need advice -transistors and Mr. Laplace-

[frank]

I have been searching on the site some info about Laplace transforms and the subject seems to be down since 2007.
Now my questions are:
1.-Do anyone know books references about math models of transistors to use in Laplace transforms?
2.-If someone knows, what happens with the model when you're out of linear region (cutoff, saturation) since effects builders use those extremes?
3.-Is it more judicious just to have in mind gain, input and output impedance to work with?  And then leave the non-linear behavior in the "MOJO" zone?
 

[alanlan]

Laplace transforms are used to model linear frequency dependent behaviour.  I don't think they will help you to analyse non-linear behaviour of transistors.  Great if you want to predict frequency or time response assuming you're operating in the linear region, but you're right to think about dealing with what happens when things saturate or cut-off separately.

[frank]

Well thank you Allan,

What you have answered me is what I know at the present time in mechanical vibrations.  But the thing is that I would like to read some Laplace theory related transistors even in the "linear portions or assumptions".  I know a bit about doing it for R-L-C but for an active device like a BJT transistor I am still scratching my head.

What I am also trying to do is ask questions about "simple" theory (this site is about enjoying and learning, right!).  The Rangemaster, Appollo and NPN Boost by Gus may be in the beginer projects, but I doubt that pushing a transistor in non-linearity is undestood by most of the newbies that have completed these projects.  And Aron have made a good choice by choosing that project for new person to electronics.  I would like to take the chance of understanding in my head and be able to analyse these circuits on paper to be a better scientist (technician, Eng, hobbyist...whatever you like) not just an guitar effect nut.  Debugging a real circuit (to make it work and understand the very basics) can learn you something, but it is not going to give you the most desirable experience in understanding a more global picture on the subject of BJTs.  And with the qualified persons that seems to be on this site and quantity of "new to electronics" I don't think that the last ones are realising their chance.

   

[mac]

Google --> "ebers-moll" laplace, to start.

Non-linear systems are a pain in the eye.
Suppose you have a perfect sine wave generator connected to a single transistor. You can bias it in two ways, voltage divider (rangemaster) or negative feedback (big muff). Forget about the DC bias point as you can use generic values for the resistors, then see what happens as you change values. You write the BJT eqs and find a way to solve the AC problem (they are non-linear ).
The output wave will never be a sine wave since the "BJT linear region" is just an idealization.
Now you ask yourself, which is the freq distribution of the output wave, or the even/odd harmonics 1 millon dollars question. The anti-Fourier analysis.
Unless you know how to solve a set of non-linear eqs you'll be in a dead end. But that's just math skills.
I guess PSpice do the math for you.  If I'm not wrong PSpice use the ebers-moll model to analyze BJT behaviour.

mac

[frank]

Hello Marcello,  very happy that you responded to me.

I've looked a bit in the Microelectronic Circuits Book (Sedra Smith) at the library and there is some stuff about  Ebers-Moll in it.  This book looks REALLY great.

As you say, in Malvino's Electric principles (I have it at home) they also say that Ebers-Moll model implies for AC signal.  But I think that this book don't go too deep in the subject.  I've remarked that in Malvino you get a good overview, but as soon as maths becomes more serious he skip on the subject.  Example: in ch. 14 on frequecy effects they talk a bit about the Miller's theorem, Bode Plots, etc...   It answers parts of my questions (as it is for linear domain), and he goes fast on the subject.  I think Malvino is good for aquiring a vast knowledge about electricity.  I would really like to have the solutions for the problems becose it's a good book for taking the first steps on active devices (and I'm not in school so, no teachers help me with this stuff).  I know also that in school you don't have time to work on your fantasies.  After the week you rather have a beer with your collegues and discuss about that F*** exam.  And then have an other beer becose that you and your pals didn't have same answers and work seems infinite.

I don't know what is Anti-Fourier analysis.  I've searched a bit and did not found. I think there is even nothing in the Advanced Engeneering Maths book by Kreyszig on the subject.  I tought that ANY output signal could be modelised by a sum of sinuses with their respective phase, amplitude and frequency.  What I understand is that the BJT amp can be viewed as a box that contains a non-linear model.  The input could be a simple constant sinus, the output is a distorted signal that can be analysed by a Fourier transform (and I don't talk about the transcient analysis).  It's the work of Mr. Laplace to work on transcients (with dirac, exp and etc... in the linear region).
What do you mean by generic resistances values for bias (?)

Spice sure is help. As doing the real thing, and sampling, and doing a FFT.  Looking at the results might provide you some insight about how the thing work (shape off waves, I , V.........).  The thing is that if you don't have a hint about subjects, it's just plug and play.  Or as other say crap-in-crap-out for beguiners.

I guess I should do just as in school:
- inventory of knowledge base
- Goals
- Discussion -Reading what you need
- Theory models -results (Anti-Fourier (?))
- Computer simulations -results - frequecy sweeps - Fourier
- Real thing - data aquisition - measures - analysis -FFT
- Put all that together and see what is similar and different - start to understand
- Discuss with yourself and your penpals on internet
- Conclusion
- Making of a simpler experience and start the circus all over again becose that npn Boost by Gus is bootsrapped.

And this IS FOR A CIRCUIT WITH ONLY ONE TRANSISTOR !!!!!

Hope to hear from you again Marcello.
À la prochaine !
Frank

[frank]

Also Thanks for Big Muff bias advice.
I've also seen a post of yours on the FF bias.
http://www.diystompboxes.com/smfforum/index.php?topic=52716.0
I have made one manhattan style so gonna check the theory against mine.
I will also try to make a simple matlab program to fool around with that.

[mac]

Frank,

Glad to hear you like the post. The calculator is at
http://www.diystompboxes.com/biascalc/
I should have to improve the model to include cases like leakage bias used in the Tonebender MKII.

1. Normally sine waves mixed in some proportion are used to generate a given function. If you have the function and want to find the harmonics you have to do the reverse job --> anti-Fourier. Sorry to confuse you. Hablo español...
2. When you bias a transistor you can set the output (collector or emiter) at any point between 0 and Vcc. This point is the zero level for AC signal and it is of great importance. When you write the transistor eqs. you use names like Rc for collector resistor. Supposing that an analytical solution exists for the model, it would be in terms of Rc and other resistor. When you put the model in the computer you have to provide values for Rc setting the DC bias point. If you look at the FF model in the link you posted you'll note that all currents are in terms of the resistors.
3. It is a good idea to fully undertstand what happens inside a transistor, fet, tube, or circuit. There are plenty of good books and pages to guide you. And powerful tools like PSpice or Matlab. But I found that the best tool I have is .. the breadboard!

mac

[frank]

OkaaaY Marcello,

I have printed and put what you have said in my logbook.  With internet and computers it's easy to put that in a folder and forget it (like an other interesting analysis of the Fuzz-Face that I have found before and can't find in all those files).

1-  AH! Une transformée de Fourier inverse.  Je parle français.
2-  Will look at that
3-  That is why I have returned to BJT and a more basic circuit, and read books.

I like Matlab because it is my main calculator, I am used to it, and for graphs its easy.  I have used it a lot in mechanical eng. even for managing production and packaging issues.
I have to learn how to make more compact breadboard circuits.

I made myself a series of music projects to do to go from basic, easy to a bit more difficult so I could do it the "right way" and with interest.  I am more used to vibrations theory than electrics !

What are your projects now ?

PS: I have looked in my posts and you are the first one who gave me a serious advice, so I now consider that you have welcomed me on this site!

Hope to talk again soon!
Frank

[mac]

I've been refreshing my memory and read some about Laplace transform and how it is used to solve some EM eqs. You can go for a direct solution or use the Laplace transform. Either way the difficulty is the same.

I am more used to vibrations theory than electrics !

I did a study of vibrations of ship plates using finite elements while at college... more than 20 yrs ago... doh!
Mine is... was physics. Lots of EM theory but no circuits, except for some R-C-L in Physics II. And BJT model was just an excercise in Quantum Statistical Mechanics.
The big difference between EEs and Physicists is that Physicists dig deeper but EEs know how to put things to work.

PS: I have looked in my posts and you are the first one who gave me a serious advice, so I now consider that you have welcomed me on this site!

There are many guys here who are EE and have a lot of experience in this area. And also some that do not have a tech formation but spent all their lives between guitars, pedals and amps. They helped me a lot.

What are your projects now ?

Off topic ... XXX

mac

[frank]

Off topic ... XXX

OK I see, a nuclear bomb.

[mac]

Off topic ... XXX
OK I see, a nuclear bomb.

No no no... Ibiza... 

mac

[The French connection]

1-  AH! Une transformée de Fourier inverse.  Je parle français.
2-  Will look at that
3-  That is why I have returned to BJT and a more basic circuit, and read books.

I dont know if it serves but in FTIR spectroscopy (i just want to spread my knowledge here... ) when we want to find the harmonics inside an optical signal we use what we call ''deconvolution'' or ''self deconvolution'' (Auto-deconvolution pour les francophones) witchs is the opposite of convolution use in FT. But it's kind of tricky and there's so much conditions you need to fullfiled to make it...But hey i'm not a Math killer, neither a EEs and nor a Physicist (i don't see everything as a sphere). Frank, it's all in your honnors to dig that deep, i'll liked to ear of your ''conclusion'', i loved those non-linear system since in the end they are all the same...Funny huh? Entropy rules!

I think you say: ''my two cents'' in english so here's my little pesos.

Dan

P.S. Sorry for the wire shorting...

[frank]

Frank, it's all in your honors to dig that deep, i'll liked to ear of your ''conclusion'', i loved those non-linear system since in the end they are all the same...Funny huh? Entropy rules!

Oh boy, I have homeworks to do...  ahh tomorrow!  Procrastination: is it a linear thing?

[frank_p]

Frank,
I should have to improve the model to include cases like leakage bias used in the Tonebender MKII.
mac

Yes I saw you had a post on that and nobody replied to you !!! 

What I would like to view is a 3D plot of a characteristic curve of a germanium that is leaking a lot.  Just can't figure for now what it will be!  I don't understand leakage in a physics perspective.  (Ic, Ib ,Vce) and difference between npn and pnp in leakage...  Where is cutoff and saturation in a leaking device, what is the shape of that surface vs an ideal non-leaking device....  A good perspective on leakage is missing in my comprension (bias wise also...).

I also viewed some posts on gain mirrors of low current gain devices.  R.G. said that it was perhaps a vain pusuit.  My question is again, what can you do (other than boosters) with a low gain and leacky germanium transistor.  How can you adapt them to make "the rejects" useful in the stompbox society !  There are so many of them in my bins and it makes me sad to do nothing with them.  And I don't want to be a reseller of devices that I don't want. I rather like to understand something new.

If you can remind me what this post was (leakage) ?  There was some equation in there...

See Ya Marcello  !

[mac]

AFAIK, leakage has no side effects if below some levels. I do not know of a relation between leakage and hiss, but too much leakage may cause the transistor to fail in the long term.

You can use your low gain transistors in darlington pairs. But leakage will multiply by the gain of the second transistor I guess so the one leaking less must be put first.
YOu can use RG test to measure gain and leakage in a home-made darlington Ge.
I used low gain low leakage Toshiba 2sa53 in Aron's Rocket once, hfe=20, iL=15ua both. Final gain was 400 and total leakage about 300ua which is not bad at all. I have some Matsushitas 2sb176 having hfe=200 iL=200ua.

I also used hfe<50 Ge in a cascading config. Nice distortion. It will be cool to have a distortion project using those low gain Ge.

mac

[bkanber]

I'm pretty upset I didn't see this thread earlier. I know Laplace transforms pretty well, as well as mathematical modeling of both electrical and mechanical systems.

Basically, you want to use Laplace when the system is linear and SISO. Laplace works pretty well for MIMO systems too, but once you get past a couple of ins and outs, the matrices become too hard to work with analytically.

You want linear systems with Laplace mainly because the transform of a nonlinear equation involves super messy convolution integrals-- the avoidance of which is the entire reason we use Laplace transforms anyway!

If you have non-linear systems, it's going to be easier to work in the time domain than it will be to work in the s-plane. Don't get me wrong, Laplace is GREAT for simpler systems, and before computers were fast and amazing (ie, Matlab), Laplace was the way to go. In the past, people would generally simplify their non-linear systems just so they could use Laplace (the most common simplification is the small-angle approximation, sin theta =~ theta) -- solving certain differential equations in the time domain is tedious, and sometimes even impossible analytically. Laplace transforms really made life a whole lot easier for electrical and mechanical engineers.

However, Laplace breaks down in non-linear situations. Laplace is really good for vanilla circuits operating normally, because standard RLC circuits don't contain non-linearities. However, vibrations analysis is almost ALWAYS done in the time domain, because your model won't break down with nonlinear terms as it would in the laplace domain, and MIMO systems are (Kind of) easier to do in the time domain. (Yes, there is the state-space representation for the Laplace domain, but as I said, that matrix math only takes you so far...)

Moral of the story: if you're looking to model non-linearities, break out the differential equations textbook and do it in the time domain. Actually, just use matlab. Lots of differential equations are not solvable analytically... fortunately, Matlab solves equations numerically

If you have any questions about Laplace, Fourier, or differential equations (or vibrations analysis... not really pertinent here..), just ask me. I'm pretty good at that stuff

Burak

[frank_p]

Thanks Burak,
I see that analysing a dist. stompbox is not very easy to do in a "black box" in/out way (frequency effects + distortion).
Its perhaps better to use laplace just for "tone".  And then work with time domain eqs for the distortion (As you say).

[frank_p]

AFAIK, leakage has no side effects if below some levels. I do not know of a relation between leakage and hiss, but too much leakage may cause the transistor to fail in the long term.

You can use your low gain transistors in darlington pairs. But leakage will multiply by the gain of the second transistor I guess so the one leaking less must be put first.
YOu can use RG test to measure gain and leakage in a home-made darlington Ge.
I used low gain low leakage Toshiba 2sa53 in Aron's Rocket once, hfe=20, iL=15ua both. Final gain was 400 and total leakage about 300ua which is not bad at all. I have some Matsush*tas 2sb176 having hfe=200 iL=200ua.

I also used hfe<50 Ge in a cascading config. Nice distortion. It will be cool to have a distortion project using those low gain Ge.

mac

Thanks a lot and again Marcello !

[mac]

I used to be good solving systems of diff eqs, analytically or numercally. Today I remember more math than physics.
An AC simple BJT can be solved analytically if you do not mess with the transistor model and just use a fixed Vbe for the B-E junction. I guess it is a good first aprox. You'll get a set of diff eqs for all currents depending on the bias resistors, caps and the signal generator at the input, typically a 1khz sine wave. After some cups of coffe and a couple of pages you'll get the answer.
A more complex model may not have an analyticall solution. But Mr.Taylor may come to rescue us.

mac