# matching spice model with formula

#### yef smith

Joined Aug 2, 2020
293
Hello,for Bjt to be in working state. we need to V_B>V_E and V_C>V_B
How do i know the saturation current of 1.3A from mathematical point of view using the data sheet.
I know that the formula is as shown bellow.
the datasheet is as shown bellow:
https://pdf1.alldatasheet.com/datasheet-pdf/view/50085/FAIRCHILD/2N2222.html

the spice model is as shown bellow,Where can i see the formula parameters at the spice model description?
Thanks.

#### Papabravo

Joined Feb 24, 2006
17,283
You can't necessarily see a direct connection between the parameters listed in the model and the results you see in a simulation. The best you can do is learn what role the various parameters play in producing results. This document may help. You can also find it with a "Goggle" search. Driving the BE junction with a voltage source would NEVER be done in practice. the currents will be "YUGE", and 1.3A of collector current is far in excess of it's maximum ratings. Review the definition of saturation to determine the best method of characterizing whether you are or are not in that region.

Also check out the following:
Saturation in transistors (BJTs) - why and how | Electronics Forums (electronicspoint.com)

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#### yef smith

Joined Aug 2, 2020
293
Is=10^-14 Vbe=1V V_T=0.025
So i get Ic=2353.852 by the formula bellow.
where did i go wrong?

#### Papabravo

Joined Feb 24, 2006
17,283
You went wrong in assuming that the domain for the function includes the entire real number line.
What values did you use for the constant in in front of the expression in parentheses?
Your lack of precision is absolutely stunning!

#### yef smith

Joined Aug 2, 2020
293
(10^-14)*exp(1/0.025)*(1)=2353

#### Papabravo

Joined Feb 24, 2006
17,283
The result of evaluating the expression has a sensitive dependence on the choice of Vt. 25 mV is on the extreme low end of the range of values it can assume. A typical range range for this value might be 26mV-52mV depending on the junction temperature which could be ambient or something else. As to the value of Vbe, understanding it's range of possible values is important as well. Let's use Vbe = 650 mV and Vt = 26 mV, then

Ic = (1E-14)(exp(.65/.026)) ≈ 720 μA

which I think you might agree is a more reasonable value. If the Beta was 200 this would imply a base current of 3.6 μA

Now let us raise the the Vbe to 690 mV, and we get

Ic = (1E-14)(exp(.69/.026)) ≈ 3.35 mA. Again if the Beta was 200 this would imply a base current of 16.8 μA

You can see that by the time you get to a Vbe of 1 volt, if that were even possible, the current would be so large that the device would destroy itself. Unfortunately a simulation will not demonstrably show us this outcome.

It might be instructive for you to compute the Vbe that would result in the collector current equal to the absolute maximum specified in the datasheet.
Also use a current source for driving the base.

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#### yef smith

Joined Aug 2, 2020
293
Hello,so given the following simulation i get Vt=0.0317.if i increase Vb to 1.1 as shown in the next simulation.
I get 0.48A in simulation where as in calculation its 10^-14*exp(1.1/0.0317)=11
Where did i go wrong?

#### Papabravo

Joined Feb 24, 2006
17,283
Why are you still using voltage sources on the base terminal?
Your equations are not valid over the domain of ALL REAL NUMBERS!!

#### Papabravo

Joined Feb 24, 2006
17,283
Do it like this:
The upper plot is Beta as a function of Vce
The lower plot is Ic as a function of Vce
The saturation region is labeled on the collector characteristic curves

My 2N2222 model is:
.model 2N2222 NPN(IS=1E-14 VAF=100 BF=200 IKF=0.3 XTB=1.5 BR=3 CJC=8E-12 CJE=25E-12 TR=100E-9 TF=400E-12 ITF=1 VTF=2 XTF=3 RB=10 RC=.3 RE=.2 Vceo=30 Icrating=800m mfg=NXP)

#### crutschow

Joined Mar 14, 2008
28,201
As noted, It is impossible to get a transistor to saturate with a pure current sources.

#### Bordodynov

Joined May 20, 2015
2,939
I think it will be useful:

#### LvW

Joined Jun 13, 2013
1,337
.......................

Also use a current source for driving the base.
@Papabravo, I think it would be very helpful for the questioner if you could give a physical/technical reason for your recommendation. (Remark: I do not agree with your advice. See the exponenential relationship between Vbe and Ic).

#### Bordodynov

Joined May 20, 2015
2,939
LvW, you keep pursuing the idea that the bipolar transistor is voltage driven! And you are not even confused by the fact that transistor manufacturers give saturation voltages at fixed collector and base currents. You can count whatever you want, but I prefer to use whatever is more convenient. A bipolar transistor has a parameter called base resistance. And it can have a variation and because of this different resistance will be different base-emitter voltage, especially in saturation mode. I have already told you how some researchers powered a LED with a voltage source and the LED burned out. When they asked me what voltage to put on the LED, I got very annoyed. It can be the same with a bipolar transistor. For you the physical principle is important, but for others it is important how to just turn the transistor into saturation mode. And the principle of the transistor is important to students. I considered the bipolar transistor to be a current-driven device and developed many circuits, the operation of which confirmed my calculations. And you only complicate your calculations with exponential dependencies.

#### LvW

Joined Jun 13, 2013
1,337
LvW, you keep pursuing the idea that the bipolar transistor is voltage driven! And you are not even confused by the fact that transistor manufacturers give saturation voltages at fixed collector and base currents. You can count whatever you want, but I prefer to use whatever is more convenient. A bipolar transistor has a parameter called base resistance. And it can have a variation and because of this different resistance will be different base-emitter voltage, especially in saturation mode. I have already told you how some researchers powered a LED with a voltage source and the LED burned out. When they asked me what voltage to put on the LED, I got very annoyed. It can be the same with a bipolar transistor. For you the physical principle is important, but for others it is important how to just turn the transistor into saturation mode. And the principle of the transistor is important to students. I considered the bipolar transistor to be a current-driven device and developed many circuits, the operation of which confirmed my calculations. And you only complicate your calculations with exponential dependencies.
I am sorry but I strongly disagree with you.
May I explain?
1) At first, we have to distinguish between (and should never mix) (a) physical realities and (b) models which can (can !) be used during analyzing BJT-based circuits.

2) I am not "pursuing" the idea that the bipolar transistor is voltage driven. Rather, it is a fact that the working principle of theBJT is based on voltage control. This was prooved several times - and it is really not a problem to verify this fact. Simply consult Shockleys famous equation which is the basis for ALL BJT models within circuit simulators.

3) No - I am not "confused" about manufactureres data sheets because I know WHY they have given saturation voltages with the corresponding currents.
Do you know the definition for saturation?
Saturation is defined as a condition, where the base-collector voltage is large enough to open the B-C-junction in forward direction. And what is the outer indication for this state which can be measured? Answer: The base current is much larger than determined by the "normal" B-value which applies to the linear mode.
Hence, such a large base current is not the "condition", but an "indication" for saturation (caused by the C-B voltage!)

4) Quote: " And the principle of the transistor is important to students. I considered the bipolar transistor to be a current-driven device and developed many circuits, the operation of which confirmed my calculations. And you only complicate your calculations with exponential dependencies."

Yes - and the students should learn from the beginning that (a) the BJT is based on pn-junction properties (known from the working principle of the diode) and (b) that there is a fixed relationship between Ic and Ib (Ib is nothing else than a part of Ic, without any control function).
As you have "developed many circuits" - I am sure you know that it is common practice to apply circuit principles (e.g. feedback) which allow us to design circuits without complicating our calculations "with exponenetial dependencies".
More than that, I am sure that you also know some applications where this exponential dependency (Vbe controls Ic) is explicitely exploited (Current mirror, log-circuits, translinear signal processing...).

5.) Finally, I have a request to you:
I am very interested to learn from you which circuits you have developed which have "confirmed your calculations".
If you are interested, I can list you several obeservations, circuit properties, design steps, theoretical BJT properties which clearly proove voltage control. Are you interested?
Regards
LvW

PS: Sorry for this long reply.
Actually, I only wanted the forum member Papabravo to explain his advice to the questioner "your approach, using voltage sources, is misleading as well.". Dont you think, such a recommedation must be explained ?
.......................

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#### Bordodynov

Joined May 20, 2015
2,939
I'm not interested. Let's take the cascade circuit as an example. How do you calculate the output current of the second transistor using the concept of voltage control? And our argument is akin to arguing about which came first the egg or the chicken? That is, it makes no sense. I once gave an example of a bipolar transistor being controlled by a photodiode. You ignored it. After all, the reverse biased photodiode is a good current generator. Usually in transistor optocouplers the photodiode is a collector photodiode, but there is a 6N136 for example. How would you calculate such a circuit? Isn't the transistor controlled by voltage. Or the source is the photodiode current which creates the base-emitter voltage, i.e. the primary is the current.
The photocurrent is almost proportional to the power incident on the photodiode.

#### LvW

Joined Jun 13, 2013
1,337
I'm not interested. Let's take the cascade circuit as an example. How do you calculate the output current of the second transistor using the concept of voltage control? And our argument is akin to arguing about which came first the egg or the chicken? That is, it makes no sense. I once gave an example of a bipolar transistor being controlled by a photodiode. You ignored it. After all, the reverse biased photodiode is a good current generator. Usually in transistor optocouplers the photodiode is a collector photodiode, but there is a 6N136 for example. How would you calculate such a circuit? Isn't the transistor controlled by voltage. Or the source is the photodiode current which creates the base-emitter voltage, i.e. the primary is the current.
The photocurrent is almost proportional to the power incident on the photodiode.
So you are not ineterested to see my arguments, That is really strange.
But it is not my task to convince you. My only aim is to take care that questioners/newcomers are not feeded with wrong information.
Do you really think that the BJT is the only part/device in the world of electronics that have not a clear and unique explanation of its working principle?
Speaking about voltage and current, this is , certainly, not a "chicken-egg case".
It is an old and basic rule: No current without a driving voltage.
Of course, this also applies to the photodiode as mentioned by you.
And, of course, it produces a voltage - did you never read about a SERIES combination of several photodiodes with the aim to produce a higher voltage? A combination of 4 solarcells gives approximately 2 volts (open-circuit voltage).
No doubt about it - there will be a current through a connected load - but with your view you even could call a simple battery a "current source" because it allows a current through a connected load. Strange argumentation.
I am really surprised to read "Or the source is the photodiode current which creates the base-emitter voltage".
So - you really think that a current through a conductor can create a voltage? Did you ever think about such a statement? Is it not an E-field within the conductor (and the originating voltage) which enables a current through it? That`s what I have learned already in school.

But I have no problem to give you my answer:

The voltage gain of both stages is simply multiplied - where each gain is determined by
(a) the transconductance gm of each stage: gm=slope of the voltage control function: gm=Ic/Vt.
(b) the gain stabilizing feedback resistor, and
(c) the effective load resistance of each stage (and, of course, the input resistance of the 2nd stage has to be considered).

If you like, I can give you all the formulas and equations.

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#### Bordodynov

Joined May 20, 2015
2,939
I'm surprised you don't know how a reverse bias photodiode works. That's a shame. In circuits, the photodiode is usually used at negative voltage or at zero voltage. I have used both modes in my circuits. The photovoltaic mode is not normally used in photodiodes. In solar cells the photovoltaic mode is used. In the first two modes, the photodiode is a current source. Look at the calculation of a transimpedance amplifier and you will see that a current generator is used as equivalent to a photodiode. And made the discovery that it is a voltage source.
About the cascode circuit. I was looking at DC series transistors. I did not ask about the low-signal gain of the cascode. I know very well how it is calculated. I asked how you calculate the DC collector current of the upper transistor. And answer what controls the top transistor in the common base circuit. Calculate this current with your method. With the method I use, the answer is instantaneous!

#### LvW

Joined Jun 13, 2013
1,337
@ Bordodynov: To be honest, I don't have much interest in working on your assignments.
A real discussion with you is probably not very productive, since you said yourself that you are not interested in my arguments.
It is not my aim to convince you. Instead, my main concern was only to present to the questioner and to other beginners - as I think - the correct explanation of the operation of the transistor: Vbe controls Ic according to the Shockley equation.
(And most important: It must be clearly stated that a current can never "create a voltage", as you have said).

In this respect, I can refer to many books - like "Art of Electronics" and "Modeling the Bipolar Transistor" (I.E. Getreu)- and other detailed contributions of US-American universities (Stanford, Berkeley, Harvard,...).
Finally, let me quote the great late Barrie Gilbert (inventor of many new BJT based applications):
"The base current is something like a defect - it is a nuisance."

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#### Bordodynov

Joined May 20, 2015
2,939
I have no interest at all in debating with a dogmatist who can only refer to authorities and, moreover, does not know how a photodiode works. I give you concrete examples of bipolar transistor control with current according to my concept, and give you the opportunity to show the correctness of your concept, and you immediately evade. I advise you to read how photodiode works, otherwise with your ignorance you compromise the statement that the bipolar transistor is controlled by voltage. I judge a theory by who adheres to it. But I agree - the discussion needs to stop here or start another thread. I will read the theory to find arguments and maybe start a new thread myself.

#### crutschow

Joined Mar 14, 2008
28,201
This is a never-ending argument I've seen many times in various electronics forms.
Technically the BJT physics shows that it is a voltage-controlled, current-output device, but that is really only useful for small-signal circuit design.
For large-signal operation (biasing and switching design) a current-controlled, current-output (black box) model is almost always used, thus the reason for the current-gain and saturation parameters in a BJT data sheet.