# BJT Model, Thoery, Usage, etc;

Discussion in 'Homework Help' started by Austin Clark, May 20, 2012.

1. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
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For a very long time I've had trouble understanding and figuring out the REAL characteristics of BJTs. Sometimes I hear them called voltage amplifiers, current amplifiers, switches, voltage-controlled resistors, etc; etc; etc;

I'm assuming that all of these are true, but each one requires a different perspective of the same event. Could someone please explain, in detail, (even at the physical layer if possible) the different perspectives, and why/how each works?

For example, placing a resistor at the base will decrease the current flowing through it, and thus will reduce current through the Collector/Emitter. HOWEVER, in reality, you're really just changing the voltage at the base because you're dropping a certain amount voltage across the series resistor. (I'm assuming).

I think, probably, the best model for me would be the voltage-controlled resistor. Given the voltage V at the base, what would the effective resistance be across the Collector/Emitter? Would the equation look something like x/V? Where x is some real number? Or like x/V^2? x/V^y? I have really no idea.

Also, to calculate the actual voltage at the base with a series resistor, would you use the same concept as described in another of my threads?

My end-game is to be able to design digital logic as efficiently as possible with BJTs, Diodes, and resistors. I don't want to use cut-and-paste logic gates, I want to know the highest-value resistors I can use and such, to minimize energy waste. Also, in general, I like to analyze the next 100 steps before taking just one.

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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I'm puzzled as to why you want to re-invent established logic technologies such DTL and RTL.

3. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
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Because it's cool, fun, and educational. Everyone should learn in the same manner that things were originally discovered, it's much more meaningful that way.

In the end, I wish to build simple computers, and then from there develop faster and more efficient versions, building up further and further, adding more and more functionality, using more and more concepts, etc; Until I feel as though I've mastered the art (which will likely never happen, as there's too much to learn in even such a specific area of science).

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Well all power to you then! May you prosper in your search for knowledge.

It might be expecting somewhat too much from forum members asking them to "...explain, in detail, (even at the physical layer if possible) the different perspectives, and why/how each works..." regarding transistor operation. Perhaps it would assist if you specify some particular points of uncertainty and ask questions in a more focused manner. Presumably you don't want to receive a 'endless' array of web links.

5. ### #12 Expert

Nov 30, 2010
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One of the most interesting things I have done is to graph Amps collector versus Volts base to emitter, Ic/Vbe

The answer was a straight line on log-log graph paper! For a 2N4250A transistor at room temperature,
.24 volts, Vbe allowed 1 nanoamp of collector current
.42 Vbe allowed 1 ua
.60 Vbe allowed 1ma

From this, I decided that an equation for Ic/Vbe can be derived, and that for every 60mv Vbe, Ic increased by a factor of 10.

If you track this down to zero Vbe, it is 4 powers of ten below 1 nanoamp (.1 picoamp), and that would be the leakage current at zero volts.

"Approximately .6 volts to turn the transistor on" is merely an inaccurate convenience of speech.

There is a definite relationship between Vbe and Ic but it is different from transistor to transistor. It changes with temperature, it changes with the part number, and it changes from batch to batch. I bet somebody has already done this work and the equation is named after him or her.

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6. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Yep - the Ebers-Moll model.

7. ### Jony130 AAC Fanatic!

Feb 17, 2009
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But when we design the circuit using BJT we don't need to know "REAL characteristics".
We design the circuit in such a manner that the BJT parameters change don't effect the circuit operation.
For example when we design a amplifier we use such a circuit that the DC bias point is almost independent the BJT beta and Vbe variation. Simply by using a negative feedback.
And when we design the switch circuit we don't even bother our head with real Vbe value and beta.

8. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
409
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You presume wrong, but regardless I understand what you mean. That's why I gave an example of what I'm wanting to do, so maybe people had input that applied there.

I've read a lot about transistors, even on the physical level, but I just haven't been able to find a model other than ebers moll, of which the complete model is pretty difficult.

A slightly more precise question might be, then, what are the ebers moll equations and how/why do they work? How were they derived? That sort of thing. That might still be too broad, but if anyone has a few key tidbits of information or intuitive descriptions I'm definitely all ears.

9. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
409
44

A few questions though. Concerning this:
************************
.24 volts, Vbe allowed 1 nanoamp of collector current
.42 Vbe allowed 1 ua
.60 Vbe allowed 1ma
************************
What was the Collector voltage that provided the 1 nano,micro,and milli amp? if I doubled that voltage, would the current also exactly double? Could you say that, given specific voltages at the base, the CE acts with a specific resistance? That would be helpful in working out the behavior with series resistors at the collector.
Also, Every .12V the amperage increased by a factor of 10, so, would:
leakage current + (10^(8.33*V)/a)
Where a is some number, be a decent model for your data? Kinda sloppy, but meh.

10. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
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Firstly, an in-depth knowledge of the components in use and the physics and mathematics will help in designing high-quality circuits, and nothing will catch you by surprise. For example, two inductors on paper might not operate the same/correctly if they're within close proximity, they'll induce currents/voltages in each-other like a transformer. That's a case where physics knowledge aided circuit design. More examples are easy to imagine from there.
No matter what, every parameter matters, even if it's only to a slight degree. So, if you want to create a circuit that's accurate, you can't ignore them.
Lastly, simply being able to assume this configuration works VS that one isn't helpful. It makes more sense to understand WHY and HOW, not memorizing the rules of thumbs. Besides, who's to say someone won't come up with new configurations?

11. ### #12 Expert

Nov 30, 2010
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IIRC I gave it 10 volts at the collector just because that was, "plenty" to keep the transistor from suffering collector voltage starvation. If you doubled that voltage, just about nothing would happen because the CE does not act as a resistance. It acts as a current gate and the current flow is already helpful in working out the behavior with a series resistor at the collector. Volts across the collector resistor = Ic X R

Also, every .06 volts the amperage increased by a factor of 10 so leakage current has nothing to do with volts per amp. The only place I can see a valid statement in this idea is that Leakage current at zero Vbe = .1 pico amp = infinity amps per volt.

Where is a decent model for my sloppy data...that is only accurate to within a nanoamp? t_n_k covered that. It's called the Ebers-Moll model.

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12. ### studiot AAC Fanatic!

Nov 9, 2007
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Quite a few people died following Ben Franklin's lightning experiments, Marie Curie and many early radiation experimenters died from their exposure.

Sometimes is better to learn from someone else's mistakes or mishaps.

From your replies I judge that you would be ready to explore two port networks which would be the logical basis for your learning programme.

For digital systems we regard the transistor as either fully on or fully off. For many purposes that is enough, however when you need to know what actually happens because the transistor is not quite on or not quite off then you need to revert to analog theory.

go well

Last edited: May 20, 2012
13. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
409
44
Learning the same way things were originally discovered doesn't necessarily performing the same experiment, simply analyzing their results would be enough. It's just that if you learn in the same order, you'll always know that you have the foundation for whatever you're learning next, and that you'll have an intuitive understanding of all the material. It's just the natural progression of things.

I'll look into the two-port network scheme, sounds interesting.
http://en.wikipedia.org/wiki/Two-port_network

How would you know how many gates you can drive from your output pin if you just assumed fully on and fully off states?

14. ### #12 Expert

Nov 30, 2010
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Either read the datasheet or make a mathematical model starting with the conductivity of silicon and the geometry that the manufacturer used in making the chip.

15. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
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I would, if I could. But I can't, so I shan't.
It's true that we abstract away much of the details, and It's also true that I want to peel away those abstraction layers. HOWEVER, I am content with a little abstraction. We don't need to start with quantum mechanics, just with basic electrical theory.

I expected that my inquiring mind would be well received, not thought tedious.

16. ### studiot AAC Fanatic!

Nov 9, 2007
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The manufacturers datasheets are good places to start.

There are also standards for different logic families.

The terms to look up are fan in and fan out.

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17. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
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What would happen if you tried fanning out to too many outputs? Also, what if you wanted to fan out to, say, an actual load and not just as an input to another piece of logic?

For TTL, TRL, TDL, etc; lets say that a 0 is represented as 0-1V and 1 is represented as 4-5V. So, so long as each "black box" logic gate follows this rule and outputs the correct voltages throughout the entire input range and under the maximum load, you're golden. I want to be able to design an array of logic gates that follows different specifications like these. To do this, what all do I need to know and where can I learn it? This would let me keep things efficient yes simple. I would simply pick a logic gate that has only the fan-out that I need, thus saving power.
Also, any lessons would be appreciated.

18. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
409
44
So, all BJTs are current amplifiers? I've heard them referred to by different things before. That doesn't seem to make much sense though, because if it always multiplied the base current, then it wouldn't matter what resistor you had in series with the collector, you could pull 100mA through a 100Mega-ohm resistor, so somehow that rule is flawed, in reality I'm assuming that, depending on the input voltage or current, you're controlling a sort of "variable resistor" between the collector and emitter.

I'm looking seriously into Ebers-Moll now, It very well might will be exactly what I'm looking for, but it's all these different, seemingly impossible or contradictory, explanations that have seriously confused me.

19. ### studiot AAC Fanatic!

Nov 9, 2007
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You could indeed if you had a 10 megavolt supply

The statement " a transistor is a current amplifier" means that it will try to drive the base current times the transistor gain through the collector resistor.

Ohms law then tells us what the voltage across the collector resistor will be.

Thus the supply must be this plus a few volts.

All the time the transistor is operating in the active region ie output is proportional to input.

This is not what you want for digital work. Here you want the output to be either within the high or low voltage spec for an input that is either within the high or low. There is no proportionality.

Incidentally controlling the switching speed will save you more than worrying about fan in/out.

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20. ### Austin Clark Thread Starter Active Member

Dec 28, 2011
409
44
After reading your post, I experimented with the simulator and did indeed verify what you were saying. That makes sense, and I'm put one step further. However, when I put a high-value resistor in series with the source voltage, it's impossible for the collector to conduct the right amount of current, so how does it "know" how much to conduct and/or what it's equivalent resistance should be?