information:

Some comments from H&H (The art of Electronics) regarding this circuit:

"Bad biasing"
"Disaster"
"Don`t do this".
"By using voltage biasing with a stiff voltage divider,.., the quiescent point is insensitive to variations in transistor beta."

W.

Remark: Voltage feedback and current biasing (at the same time) cannot work properly.

 

[ericgibbs]

Hello to all.
Just for information:

Some comments from H&H (The art of Electronics) regarding this circuit:

"Bad biasing"
"Disaster"
"Don`t do this".
"By using voltage biasing with a stiff voltage divider,.., the quiescent point is insensitive to variations in transistor beta."

W.

Remark: Voltage feedback and current biasing (at the same time) cannot work properly.

hi W,

With respect you are missing the point that 'Al' is making and you are now moving the 'goal posts'

Eric

 

[Winterstone]

hi W,

With respect you are missing the point that 'Al' is making and you are now moving the 'goal posts'

Eric

Eric, also with respect: I don`t understand your comment. Anything wrong with my post?
MrAl has suggested to "throw a few calculations for this circuit" and to "take a look".
That`s what I did. I took a look and I have placed a comment to this particular circuit.
Please inform me why I have missed the point.
Thank you.
W.

By the way: Because of my limited knowledge of your language I really don`t understand the meaning of the last words ("moving the goal posts")

 

[Jony130]

Anyway, for those who would like to see an emitter resistor in the circuit i've included that in this next circuit. The values are:
Rc=1k as before,
Re=100 ohms
Rb=497k
Vbe=0.65 as before.

If you would like to throw a few calculations for this circuit in, we can take a look.

Now for the circuit with Re resistor and 2N2222 and the beta spread between 50 and 300.
The collector current will be in the range Ic = 0.93mA to 5.3mA.
I'm a little surprised because I don't see any improvement compared to previous circuit without Re resistor.

Interesting question arise. For example if we use a Shockley equation (Ic=Is*(e^(Vbe/VT)-1)) to find ( determined) the collector current for a constant Vbe = 0.65V the collector current should also be constant? Or maybe I missing something in Shockley equation?

 

[Winterstone]

I'm a little surprised because I don't see any improvement compared to previous circuit without Re resistor.

I have tried to explain the reason (current biasing with voltage feedback) - however, surprisingly I was told that I had "missed the point".

Interesting question arise. For example if we use a Shockley equation (Ic=Is*(e^(Vbe/VT)-1)) to find ( determined) the collector current for a constant Vbe = 0.65V the collector current should also be constant? Or maybe I missing something in Shockley equation?

No, you didn`t miss anything. This equation clearly shows which three parameters determine the current Ic (saturation current, temperature, voltage Vbe).
When not all of the three are known, you cannot determine the value.
That means - the rule stating that the voltage Vbe controls the Ic value does not mean that Vbe alone determines this value (a common misconception).

Winterstone

 

[MrAl]

Hello again,

Jony:
Yes the collector current should be constant. Vbe is held constant. We
are going to look more into the Shockley equation too.

Winterstone:
Well i dont see any analysis from you for the circuit with the emitter
resistor nor for the circuit without the emitter resistor. You wanted a
emitter resistor so now there is one in the circuit so feel free to analyze
that circuit. If you would like to show how you would use the Shockley
equation that would be nice too, and feel free to explain.
But i dont understand yet what you mean by 'control' vs 'determine'.
As i said, we call the technique "voltage control" but we want to use
it to determine the bias operating conditions, if possible, and it should
be possible somehow, some way.

All:
For my own comparative analysis, i repeat the two formulas we are looking at
here:
1. Ic=Beta*Ib
2. Ic=Is*(e^(Vbe/VT)-1) [perhaps modified later for non ideal device]

The comparative analysis goes like this...
Using #1 above, we see a range of Ic no matter what we do because Beta ranges from 50 to 300.
Using #2 above, since we know we see a range of Ic no matter what we do, and Vbe and VT
are constant, the only thing that can change is Is. And Is must change in a manner
that is consistent with #1. Therefore it should not be any more accurate to use #2 than to use #1.

 

[Winterstone]

But i dont understand yet what you mean by 'control' vs 'determine'.
As i said, we call the technique "voltage control" but we want to use
it to determine the bias operating conditions, if possible, and it should
be possible somehow, some way.

Hi MrAl,
you will remember that I`ve tried to explain the difference (more than once) in a forgoing thread, however, I`ll do it again:


1.) According to Shockley`s equation, the collector current is determined by three quantities (Vt, Vbe, Is), however, there is only one external parameter that can control (modify, vary)
the current Ic - and that is undoubtly the base-emitter voltage Vbe.

2.) A particular value for Ic can be calculated only if all parameters that determine this value are known. In particular, this applies to the saturation current Is. However, this is a theoretical statement without practical background because of the large parameter uncertainties (tolerances) for each transistor type.

3.) By the way - this parameter uncertainty is the only reason for providing DC feedback with the aim to meet the desired Ic value (approximately) and to stabilize Ic against tolerances and environmental influences.

4.) Here is a very illustrative example: You can control the speed of a car with a corresponding pedal position - but you cannot derive from this information (position) the momentary speed of the car.
The speed is determined - in addition - by some other environmental parameters.

I appreciate your desire to use Shockley`s formula to "determine the bias operating conditions".
However, as said above, I am afraid this will be not possible in practice.

W.

 

[Jony130]

For my own comparative analysis, i repeat the two formulas we are looking at
here:
1. Ic=Beta*Ib
2. Ic=Is*(e^(Vbe/VT)-1) [perhaps modified later for non ideal device]

OK so for RB = 518KΩ and Vbe = 0.65V and I assume Is = 10x10^-15 and VT = 26mV and β = 50.

Ib = (Vcc - Vbe)/RB (1)

Vbe = VT*ln(Ib/Ise) where

Ise = Is/β = 200x10^-18

So in first iteration I get this

Ib = (10V - 0.65V)/518kΩ = 18.05μA

And the new Vbe value

Vbe = VT*ln(Ib/Ise) = 26mv *ln *(18.05μA/200x10^-18 ) ≈ 0.65587V

Second iteration

Ib = (10V - 0.65587V)/518kΩ = 18.0388μA

Vbe = 0.655856V

third iteration

Ib = 18.0388μA

Vbe = 0.655856V

So I end iteration here and Ic current for β = 50 is equal to

Ic = 0.901944mA and Vbe = 0.655856V

And if we do the same for β = 300 I end up with this solution

Vbe = 0.702312V and Ic = 5.38476mA

So in this case I get almost the same result as before.
But the first method is much simpler to use. All we need is assume Vbe value and use a "current control" view to determined Ib and Ic.
I'm aware that "current control" wins here because Vbe<<Vcc.

 

[crutschow]

Hi crutschow,

it seems I have expressed myself not clear enough.
Of course, you are right that B (resp beta) has an effect on the bias point. Did I state there would be no influence?

Not explicitly. But you stated that

* B=infinite (and that is the background for ignoring Ib)

which, to me, means that your are assuming Beta has no significant influence. But if you assume Beta is infinite and there is no base current, then you could design a base bias network using very high value resistors, and that obviously could give an incorrect bias point with a real transistor that does draw base current. My point is that, implicitly or explicitly, you need to account for base current when you design a BJT bias network.

 

[audioguru]

Why doesn't the discussed transistor have a voltage divider providing the base bias voltage? If it did then the emitter resistor provides bias stability.

 

[hanhan]

Jony,
what is the method you used here?

OK so for RB = 518KΩ and Vbe = 0.65V and I assume Is = 10x10^-15 and VT = 26mV and β = 50.

Ib = (Vcc - Vbe)/RB (1)

Vbe = VT*ln(Ib/Ise) where

Ise = Is/β = 200x10^-18

So in first iteration I get this

Ib = (10V - 0.65V)/518kΩ = 18.05μA

And the new Vbe value

Vbe = VT*ln(Ib/Ise) = 26mv *ln *(18.05μA/200x10^-18 ) ≈ 0.65587V

Second iteration

Ib = (10V - 0.65587V)/518kΩ = 18.0388μA

Vbe = 0.655856V

third iteration

Ib = 18.0388μA

Vbe = 0.655856V

So I end iteration here and Ic current for β = 50 is equal to

Ic = 0.901944mA and Vbe = 0.655856V

And if we do the same for β = 300 I end up with this solution

Vbe = 0.702312V and Ic = 5.38476mA

So in this case I get almost the same result as before.
But the first method is much simpler to use. All we need is assume Vbe value and use a "current control" view to determined Ib and Ic.
I'm aware that "current control" wins here because Vbe<<Vcc.

 

[Winterstone]

Why doesn't the discussed transistor have a voltage divider providing the base bias voltage? If it did then the emitter resistor provides bias stability.

Yes audioguru - that`s what I have already elaborated in my reply#16.

W.

 

[Winterstone]

..................
your are assuming Beta has no significant influence. But if you assume Beta is infinite and there is no base current, then you could design a base bias network using very high value resistors, and that obviously could give an incorrect bias point with a real transistor that does draw base current. My point is that, implicitly or explicitly, you need to account for base current when you design a BJT bias network.

Yes, you are right. It was a misunderstanding, because in my reply#16 it was my only intention to show that - even without any information about B or beta - a very good approximation for the actual Ic value can be found if we have sufficient DC feedback.
But if you have a second look on my calculation results in reply#16 you will notice that I have calculated a realistic bias network without an "account for the base current".
However, as I have stated also (see my reply#18), the calculation of the bias resistors to meet the desired current Ic is, of course, more accurate if we include an assumption for the base current in the calculation.

In summary: As shown in reply#16, the desired value for Ic can be established with good accuracy (example:4...8%) if we provide DC voltage feedback - even without knowing B or beta and based on a rough assumption Vbe=(0.65...0.7)V .

W.

 

[MrAl]

Hello again,


Audioguru:
This circuit is as given, we are to analyze it. The input bias is from a single resistor. Perhaps later we can look at the two resistor input bias circuit, but for now we're using this one. We can get away with this because for one it's the given circuit, and two because we are assuming a set base emitter voltage that does not change, nor does anything else change including the input if there was one, which there is not (yet).


Winterstone:

Hi MrAl,
you will remember that I`ve tried to explain the difference (more than once) in a forgoing thread, however, I`ll do it again:


1.) According to Shockley`s equation, the collector current is determined by three quantities (Vt, Vbe, Is), however, there is only one external parameter that can control (modify, vary)
the current Ic - and that is undoubtly the base-emitter voltage Vbe.

2.) A particular value for Ic can be calculated only if all parameters that determine this value are known. In particular, this applies to the saturation current Is. However, this is a theoretical statement without practical background because of the large parameter uncertainties (tolerances) for each transistor type.

3.) By the way - this parameter uncertainty is the only reason for providing DC feedback with the aim to meet the desired Ic value (approximately) and to stabilize Ic against tolerances and environmental influences.

4.) Here is a very illustrative example: You can control the speed of a car with a corresponding pedal position - but you cannot derive from this information (position) the momentary speed of the car.
The speed is determined - in addition - by some other environmental parameters.

I appreciate your desire to use Shockley`s formula to "determine the bias operating conditions".
However, as said above, I am afraid this will be not possible in practice.

W.

Well Eric (post #9) used the data sheet and came up with some useful results, and Jony130 (post #28) used the formula and came up with some useful results. How do you explain that and then what would you use that formula for? Also, that formula was in the post that Ratchit linked to in the other thread and he and the original poster seem to think it's the greatest formula.
We dont need a double resistor input because the circuit is given with only one resistor. We can look at double resistor input biasing later if you like.
But when someone gives a circuit to be analyzed we dont change it the way we want it to be we just calculate what the operating point is. If we are given a resistor value of 10k and voltage source of 10 volts we dont say, "Well i want a 20k resistor and 100 volt voltage source because i think it is better". We just take 10 and divide by 10000 and get 1ma. When we DESIGN a circuit then we have more flexibility, but when we ANALYZE a circuit we dont change it around and then do the analysis, we have to work with what we are given.
For example, what is the current with a 1N4004 diode and 1 ohm resistor in series, driven by a 10000 volt DC source? Yes it seems absurd but the right result is that the diode burns out, very quickly. We could suggest that the resistor be raised and the diode changed to a different type, etc., but if that's the circuit we are stuck with that UNLESS we can redesign the circuit and then and only then we have the flexibility to change the circuit so that it will work the way we think it will work better.

 

[Jony130]

Jony,
what is the method you used here?

I use iterative method.
https://en.wikipedia.org/wiki/Diode_modelling#Iterative_solution

 

[MrAl]

Hello again,


That's an interesting Wikipedia article. That's the first time i ever saw anyone other than myself use the Lambert W function to solve a diode circuit.

Also i want to point out that they did in fact include the emission constant which i was going to get into a little later on in the discussion.

 

[hanhan]

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.

So in this case I get almost the same result as before.
But the first method is much simpler to use. All we need is assume Vbe value and use a "current control" view to determined Ib and Ic.

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

 

[Winterstone]

Hello MrAl,

in your reply#26 you have asked for some clarification regarding the terms "control" and "determine".
I gave you an answer in my reply#27.
It would be interesting to learn if you agree or if you disagree.
To receive no comment at all is rather unsatisfying.

Nevertheless, I will respond to your last contribution#34 as follows:

1.) Quote MrAl:"Well Eric (post #9) used the data sheet and came up with some useful results, and Jony130 (post#28) used that formula ........ How do you explain that and then what would you use that formula for? Also, that formula was in the post that Ratchit linked to in the other thread and he and the original poster seem to think it's the greatest formula."

My comment:

Was Eric`s reply#9 really the answer you have expected?
I couldn`t imagine that you simply want us to insert some values into a formula only.

He has used ohms law for the given Rb value to arrive at a base current Ib.
Not very surprising.
And then he has used Ic=B*Ib with a rough assumption for B (because B is not known).
I could not imagine that you have asked for this information because such a basic procedure can be found in each beginners textbook.

As a second approach he has used a graph Ic=f(Vbe) to read the value of Ic for a given Vbe=0.65V.
Also not a challenging task.
Finally, he arrived at two different Ic values (3.2 and 5mA, respectively).

Did you ever use such an approach for designing an amplifier stage in practice? (as you consider it as "useful"). I can`t believe.

2.) Yes - you are right. In one of my contributions I gave some results for a circuit (with a resistive voltage divider) other than the circuit as specified by you.

Here is my justification:
* The circuit as given by you was so simple that it does not require any design actions. Just ohms law and the knowledge of multiplication is necessary (see my comments under 1.) above).
And the results - as expected - are not satisfying (unacceptable Ic spread because of unknown parameters, no stabilizing feedback).

* I thought it could be an interesting task to show - in comparison with your circuit - that there is another approach to determine the bias point for a given Ic without knowing the values for B or beta and without using the very rough Ic-Vbe characteristic (as Eric did). For my opinion, this could be an interesting information for some other readers of this thread.

* And finally, the results have justified this approach: The simulation results based on a realistic BJT model have shown that the error in Ic was just 4...8%.
(If you like you can compare this error with the two different values obtained by Eric and Jony130).

_______________
I must confess, there are some other parts of our contribution, which I cannot answer upon because I don`understand the meaning (...the original poster seem to think it's the greatest formula.)
Which formula are you referring to?

 

[Winterstone]

I use iterative method.
https://en.wikipedia.org/wiki/Diode_modelling#Iterative_solution

Yes Jony, what you did was a computational approach for finding Vd - in analogy to the graphical solution (shown on the wiki page).
However, unfortunately a shortcoming of the method is (still) the necessity to know the value of Is.
This is equivalent to the uncertainty connected with the Ib=f(Vbe) diagram in the data sheets - and that is the reason these curves cannot be used for a good BJT circuit design.
Nevertheless, a good link. Thank you.

 

[The Electrician]

That's the first time i ever saw anyone other than myself use the Lambert W function to solve a diode circuit.

You need to get out more.

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