The 'resistor' Re or 're' is used in that way in various texts.
................................
People have been doing this for years and you even do it, yet you dont understand how to take it one step further so that puzzles me. I dont understand why you keep referring to a different way to interpret the circuit using 'gm' when clearly using 're' is an accepted way to do it and Jony did it that way too. We've all done it that way so it makes no sense to reject that.

MrAl, I am very sorry, but everything - as quoted above - is not correct.

* At least 5 times I have told you that re=1/gm is a differential quantity.
Hence, there is no static (ohmic) part Re, which could be calculated - as you claim - before the DC quiescent current is found.
Yes - "people have been doing this for years", as far as the element "re" (inverse of the slope of the Ic=f(Vbe) curve) is concerned.

* Of course, I am not "keep referring to a different way to interpret the circuit using 'gm'Using the transconductance gm" .
Since decades, the transconductance gm is used as a pure diff. quantity in the PI model for the BJT.

* In another thread (closed) Jony130 did exactly the same as I did. He clearly stated that "re" as a differential part does NOT appear in any DC calculation . You shouldn`t claim the opposite - read again his contribution.

* May I ask you: What is the meaning of your last sentence "We've all done it that way so it makes no sense to reject that".
This sounds as it is me who is not in accordance with well-proven techiques. May I point to the fact, that I am in full accordance with books and the small-signal theory. In contrary, you are the one who claims that you have developped a new - more exact - method for analysing DC and AC properties of BJT amplifiers.

* Finally, I ask you cordially not to accuse me of opinions and statements that I have never formulated.

 

The real question here is whether the results using your approach are sufficiently better so as to warrant the additional effort and complexity. For all of cases where the linearized approach is good enough, the answer is clearly no -- why? Because the linearized approach is good enough.

Yes - I agree. It is the classical approach to analyze new methods: Where are the advantages? Are the results more or less exact?
But I think, the two first questions to be answered are:
* What does the new method consist of? (A clear description with the help of an example circuit)
* Where is the proof that the results are really correct and accurate?

 

MrAl, I am very sorry, but everything - as quoted above - is not correct.

* At least 5 times I have told you that re=1/gm is a differential quantity.
Hence, there is no static (ohmic) part Re, which could be calculated - as you claim - before the DC quiescent current is found.
Yes - "people have been doing this for years", as far as the element "re" (inverse of the slope of the Ic=f(Vbe) curve) is concerned.

* Of course, I am not "keep referring to a different way to interpret the circuit using 'gm'Using the transconductance gm" .
Since decades, the transconductance gm is used as a pure diff. quantity in the PI model for the BJT.

* In another thread (closed) Jony130 did exactly the same as I did. He clearly stated that "re" as a differential part does NOT appear in any DC calculation . You shouldn`t claim the opposite - read again his contribution.

* May I ask you: What is the meaning of your last sentence "We've all done it that way so it makes no sense to reject that".
This sounds as it is me who is not in accordance with well-proven techiques. May I point to the fact, that I am in full accordance with books and the small-signal theory. In contrary, you are the one who claims that you have developped a new - more exact - method for analysing DC and AC properties of BJT amplifiers.

* Finally, I ask you cordially not to accuse me of opinions and statements that I have never formulated.

Hello again,

I dont see you addressing the variable +Vcc problem circuit yet.

It appears that you are never going to accept any other way ot doing things other than the way you are accustomed to.
If someone calculates a circuit and gets result 1.002 and you get 1.001 you cant accept the result 1.002 simply because it came from a mthod which you dont seem to understand yet.
In this case there is a good reason for doing it the 'new' way and that is to make the calculation more widely applicable. We can also develop a simple equation to calculate this circuit for other operating conditions.

Are you ever going to address the variable +Vcc problem or no?
It's up to you of course, but it's very informative to look at that problem in relation to the circuit in question.

 

No one is saying that the linearized model is not an approximation to the real circuit -- but I assume that you understand that the approach you are advocating is also an approximation.

No one is saying that the linearized model always yields results that are "good enough" for the application at hand. You should only use it in situations where you believe that it is. I assume that you understand that the exact same thing applies to the approach you are advocating.

There are better methods that yield more accurate solutions to nonlinear systems. We generally try to design circuits so that the linear methods are "good enough" precisely so that we can avoid using the nonlinear methods because they are significantly more complicated, time-consuming, and error-prone.

Where is the boundary where your approach stops being "good enough"? Let's assume that it is beyond the boundary where the linearized approach has ceased to be so -- how far beyond that boundary is it?

The real question here is whether the results using your approach are sufficiently better so as to warrant the additional effort and complexity. For all of cases where the linearized approach is good enough, the answer is clearly no -- why? Because the linearized approach is good enough.

So the real question then becomes one of just how large is the problem space where the linearized approach is NOT good enough, but your approach IS? After all, in situations in which neither approach is "good enough", then the distinction is moot.

My guess -- and it's only a guess -- is that this space is pretty small. That doesn't mean that espousing your approach serves no purpose -- please don't take it to imply that.

Of course, today we often just jump straight to a circuit simulator but, in doing so, we are faced with exactly the same issues -- are the device models we are using "good enough" to adequately solve the problem at hand. I've worked with device models that, to achieve that status, consisted of a 300+ component subcircuit for each transistor (talk about slow simulation times!). There is even the question of whether the basic simulator is "good enough" -- and many are not. This is often the case with digital and mixed-signal simulators because there are a lot of digital simulation engines out there and many of them are pretty simplistic. Analog simulators often use the same underlying SPICE engine (at least up to whatever device model level they support) and so the differences aren't as pronounced. But current simulators and device models are generally not charge conserving. For most purposes they are close enough for this not to be a critical factor, but there are circuits for this this very much IS a critical issue and it can take rather herculean efforts to get adequate design validation as a result.

Hi,

Yes i have to agree that we eventually reach a point where it is good enough. In this case the error between 'techniques' is so small though it leads me to believe that anyone that rejects it outright has to be ignoring facts. For results that are only around one half of one percent, they must be at the very least similar.

There are other views too though, as you guessed, and one is when we have a variable +Vcc supply line.
With a variable +Vcc line, the value of 're' is almost 'automatically' calculated without much trouble, and the way theory works sometimes is we go a little farther out in the analysis and we end up with a more widely applicable method, and sometimes it even gets simpler in the long run.
This is one of those times, but i was holding off to see what LvW comes up with in the variable +Vcc case first. I'd like to see how he intends to handle that case. Using a current controlled resistor Re(i) instead of just Re actually makes things simpler and i'd like to show that simplification soon too.

 

Quote: "I dont see you addressing the variable +Vcc problem circuit yet."

Vcc variation has nothing to do with the main question we have discussed up to now: Is 1/gm=re is a differential quantity, yes or no.

Quote: "It appears that you are never going to accept any other way ot doing things other than the way you are accustomed to."

If the new way is clearly described and can be proven to be correct - I never will have problems to feel convinced.

Quote: "If someone calculates a circuit and gets result 1.002 and you get 1.001 you cant accept the result 1.002 simply because it came from a mthod which you dont seem to understand yet."

Thank you for the compliment. But you miss the point. The difference is "a bit" larger.
In post #1 you have asked a question ("old" and your "new" approache) - and I gave you my answer in post#2.
For convenience, I repeat:
Case 1:
I=2V/2k=1mA and
re=0.25/1mA=250 ohms.

Case 2:
I=2V/(2k+0.25/I)=...=0.875mA and
Re=0.25/0.875mA=285.7 ohms.

You were claiming that the solution Case 2 is the correct one - however, up to now, without any prove.
For example, can you explain the background of the expression as defined in your post#1 for case 2 :
(Quote) : Re=K/iR3, where K=0.25 and iR3 is current through R3.

Have you realized that the division by the current I originates from the diferential quotient (slope) of an exponential function I=f(V) ?
And this leads to an ohmic resistor Re ??

 

Quote: "It appears that you are never going to accept any other way ot doing things other than the way you are accustomed to."

If the new way is clearly described and can be proven to be correct - I never will have problems to feel convinced.

@MrAl : Here's a suggestion that might let you make headway.

Come up with a circuit (perhaps the one you started with in this thread) and perform the analysis three ways for a variety of situations. One using the standard large-signal/small-signal linearized approach, one using your approach, and one using the Ebers-Moll model directly (for convenience, we'll accept the Ebers-Moll as our "ground truth" data). Ideally you would want to craft a circuit in which your approach agrees with the Ebers-Moll analysis within something like 1% while the linearized approach is significantly further away (even 2% might be sufficient for your purposes). But it might be difficult to construct such a circuit. A way of dealing with that, at least potentially, is to increase the signal size until both your method and the linearized method are in error by, say, 10% from the Ebers-Moll and plot the deviation of both as a function of signal amplitude.

 

Wbahn - I appreciate your proposal.
In addition I would say that for such analyses the supply voltage must, of course, be kept constant.
This remark is necessary because - suddenly - a certain variation of Vcc was brougt up which has nothing to do with the original task.
Such additional parameter variation will overshoadow the results we need for a clean and fair evaluation.

 

Quote: "I dont see you addressing the variable +Vcc problem circuit yet."

Vcc variation has nothing to do with the main question we have discussed up to now: Is 1/gm=re is a differential quantity, yes or no.

Quote: "It appears that you are never going to accept any other way ot doing things other than the way you are accustomed to."

If the new way is clearly described and can be proven to be correct - I never will have problems to feel convinced.

Quote: "If someone calculates a circuit and gets result 1.002 and you get 1.001 you cant accept the result 1.002 simply because it came from a mthod which you dont seem to understand yet."

Thank you for the compliment. But you miss the point. The difference is "a bit" larger.
In post #1 you have asked a question ("old" and your "new" approache) - and I gave you my answer in post#2.
For convenience, I repeat:
Case 1:
I=2V/2k=1mA and
re=0.25/1mA=250 ohms.

Case 2:
I=2V/(2k+0.25/I)=...=0.875mA and
Re=0.25/0.875mA=285.7 ohms.

You were claiming that the solution Case 2 is the correct one - however, up to now, without any prove.
For example, can you explain the background of the expression as defined in your post#1 for case 2 :
(Quote) : Re=K/iR3, where K=0.25 and iR3 is current through R3.

Have you realized that the division by the current I originates from the diferential quotient (slope) of an exponential function I=f(V) ?
And this leads to an ohmic resistor Re ??

Hi,

No it is not the difference in resistance that is similar, it is the gain of the circuit which is the all important result.
The difference in gain is around one half of one percent difference. I stated this probably FOUR times but you like to overlook what you dont want to talk about.

It doesnt matter to me of the slope of the exponential function has anything to do with this or not. What matters to me is the typical way to calculate 're' and it's use. THAT IS ALL.
To calculate 're' we used K/i where i is emitter current, period. That's it. Nothing more. I dont care how YOU wish to calculate it and i dont care if it works in a REAL transistor circuit or not.

If you would like to talk about another way completely of doing this circuit, that's fine, but i was talking about a certain specific way to do this circuit and you cant seem to stick to that. It makes no sense for me to talk to you about this circuit because you'll just keep skewing the topic and not reading the results i presented.

 

@MrAl : Here's a suggestion that might let you make headway.

Come up with a circuit (perhaps the one you started with in this thread) and perform the analysis three ways for a variety of situations. One using the standard large-signal/small-signal linearized approach, one using your approach, and one using the Ebers-Moll model directly (for convenience, we'll accept the Ebers-Moll as our "ground truth" data). Ideally you would want to craft a circuit in which your approach agrees with the Ebers-Moll analysis within something like 1% while the linearized approach is significantly further away (even 2% might be sufficient for your purposes). But it might be difficult to construct such a circuit. A way of dealing with that, at least potentially, is to increase the signal size until both your method and the linearized method are in error by, say, 10% from the Ebers-Moll and plot the deviation of both as a function of signal amplitude.

Hi,

That's interesting but not to the point of what i intended with this discussion.
The point was to SIMPLY calculate 're' using two slightly different methods, one of which was ACCEPTED long ago.
The second method produces nearly identical results.
It's that simple.
LvW just tries to skew the discussion and in doing so changes the whole point of the topic. It makes no sense to discuss it with him because he doesnt read the replies or just does not understand the main point of the discussion.

In brief:
We have a circuit and analyze it and get a result of 0.263 and someone else uses a different method and gets 0.265 so the difference is 0.002 which is a small percentage so the results are close and so the methods must be similar enough. Then the first person comes back and tries to argue that the resistances show a bit larger difference 286 vs 250 and that is after the two results have been presented and the percentage of 0.5 percent quoted over and over again, then ask for more proof that the methods are similar.
So you see what has happened here, proof has been submitted and the receiver has chosen to ignore some facts and present other facts as some OTHER point.
It doesnt matter what circuits we analyze he's never going to accept any results that he himself has not done the way he himself thinks it should be done.

Your idea of doing several scenarios is a good one too, and i proposed changing +Vcc to show how 're' would HAVE to change with each supply voltage choice, and that would lead to the CURRENT CONTROLLED resistor variation i had proposed all along.
Would it be that much different than the normal way of doing it (we called it the 'old' way)? Probably not, but we could not come up with a nice concise formula for the ENTIRE circuit, complete with +Vcc variation, unless we use the current controlled resistor method (we called the 'new' method but it's not new).
Notice he ignores this because it is a "different circuit". So keep that in mind now, when you post a circuit if you post a different circuit later you cant expect anyone to want to analyze it because they might complain, "It's a different circuit". <chuckle>
Oh i almost forgot, it's OK to introduce a different circuit as long as it is HIS different circuit <even bigger chuckle>

Jeeze, it's just a circuit

 

Quote:
" No it is not the difference in resistance that is similar, it is the gain of the circuit which is the all important result.
I stated this probably FOUR times but you like to overlook what you dont want to talk about. "

Interestingly, I have never seen a gain formula - or even gain values - for your circuit
(but for you: "...important result"). Where are the results???
Quote:
" It doesnt matter to me of the slope of the exponential function has anything to do with this or not. What matters to me is the typical way to calculate 're' and it's use. THAT IS ALL.
To calculate 're' we used K/i where i is emitter current, period. That's it. Nothing more.
I dont care how YOU wish to calculate it and i dont care if it works in a REAL transistor circuit or not.
If you would like to talk about another way completely of doing this circuit, that's fine, but i was talking about a certain specific way to do this circuit and you cant seem to stick to that. It makes no sense for me to talk to you about this circuit because you'll just keep skewing the topic and not reading the results i presented."

This is not the style I prefer in a technical discussion. I get out .

 

Quote:
" No it is not the difference in resistance that is similar, it is the gain of the circuit which is the all important result.
I stated this probably FOUR times but you like to overlook what you dont want to talk about. "

Interestingly, I have never seen a gain formula for your circuit .

Quote:
" It doesnt matter to me of the slope of the exponential function has anything to do with this or not. What matters to me is the typical way to calculate 're' and it's use. THAT IS ALL.
To calculate 're' we used K/i where i is emitter current, period. That's it. Nothing more.
I dont care how YOU wish to calculate it and i dont care if it works in a REAL transistor circuit or not.
If you would like to talk about another way completely of doing this circuit, that's fine, but i was talking about a certain specific way to do this circuit and you cant seem to stick to that. It makes no sense for me to talk to you about this circuit because you'll just keep skewing the topic and not reading the results i presented."

This is not the style I prefer in a technical discussion. I get out .

Hello,

Ok then good luck to you in your future circuit analysis/building/etc.

 

We have a circuit and analyze it and get a result of 0.263 and someone else uses a different method and gets 0.265 so the difference is 0.002 which is a small percentage so the results are close and so the methods must be similar enough.

Actually, that's quite a leap. I can easily come up with a circuit in which if you calculate the current in a particular branch in the middle of a circuit using any of the standard techniques you get a certain value and if you use a different method wherein you take the voltage of some source way over on the left and the resistance of the middle resistor in a three series string of resistors way off on the right you get exactly the same value. This does not warrant a conclusion that the different method must be similar enough to the standard techniques of analysis.

 

Hi,

No it is not the difference in resistance that is similar, it is the gain of the circuit which is the all important result.
The difference in gain is around one half of one percent difference. I stated this probably FOUR times but you like to overlook what you dont want to talk about.

It doesnt matter to me of the slope of the exponential function has anything to do with this or not. What matters to me is the typical way to calculate 're' and it's use. THAT IS ALL.
To calculate 're' we used K/i where i is emitter current, period. That's it. Nothing more. I dont care how YOU wish to calculate it and i dont care if it works in a REAL transistor circuit or not.

If you would like to talk about another way completely of doing this circuit, that's fine, but i was talking about a certain specific way to do this circuit and you cant seem to stick to that. It makes no sense for me to talk to you about this circuit because you'll just keep skewing the topic and not reading the results i presented.

Now I'm completely lost on what the point is. You seem to be saying that you don't care if your results match the behavior in a real transistor circuit or not, let alone whether it matches it better than the standard approach.

 

Now I'm completely lost on what the point is. You seem to be saying that you don't care if your results match the behavior in a real transistor circuit or not, let alone whether it matches it better than the standard approach.

Hello again,

That is almost correct let me explain.

1. I dont care if the results match the behavior of a real transistor circuit. I dont believe it ever could. A real transistor is much more complex than the 're' model i brought up in the first post, assuming we use that idea for the attenuator circuit. The model that uses 're' is an approximation, and that approximation has been accepted throughout the years as one technique. It's not perfect, that's ok with me.
2. It does match the standard approach and goes one step further, but you have to analyze a few circuits to be able to see why this idea helps the situation. I believe it is more accurate but more importantly more widely applicable.

Back when i worked in the industry we were often required to come up with solutions that were in the form of a function rather than tables or as a set of conditionals. Back then computer storage was at a premium. Today that's a lot different, but i still prefer a function over a set of rules or a table if i can get that. Sometimes we cant, but sometimes we can.

To see the way this plays into this circuit, we only have to look at a few different scenarios where we may have the same circuit but with different +Vcc levels. For example, we might find ourselves with +5v, and back in the 1970's it could be very common to find a +15v supply being used. Now the question is, do we want to have to calculate 're' every time we get a new power supply voltage level, then analyze the circuit again, or do we want a functional form such as:
Av=f(K,Vcc)
where K is the thermal voltage and Vcc is the power supply voltage.

The method i had been talking about allows the complete solution of this circuit in a functional form. This means we dont have to keep calculating 're' every time we see this circuit pass by our desk.

There's no way in heck that it can be wrong because it builds on the previous method in such a way as to retain the benefits yet loose the undesired side effects.

Here's another example of how the standard and updated methods differ ('ie' is emitter current, R1 and R2 upper and lower resistors):
Method 1:
If Vcc=2 then
ie=f(R1,R2,Vcc)
re=f(ie,K)
Vout=f(Vin,re)
Gain=Vout/Vin
elsif Vcc=3 then
ie=f(R1,R2,Vcc)
re=f(ie,K)
Vout=f(Vin,re)
Gain=Vout/Vin
elsif Vcc=4 then
ie=f(R1,R2,Vcc)
re=f(ie,K)
Vout=f(Vin,re)
Gain=Vout/Vin
etc., etc.

and here is Method 2:
Gain=f(Vcc,R1,R2,K)

and this last function f() is not a composite function but is a simple algebraic function.

So even if we could argue that there is no other benefit, that is one that stands.

If you are unhappy with the point that the results are similar, i guess i could produce some numerical results. You think you'd be happy with that though?

 

Hello again,

I have now a graph that i prepared that shows the ratio of the gains of the standard method and the non standard (current controlled Re) methods. It is the ratio of the 'new' over the 'old. Note there is very little difference except when K grows larger. That is when the new method would shine over the old method, but i realize that is also not typical of the average transistor circuit where K is usually smaller.

The ratio is graphed over the supply voltage E2 which is the +Vcc, and over K. This allows us to see the differences as both of those two vary.
Note even the most extreme value on the graph is only around 12 percent (1.12 means method 2 is 12 percent higher than method 1).
Also note that this is with all resistors equal, because the full blown ratio is really dependent on all four resistors and so is somewhat messy.
I used a pseudo function to mimic the standard method.

Here are the two functions used in the graphical comparison:
Gain1=(2*K+E2)/(2*(3*K+2*E2))
Gain2=(K+E2)/(2*(K+2*E2))
where
Gain1 uses the standard method and
Gain2 uses the 'new' method.

The graph shown plots the ratio:
Ratio=Gain2/Gain1
with K and E2 varying over the ranges as shown in the graph.

 

Hello again,

Found a new angle for this discussion. That is, when trying to use the transistor model with 're' in it in a spice program. It makes it much easier to make 're' a simple current dependent resistor re(i) with (i) being the emitter current.
So what is the difference?
Well, in the standard way of doing it, we have to FIRST evaluate the DC conditions in order to calculate the value of 're'. After we do that, then we have to insert the value of 're' into the schematic, then we can proceed with the AC analysis in the usual way. If we happen to change the DC supply voltage, well then we have to recalculate 're' again and then change the value manually before we can do the AC analysis because the old value of 're' no longer applies.
However, in this 'new' way where we make 're' a current dependent resistor re(i), we only have to insert that resistor one time and one time only, then do the AC analysis. The simulator will (or should) calculate the DC operating conditions and make the value what it needs to be for that set of DC conditions (which we would have had to do by hand before with the standard method), then proceed to the AC analysis. Alternately, the simulator will calculate the running value of re(i) as the current is changing which will ALSO show a little distortion in the wave output, and interesting side effect. We all know that a transistor creates some distortion but how well this new action mimics the distortion in a real amplifier would have to be investigated. I was not particularly interested in that part for now though, just in obtaining a model that mimics the standard 're' method without having to bother recalculating.

Now all this has to be taken a little lighter than it might seem by reading all that. Namely, the accuracy which WBahn pointed out would have to be investigated more carefully compared to better models if a claim of better accuracy was going to be put forth as a true advantage. I agree with that quite strongly, with just one exception, and that is for when something changes like the DC bias point and we dont bother to recalculate a new value. However, even then, with normal values of K commonly seen in transistors the difference should still be small. Therefore the main advantage seems to be that once the value of 're' is changed to re(i) we NEVER have to calculate 're' again, ever, in order to calculate the gain, unless of course we choose to do so for some sort of sanity check. Of course when used in a spice simulation, the value of re(i) will be a constant function and so will never have to be changed, as long as the simulator you are using can handle functional resistances.

BTW the graph i presented earlier (last post) shows a very high point near the center of the graphic. That point is really only around 1.11 in 'height' and so that's only 11 percent higher than the standard method. It looks higher at first glance because the drawing is at an angle as is normally used to show 3d diagrams.

And to everyone, have a Happy New Year!

 

Well - I am not quite sure if I was able to understand the real background of the above contribution.
It is my only intention to point to the fact that all Spice based BJT models (used in all simulation programs) make no use of such an artificial part called "re" (differential resistance, controlled by the collector current).
The reason is simple: Simulation programs make no use of different models for DC, AC and TRAN simulation runs.
Hence, no separate small-signal model (including re=1/gm) is used.
All the transistor models (BJT) are based on the extended Gummel-Poon model which, of course, uses the exponential Ic=f(Vbe) characteristic.
Therefore, the transconductance gm (identical to the small-signal parameter 1/re) is always determined by the DC current - and varies continuously with this current (if it changes).
More than that, the Gummel-Poon model contains, of course, the non-linear properties of the BJT transfer curves which can be observed during the time-dependent simulation runs (TRAN analyses).

We should keep in mind, that all the known BJT small-signal models (Pi-model, T-model,..) and the small-signal parameters we are using (hie, hfe,...) are for the purpose of hand calculations only.

 

Well - I am not quite sure if I was able to understand the real background of the above contribution.
It is my only intention to point to the fact that all Spice based BJT models (used in all simulation programs) make no use of such an artificial part called "re" (differential resistance, controlled by the collector current).
The reason is simple: Simulation programs make no use of different models for DC, AC and TRAN simulation runs.
Hence, no separate small-signal model (including re=1/gm) is used.
All the transistor models (BJT) are based on the extended Gummel-Poon model which, of course, uses the exponential Ic=f(Vbe) characteristic.
Therefore, the transconductance gm (identical to the small-signal parameter 1/re) is always determined by the DC current - and varies continuously with this current (if it changes).
More than that, the Gummel-Poon model contains, of course, the non-linear properties of the BJT transfer curves which can be observed during the time-dependent simulation runs (TRAN analyses).

We should keep in mind, that all the known BJT small-signal models (Pi-model, T-model,..) and the small-signal parameters we are using (hie, hfe,...) are for the purpose of hand calculations only.

Hello again,

Thanks for the reply.
You can use a circuit simulator to check a hand calculation, something i recommended many times in the past.
Wouldnt it make sense to use a circuit simulator to see if you got the result correct and thus self-check your results?

 

Hello again,

Thanks for the reply.
You can use a circuit simulator to check a hand calculation, something i recommended many times in the past.
Wouldnt it make sense to use a circuit simulator to see if you got the result correct and thus self-check your results?

Yes, of course. Or vice-versa - because we never should blindly trust simulation results.

The only point was: It was not clear to me (and it still is) if your suggestions were related to Spice simulation models or to the well-known small-signal ac models .

 

Yes, of course. Or vice-versa - because we never should blindly trust simulation results.

The only point was: It was not clear to me (and it still is) if your suggestions were related to Spice simulation models or to the well-known small-signal ac models .

Hi,

Oh yes, that's a good point too. Most of the students that come through here are doing it by hand to start with so i naturally thought it through in that direction.

Well, none of the models can match a good spice model i dont think, and the original "T" model with 're' is no exception. That's one reason why i thought it would not make too much sense to compare it to a good spice model. For one thing, we were not even considering the "Early" effect, and i didnt really care about that to begin with anyway. I was just looking for what seemed to me to be a natural extension of the 'standard' way of doing the "T" model with only 're' because that has come through these pages several times and on other sites too. The extension came natural to me because i had done a lot of work in nonlinear circuits and had to come up with models that had some very strange characteristics but they had to be functions, or at least should have been. The beauty of using functions is that they are so functional
The results seem to 'pop' out of the math, even for circuits that have different operating conditions.

BTW congrats on your long and illustrious teaching career.