Help me understand: simple transistor action--SOLVED

[ledtester]

Referring to the same textbook I took the AGC example from:

Starting on page 194 sections 9-2 and 9-3 cover the relationship between the gain, r_e and I_E.

Note equation (9-3), equation (9-3a) and Example 9-1.

OK; equation 9-3a, which is simplified by ignoring r_E, is this:

\$\displaystyle A\cong\frac{r_C}{r'_e}\$

And in Example 9-1 there is this relationship between r'_e and I_E:

\$\displaystyle r'_e \cong \frac{25mV}{I_E} \$

Putting the two together yields that gain varies proportionally with I_E. Decrease I_E -> decrease gain; increase I_E -> increase gain.

Of course, you have to verify that Eq. 9-3a is valid for this circuit.

The formula for r'_e is first discussed on page 183.

[TimFox]

Again, those equations for r’_e are equivalent to the equations I posted for g_m.
The difference between 25 and 26 mV is slightly different parameters in the computation.
Simple amplifiers, and the appropriate gain:
Voltage in, voltage out:  voltage gain (dimensionless)
Current in, current out:  current gain  (dimensionless)
Voltage in, current out:  transconductance (S or 1/\$\Omega\$)
Current in, voltage out:  transresistance ()

The basic equation for transconductance of a BJT as a function of emitter current is simpler than those for FETs or tubes.

[PGPG]

Do you not understand transconductance?

No, not really.

If your amplifier input is voltage and your amplifier output is voltage you get gain expressed in V/V - they reduce so you have simply number. (the same with current/current=A/A).
If your amplifier input is current and your amplifier output is voltage you get gain expressed in V/A=Ω - the same as resistor, but we don't say of this gain as being resistance. To express that we are speaking about gain we call it transresistance.
I believe (but to say truth I'm not sure) you should be able to get which way we come to transconductance term.

Edit.
When answering I didn't noticed that we are already at page 3 so my answer can be seen as duplicating something that already was said.

[magic]

When answering I didn't noticed that we are already at page 3 so my answer can be seen as duplicating something that already was said.

It's page 3 of thread 3 or something like that, as others have been alluding to.

Some people just arbitrarily refuse to look at any answer which isn't "small base current controls large collector current", and no such answer exists to certain questions.

I blame transistors. We wouldn't have this problem with electron lamps (and stop calling them "tubes" and "valves", ffs).

[SteveThackery]

It is explained in the reference I gave.

If you can't be bothered to spend a little time looking at that, I can't be bothered to spend a little time failing to help you.

I'm not taking sides here, and I have downloaded and studied the document you referenced. However, maybe I can see where AK is coming from. The document doesn't actually explain anything - it describes what a transistor does using a big bunch of scary-looking equations.

I think AK might be a bit like me: "understanding" is not about knowing a load of equations; it's more intuitive. It's about "visualising" what is going on. It's about understanding the underlying phenomena at a "gut level"; it's about intuitively grasping what is going on.

I probably shouldn't speak for AK, but I certainly can speak for myself, and maybe others. A similar situation arose when I was studying for my Master's in Audio Engineering. One of my lecturers literally "explained" everything using mathematical equations. I remember one particular lecture where he walked us through analogue filter design using masses of equations, manipulation of complex numbers, and other scary stuff.

Through the lecture I became more and more frustrated, until at the end, after maybe getting on for a hundred slides of equations, I put my hand up and said, "Yes, but how does it actually work?" I was annoyed, and I think my question annoyed him.

Afterwards, I began to wonder something: does he really understand it? He obviously thinks he does because he can derive the equations describing it from first principles. But is that actually" understanding"? It obviously depends on your definition of the word. Maybe there are two types of understanding - the mathematical understanding and the intuitive understanding.

One last example. He gave us a circuit that we had to analyse for our homework. I can't remember exactly what it was, but it had two or three transistors. He wanted us to use the equations he had just described to calculate the transfer function, and then answer some questions about specific voltages and currents at points in the circuit.

Instead of cranking the handle on the maths, I studied it for a while and got a rough - intuitive - idea of what the circuit did. Eventually I saw that I could calculate the current in one of the resistors just using Ohm's law. I then had a voltage at one point to work with. This opened up the next step. My analysis rippled outwards from that point until I had a full picture of what the circuit did and the voltages and currents at each point. As far as I recall I used nothing other than Ohm's law and the equation for the impedance of capacitors with frequency. I literally used none of the maths he had just taught us.

But this is the important bit: I showed him my homework and how I had achieved the goals, and he was gobsmacked. I remember him reading through my work in silence. He had no idea that what I had done was even possible. I could see he was going through "Wow!" to "What the fuck?" in his mind. Eventually he used the word "intuition" to describe my approach, which was probably accurate.

But the big takeaway from me was that he had no idea that the "intuitive" approach was possible or even existed. He looked at a circuit and saw a bunch of equations. I look at a circuit and see current flows and voltages and frequency-dependent resistances.

I don't know - is mine a "true" understanding? Do equations describe rather than explain? If you can only explain something mathematically, do you really understand it?

[tggzzz]

It is explained in the reference I gave.

If you can't be bothered to spend a little time looking at that, I can't be bothered to spend a little time failing to help you.

I'm not taking sides here, and I have downloaded and studied the document you referenced. However, maybe I can see where AK is coming from. The document doesn't actually explain anything - it describes what a transistor does using a big bunch of scary-looking equations.

I think AK might be a bit like me: "understanding" is not about knowing a load of equations; it's more intuitive. It's about "visualising" what is going on. It's about understanding the underlying phenomena at a "gut level"; it's about intuitively grasping what is going on.

I probably shouldn't speak for AK, but I certainly can speak for myself, and maybe others. A similar situation arose when I was studying for my Master's in Audio Engineering. One of my lecturers literally "explained" everything using mathematical equations. I remember one particular lecture where he walked us through analogue filter design using masses of equations, manipulation of complex numbers, and other scary stuff.

Through the lecture I became more and more frustrated, until at the end, after maybe getting on for a hundred slides of equations, I put my hand up and said, "Yes, but how does it actually work?" I was annoyed, and I think my question annoyed him.

Afterwards, I began to wonder something: does he really understand it? He obviously thinks he does because he can derive the equations describing it from first principles. But is that actually" understanding"? It obviously depends on your definition of the word. Maybe there are two types of understanding - the mathematical understanding and the intuitive understanding.

One last example. He gave us a circuit that we had to analyse for our homework. I can't remember exactly what it was, but it had two or three transistors. He wanted us to use the equations he had just described to calculate the transfer function, and then answer some questions about specific voltages and currents at points in the circuit.

Instead of cranking the handle on the maths, I studied it for a while and got a rough - intuitive - idea of what the circuit did. Eventually I saw that I could calculate the current in one of the resistors just using Ohm's law. I then had a voltage at one point to work with. This opened up the next step. My analysis rippled outwards from that point until I had a full picture of what the circuit did and the voltages and currents at each point. As far as I recall I used nothing other than Ohm's law and the equation for the impedance of capacitors with frequency. I literally used none of the maths he had just taught us.

But this is the important bit: I showed him my homework and how I had achieved the goals, and he was gobsmacked. I remember him reading through my work in silence. He had no idea that what I had done was even possible. I could see he was going through "Wow!" to "What the fuck?" in his mind. Eventually he used the word "intuition" to describe my approach, which was probably accurate.

But the big takeaway from me was that he had no idea that the "intuitive" approach was possible or even existed. He looked at a circuit and saw a bunch of equations. I look at a circuit and see current flows and voltages and frequency-dependent resistances.

I don't know - is mine a "true" understanding? Do equations describe rather than explain? If you can only explain something mathematically, do you really understand it?

Oh, that raises interesting questions!

For me understanding involves both the maths and visualisation/intuition, plus understanding how/when to use the maths and the limitations of the maths. Both are necessary, neither is sufficient. Similarly, theory without practice is mere mental masturbation, and practice without theory is mere blind alchemical fumbling.

Sometimes I understand circuits via handwaving and intuition, but then I want to understand the maths so that I can do and predict new and more interesting things. A classic example of that is an n-path bandpass filter with Q>>1000. Some people like thinking about the time domain behaviour of the voltage on one of the capacitors. Others like thinking in terms of sampling causing the frequency translation of a baseband filter to IF. The first gives a gut feel to how the filter works; the second allows you to understand its performance (e.g. how 10% component can give a filter with Q>>1000). Once you understand that maths operation, it becomes possible to realise the circuit is also a mixer. Add maths to that and you can see how it exceeds what was thought to be a fundamental limit in mixers. (When I returned to thinking about the n-path bandpass filter after 35 years, I was pissed off to see that other people had spotted the mixer concept before I did!) FFI, see maywatt's posts

To get back to AK's circuit equations. I don't think there can be a hand waving explanation without equations: g_m and r_e are solely modelling concepts that have no direct basis in electron/hole physics nor in physical components. OTOH, knowing the simple relationships expressed in the equations it is possible to see that if the external circuit causes X to go up, then Y will go down, and the circuit's operation will change by Z.

Understanding is always based on an abstraction of reality, and these abstractions are built on other abstractions. The whole point about an abstraction is to be able to make predictions at one level without having to consider the other levels. Partial example:

• computer program in a high level language
• machine code instructions
• microcode
• register transfers operations
• gate level operations
• transistors behaviour
• linear components
• semiconductor physics
• electromagnetism
• atomic physics

Ideally phenomena are defined and explained at a single - carefully chosen - level of abstraction. In practice it is usually highly beneficial to understand and use neighbouring abstractions, to ensure the  phenomenon do not exceed the abstractions' limits.

As for the meaning of "true understanding", that's philosophy

[TimFox]

How does a BJT “actually work”?
It’s easiest to treat the common-base circuit (NPN here).
Equations can be added later from the textbooks.
Forward bias the BE junction: emitter slightly negative with respect to base.  Current flows out of emitter (conventional or adult current), following the arrow.  Therefore electrons (majority carrier for NPN) flow into base region.  The same equation as for a PN diode for current as approximately exponential function of voltage.
Reverse bias the CB junction: apply higher positive voltage to collector with respect to base.
With the high field from the collector voltage, almost all of those electrons flow to the collector pin.  The small fraction that don’t go to the collector flow to the base pin, which can be considered a parasitic current.  A typical fraction might be 1/100 of the emitter current, often described as beta = 100.  Beta is not constant (wrt voltages and currents), not monotonic, not repeatable for a batch of 2N3904s, nor does it have easy equations.
The relationship between I_e and V_be has easy equations, and almost all becomes I_c.

“Beta” does not affect the transconductance of a common-emitter voltage-input amplifier, but it directly determines the input resistance, since the base current (at the input) depends directly on beta.

If you need more details, you have to bite the bullet and learn the diode equations, how to differentiate them, and proceed to Ebers, Moll, et al. to deal with important second order effects, frequency response, output resistance, etc. to get more accurate results.
Note that the internal geometry is important: a 2N3904 is not two 1N4148s connected in series.  For the next level up in complexity of descriptions, add the depletion region at the base-collector junction.

[tggzzz]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

[TimFox]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

The solid-state physics, including bandgaps, are very important, but some people are frightened by quantum mechanics.  I gave an elementary description of the device, and how it “works”.

[tggzzz]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

The solid-state physics, including bandgaps, are very important, but some people are frightened by quantum mechanics.  I gave an elementary description of the device, and how it “works”.

Your description was too complex. Simpler explanation: emitter at GND, collector is floating/open unless V_BE is >0.6V.

In other words, it is extraordinarily difficult to pitch an explanation at exactly the level the questioner "wants". Doesn't help if the questioner can only say what they don't want, after you have provided an explanation. But you know all that

[golden_labels]

@Analog Kid, for a common emitter configuration with signal not going through the emitter resistor,⁽¹⁾ a first order approximation is:

Gain ≈ V_{(collector resistor)} / 26 mV

This V_{(collector resistor)} is the average voltage we get from biasing. And that is controlled by R_E.


Be sure you paid attention. The first sentence deals with AC signal only and completely removes R_E from the image. However the equation uses V_{(collector resistor)}, which is calculated from the opposite side, completely ignoring small-signal concerns and depending on R_E.

In other words, we first get the big picture of how things are biased. Then we apply this knowledge to the small-signal analysis.


The AGC affects biasing of the entire amplifier in a way that makes V_{(collector resistor)} go lower or higher. Biasing depends greatly on the resistance seen by the emitter. Be it physical resistor R_E or virtual resistance created by AGC. The circuit above can’t tell if we attached an additional resistor or are we just doing funny things with voltages.

Let’s look at a simpler version:



In this circuit DC voltage across collector resistor (R1) is about 1.27 V. From our earlier equation the gain is: 1.27 / 0.026 ≈ 48.9. Checking with simulation, it comes out as 46.6:



Now, let’s try increasing R2:
+1 kΩ (=3.2 kΩ) makes R1 voltage to be 0.902 V, and amplification of 34.7
(33.1 in sim).
+2 kΩ (=4.2 kΩ) makes R1 voltage go 0.703 V, and reduces amplification
to 27 (25.8 in sim).
+10 kΩ causes amplification to be barely 11.4, and +20 kΩ only 6.

The attachment shows waveforms for consecutive increases of emitter resistance, from bold line to dashed. Dotted is the original 2.2 kΩ.

A corresponding presentation in Paul Falstad’s simulator. Note that you may need to wait or even speed up the simulation for values to settle. See what happens, if you change R2 (slider on the right).

The rest is in my earlier post. AGC circuitry “manipulates” the amplifier into “thinking” there is a higher resistance attached to the emitter. It does that by setting voltage on one end of R_E, but the amplifier has no way of telling the difference. All it sees is that the current decreases.

⁂

So much for providing an image.

I do agree with a lot people here, that trying to understand mathematical models behind all this is relevant. The way I described it may offer nice picture answering a particular question. But you can make almost no predictions from that, if hard numbers are needed. For instance see I just given voltage on the collector resitor, but never explained why it’s  this value and not some other. I said 26 mV, but why 26? Unlike others I never uttered symbols g_m and r_e. The reason I didn’t is not because they’re irrelevant, but because I wrapped them in other symbols.⁽²⁾ You’ll not see why transistor’s β plays no role, assuming it’s big enough.

On the other hand I don’t believe in bottom-top approach where bottom may be too hard to grasp all at once. Lying to children is good.

⁽¹⁾ The 0.47 µF capacitor is almost a short at 1 MHz, and
is negligible for 10 kHz.
⁽²⁾ The gain equation in this post is directly derived from -g_m · R_C.

[magic]

Gain ≈ V_{(collector resistor)} / 26 mV

This is actually true and it offers a perfect and concise way of explaining how this AGC scheme works:

Varying bias changes the value of collector resistor voltage drop, but it doesn't change the value of 26mV.
That's all there ever was to it, move along

[temperance]

As I wrote before, the problem Analog Kid has with all this seems more fundamental.

I wrote it here:
https://www.eevblog.com/forum/beginners/help-me-understand-simple-transistor-action/msg6125589/#msg6125589

The evidence is in the question asked in the first post made by Analog Kid and what follows:

https://www.eevblog.com/forum/beginners/help-me-understand-simple-transistor-action/msg6124601/#msg6124601

[TimFox]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

The solid-state physics, including bandgaps, are very important, but some people are frightened by quantum mechanics.  I gave an elementary description of the device, and how it “works”.

Your description was too complex. Simpler explanation: emitter at GND, collector is floating/open unless V_BE is >0.6V.

In other words, it is extraordinarily difficult to pitch an explanation at exactly the level the questioner "wants". Doesn't help if the questioner can only say what they don't want, after you have provided an explanation. But you know all that

Your over-simplified explanation says nothing about gain dependence on emitter current, the crux of his question about AGC action.

[tggzzz]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

The solid-state physics, including bandgaps, are very important, but some people are frightened by quantum mechanics.  I gave an elementary description of the device, and how it “works”.

Your description was too complex. Simpler explanation: emitter at GND, collector is floating/open unless V_BE is >0.6V.

In other words, it is extraordinarily difficult to pitch an explanation at exactly the level the questioner "wants". Doesn't help if the questioner can only say what they don't want, after you have provided an explanation. But you know all that

Your over-simplified explanation says nothing about gain dependence on emitter current, the crux of his question about AGC action.

Of course! But does the questioner want/need that or will they reject it as too complex and irrelevant?

(I did choose "questioner" rather than "OP", since the general issue is wider than this thread.)

[TimFox]

How does a BJT “actually work”?

Start with the bandgaps  That's the way it was taught in school, and largely repeated at university.

Yup, there is more than one level of abstraction

The solid-state physics, including bandgaps, are very important, but some people are frightened by quantum mechanics.  I gave an elementary description of the device, and how it “works”.

Your description was too complex. Simpler explanation: emitter at GND, collector is floating/open unless V_BE is >0.6V.

In other words, it is extraordinarily difficult to pitch an explanation at exactly the level the questioner "wants". Doesn't help if the questioner can only say what they don't want, after you have provided an explanation. But you know all that

Your over-simplified explanation says nothing about gain dependence on emitter current, the crux of his question about AGC action.

Of course! But does the questioner want/need that or will they reject it as too complex and irrelevant?

(I did choose "questioner" rather than "OP", since the general issue is wider than this thread.)

58 years ago, in college, my version of this description was earthier:  “When the electron gets into the base region, he says ‘f*** this small voltage, I’m heading to the high voltage at the collector’.”
I’m more mature now, and tightened up the description of device function, leaving equations to the interested reader to find in the (extensive) literature.
I’m reminded of a boy’s book on electronics from 65 years ago that explained vacuum tubes for kiddy-winkies with little demons sitting on the grid manipulating trap doors to throttle the flow of electrons past the grid to the plate.

[Analog Kid]

Wow; this thread has certainly burgeoned since last night when I left it.
I actually appreciate that, as this is evidently not a trivial topic.
Just a few things to say before I return to the meat of the discussion:

@Steve Thackery: Thanks for your observations, which are somewhat sympathetic to me. They do explain my questioning here pretty well.

Here's the deal: This whole thread is basically due to my lack of understanding of some very basic electronic principles. I can only be honest about that.

I just don't grok certain fundamental mechanisms, ones that most everyone else here seems to take for granted (assuming that they really understand them). And I can't just force myself to "get" it: if I have a mental block about something, then it's going to take a minor epiphany for it to finally click into place in my poor brain. Which obviously hasn't happened yet here. Believe me, I'm not being intentionally obtuse here: I really just don't get it.

@tggzzz: I realize you're trying to help me here. But you're really not, and I consider it quite presumptuous of you to insist that I read the material you provided before proceeding. As @Steve pointed out, there's just waaaaay too much math in that text (the Purdue PDF you posted a link to). I could spend a couple days poring over that and still not have an intuitive understanding of transistor action.

Not to denigrate math: it's absolutely essential to explain the phenomena we're discussing here; I get that.
It's just that a purely math-oriented analysis is probably not going to help me here at this point.

There have been some very helpful posts here, like @PGPG's "raised table" analogy which actually helped me answer my original question (why an increase of AGC voltage reduced voltage across the emitter resistor). Those are the kinds of approaches to my questions that I was hoping to find here.

Again, I would really hope that I could find an intuitive explanation of the outstanding question of mine (why does a change in emitter voltage change the gain?) on a basis that's as simple as possible: no more complex than necessary, and no simpler than required to explain the phenomenon. Which to me would exclude such second- and third-order things as quantum effects (sorry, @TimFox) and other things which could be considered "icing on the cake". Does that make sense?

Anyhow, I'm currently reading up on transconductance, and may have something to post about that soon. (Be prepared for more questions!)

Thanks to those who helped here, or even tried to help.

[tggzzz]

Do not expect to learn electronics quickly, it takes years+ and a lot of work - even when you are young.

As you get older you realise there will be some things you can never understand or do, however hard you try. Life is about masking making choices about what not to do.

[Analog Kid]

As you get older you realise there will be some things you can never understand or do, however hard you try. Life is about masking choices about what not to do.

Dunno if you meant to write "making" or "masking", but both seem valid here.

[tggzzz]

As you get older you realise there will be some things you can never understand or do, however hard you try. Life is about masking choices about what not to do.

Dunno if you meant to write "making" or "masking", but both seem valid here.

Blasted fondleslab keyboards plus autokorrupt! Edited.

[TimFox]

@Analog Kid
My prose description of “how BJTs really work” explicitly ignored quantum and higher-order effects.
It answered your question about gain dependence on emitter current very simply on the basis of the I-V curve for a PN diode, which I am sure you have seen.

[PGPG]

This whole thread is basically due to my lack of understanding of some very basic electronic principles.

I think understanding of 'how transistor works' can be divided into two steps:
1. You have to understand how diode works.
2. Then transistor is simple: Ic = β * Ib (B-E junction is a diode).

Diode.
You have to accept that whenever voltage drop at diode increases by 26mV its current increases 2 times (I prefer to use 25mV here as 1/25 is simpler to count than 1/26 and nothing in electronic is so precision to worry about whether 25 or 26).
It is not true, but for 'small signal' it can be assumed as true. So trying to no lie ... Whenever voltage drop at diode increase by small voltage its current increase in such way than for 26mV it will be doubled, but as on the way (from 0mV to 26mV) current rises then at each point doubling means something different (higher and higher) and really for 26mV voltage increase the current will rise 2.72 times.
But until voltage change is small (much smaller than 26mV) you can forget about this 2.72 as at the beginning current changes like it will be only doubled.

Think about it as long as you have to and don't go any farther until you assume that 'you feel it enough good'.

Now transistor.
(I write like what happens for small signals (much smaller than 26mV) would be also true (even it is not) for big signals).
Its Ic multiplied by Rc gives a DC voltage drop at Rc (I assume Ohms law you understand).
Whenever Vbe will increase by 26mV the Ib will be doubled and also Ic=β*Ib will be doubled (in our simplification β is constant).
So for 26mV voltage increase at base you get Rc voltage drop increase 2 times so increase by the same voltage as is DC voltage drop.
As gain is (output voltage change)/(input voltage change) you get Gain=VRc(dc)/26mV.

And we get this:

Gain ≈ V_{(collector resistor)} / 26 mV

I hope I simplified it by reducing transistor understanding to diode understanding and then simple multiplying diode current by β constant.

[magic]

You have to accept that whenever voltage drop at diode increases by 26mV its current increases 2 times (I prefer to use 25mV here as 1/25 is simpler to count than 1/26 and nothing in electronic is so precision to worry about whether 25 or 26).

Right for 170°C and maybe discrete diodes with poor "ideality factor", not so much for BJT at room temp.
I would suggest "accepting" 2x increase for each 18mV, 10x increase for each 60mV (probably most convenient in practice) and e x increase per 26mV.

[PGPG]

You have to accept that whenever voltage drop at diode increases by 26mV its current increases 2 times (I prefer to use 25mV here as 1/25 is simpler to count than 1/26 and nothing in electronic is so precision to worry about whether 25 or 26).

Right for 170°C and maybe discrete diodes with poor "ideality factor", not so much for BJT at room temp.
I would suggest "accepting" 2x increase for each 18mV, 10x increase for each 60mV (probably most convenient in practice) and e x increase per 26mV.

I'm trying to use a derivative without using a derivative

[magic]

Doesn't matter, what I'm saying is that the numbers you posted are wrong.