Derivative of I-V curve

[g1lai]

It could be a simple question, but my brain stops running ...

I have I-V test data, and try to derive the 1st derivative (dV/dI) and/or followed by smoothing. Is there any build-in function to do this?

Thanks a lot.

[g1lai]

On 7/14/2009 4:16:09 AM, Tom_Gutman wrote:
>It is not at all clear that
>eq(1) in that paper applies to
>your system as measured. That
>paper does not even show the
>assumed circuit for the solar
>cell, much less show the sign
>conventions used. Presumably
>you are supposed to know that
>from other sources. You need
>to know the sign conventions
>(which can differ from paper
>to paper) to be able to
>interpret the results.
>
>To the extent that they show
>data (I don't see an actual
>I-V curve) they seem to use
>conventions that result in
>positive values for I and V
>(for their solar cell). But
>their very first plot seems
>inconsistent. They show Voc
>varying with Rs. But under
>open circuit conditions I is
>zero, and Rs should have no
>effect whatsoever. It's hard
>to know how seriously to take
>anything else in this paper.
>
>But it's easy enough to use
>their equation is the work
>sheet. And since their
>equation differs from the
>previous one only in the
>convention for the sign of I
>we get (using the uninverted
>current figures) exactly the
>same negative Rs.
>
>I notice that the authors of
>the paper note that negative
>values for Rs do occur. While
>they put it down to a large
>error, it is possible that it
>is simply a attribute of this
>model, and that the model is
>just not really right.
>__________________
>� � � � Tom Gutman

I hope this link will be helpful, although the symbol is like German.

http://www.tf.uni-kiel.de/matwis/amat/semitech_en/index.html

According to this site, the Junction Voltage should be smaller than the external measured voltage (or Vd in the worksheet), indicating Vd-abs(I*Rs) in the equation. It seems Lambert W function always generates Vd+abs(I*Rs).

You may also want to try the 2 diode model as suggested in the site. Thanks.

[g1lai]

>http://www.tf.uni-kiel.de/matwis/amat/se
>mitech_en/index.html
>
>According to this site, the Junction
>Voltage should be smaller than the
>external measured voltage (or Vd in the
>worksheet), indicating Vd-abs(I*Rs) in
>the equation. It seems Lambert W
>function always generates Vd+abs(I*Rs).

Sorry Lambert W function does generate Vd-abs(I*Rs) --- I did not notice the change of sign in your YY(25) worksheet. Both YY(24) (for positive I) and YY(25) (for negative I) are pretty good fit!

[g1lai]

>I hope this link will be helpful,
>although the symbol is like German.

http://www.tf.uni-kiel.de/matwis/amat/se
mitech_en/index.html

Ch.8.1.2

[ptc-1368288]

Too many papers and no "solution", too much blabla instead of the appropriate maths. Your model solar cell is solved as given and as per your original data set. What that means for you is to take over and carry more study as required. All collabs have assumed T = 300�K, but you could solve for a family of 'T' if you would have those 'T' data sets. Once a project is done, if you come backbackback ... that is too circular for generalist collabs at least for me. @ 70 collaborations and "project done", it's really up to you to work what more you need and revisit. In fact, in your project, you have supplied only the data set and painfully and supplied the papers.
What you must understand is that those papers go nowhere because they lack the appropriate maths. That 20 techniques paper is all resumed in the attached version 11. Open this work sheet in your 14, if it does not work ... I'm out after so many circular hours doing a project from scratch.

Please read with attention and comment.
You keep saying "Lambert not bad...." How can you say that if you never show anything... Lambert solves your model exactly and that's it. At this point of your discussion about the model, it has nothing to do with the solution of the model you suggested and that you didn't even plug in a work sheet.

jmG

[g1lai]

On 7/14/2009 12:12:04 PM, jmG wrote:
>Too many papers and no
>"solution", too much blabla
>instead of the appropriate
>maths. Your model solar cell
>is solved as given and as per
>your original data set. What
>that means for you is to take
>over and carry more study as
>required. All collabs have
>assumed T = 300�K, but you
>could solve for a family of
>'T' if you would have those
>'T' data sets. Once a project
>is done, if you come
>backbackback ... that is too
>circular for generalist
>collabs at least for me. @ 70
>collaborations and "project
>done", it's really up to you
>to work what more you need and
>revisit. In fact, in your
>project, you have supplied
>only the data set and
>painfully and supplied the
>papers.
>What you must understand is
>that those papers go nowhere
>because they lack the
>appropriate maths. That 20
>techniques paper is all
>resumed in the attached
>version 11. Open this work
>sheet in your 14, if it does
>not work ... I'm out after so
>many circular hours doing a
>project from scratch.
>
>Please read with attention and
>comment.
>You keep saying "Lambert not
>bad...." How can you say that
>if you never show anything...
>Lambert solves your model
>exactly and that's it. At this
>point of your discussion about
>the model, it has nothing to
>do with the solution of the
>model you suggested and that
>you didn't even plug in a work
>sheet.
>
>jmG
>

Math means nothing if the number does not make sense or no physics meaning. I am working with at least one collab trying to understand better of the model and we are making progress.

Why appropriate data analysis is important for me? Let me tell you how much it cost for a worksheet. In order to generate the worksheet, I have to arrange the experiment that meets the requirement of industrial testing standard (BTW, the temperature is fixed). I also have to require cells from the PV industry. It is about 2,000 USD for each worksheet!

We probably have different understanding of the words "experimental verification". My understanding is that the model should be tweaked to satisfy the experimental data. In my case, there are 5 parameters in the equation. It is hard to believe that those parameters can be totally decoupled during fitting. Since I know the Rs and Rsh range for those cells, I am chatting with the collab about the possibility of modifying the model. You probably are not interested. However, I think the readers could benefit from our discussion if they want to solve an engineering problem.

[ptc-1368288]

I understand why you thinking of modifying the model, because of different technologies in the solar cells you would like to try and fit, I may be a "generalist" but not as stupid as you might think. This is why I was talking about a more generalised solar cell model (years ago), and based on continued fractions that I carried to end use.

>It is hard to believe that those parameters can be totally decoupled during fitting.<<br>
That's where the curve fitting expertise comes into play, and you have seen nothing yet from the Mathcad tool box that goes ON & ON for about 10 years and on the 100's of curve fitting done.

The cost of a worksheet, is detrimental to other collabs if the visitor is too circular and can't fix the project to some reference. How many models do you figure will cost $ 0.00 but a huge # hours. I'm saying that in reference to the number of various papers you have linked and that go about nowhere.

Considering that Mathcad 14 may not deal well with Lambert W as I have passed and explored deeper, considering that the W argument for this particular model ranges -1.913E-6, -0.168 ... I started working on some other aspects in the more general sense than this simple model, but if you wish, I will be glad to leave this thread. However, if eventually you end with a more generalised model, I will be glad to collaborate again.

As you haven't replied about how the last work sheet behaves in Mathcad 14 and eventually in the case the "defective Mathcad 14 Lambert" is unsatisfactory, there may be a much different route that I'm going to try tonight but that you would have to reply about.

Conclusion:
The project is in your hands, the tool box in this collaboratory.

jmG

[ptc-1368288]

Your thread:

http://collab.mathsoft.com/~Mathcad2000/read?125964,16

This work sheet replots I(V) as per the fitted parameters from Lambert W (previous work). This step can be replaced by optimizing the parameters of the function, thus getting rid of Lambert W. Assuming you have experimentally determined some valid parameters by yet unknown method, you can play with any parameters for their "influence" on the solar cell model eq1. This proposal is inductive of "tracking" the experiment of a typical unique model adapted to whatever could be the real physical model. What all that means is that you don't need to have thisthisthis or that, just to conclude to the appropriate procedure for generalised use. And the point is there of dramatic consequence, i.e: if no procedure fits then the model in incorrect. That was my point from the very beginning. At this point, use the imagination to construct an "eq1" that will be representative of the solar cell plugged in the lab.

Mathcad 14 is assumed to crunch this work sheet,
if it does not and turns red, just too bad.

jmG

[ptc-1368288]

... the above Given/Find is the previously mentioned option:

4. iterative solving........ [Mathcad]

The 3 other methods listed persist solving via Lambert W.

jmG

[TomGutman]

Talking about a voltage being larger or smaller is meaningless unless and until the sign conventions for current and voltages is well established. Is the voltage positive or negative? Does larger mean more positive or larger in magnitude?

Taking abs(I·R_s) is nonsensical. The voltage across the diode will be V_d+I·R_s or V_d-I·R_s depending on the sign convention for I.

The Lambert W solution does not generate any value for the junction voltage. The junction voltage is a term in the original equation, either V_d+I·R_s or V_d-I·R_s depending on the sign convention for I. I have laready posted two sheets which differ in the sign convention for I, one using the sign conventions (as near as I can figure them out -- you should really verify them) from the first paper and one using the sign conventions from the second paper (and, apparently, your data). While the sign conventions affect the form of the equation, and the sign of some values, it has no effect on the underlying physics or the results in physical terms.

I took a quick look at the most recently referenced site. But it looks big and I don't have time right now to read through the whole site. What area of the site do you think is relevant?

A two diode model might be a solution. An incorrect model for the diode current could force a negative R_s. The second referenced paper does start with a general equation with N diodes in parallel. It's easy enough to set up the equation for multiple diodes. But then the equation cannot be solved for I (or at least Mathcad's symbolic processor cannot solve it). So using it will require going one of the routes I originally indicated, a function based on a solve block or a differential equation.
__________________
� � � � Tom Gutman

[TomGutman]

Here is a solution for the two diode model, using a solve block to get I(V). It does give a solution with reasonable resistances. But, as expected, it's quite slow.
__________________
� � � � Tom Gutman

[TomGutman]

Here is the two diode solution based on an ODE. Due to ease of implementation considerations it is in MC13 and uses MC13 facilities.

The ODE based solution runs much faster than the solve block based solution in MC11. But, rather to my surprise, it is not as fast as the solve block based solution in MC13, which is much faster than in MC11.

The three solutions produce similar, but far from identical, results. Sensitivity analysis, with variance estimates for the parameters, might be in order. PaulW had some sheets for doing such analysis. Reducing TOL might narrow the differences.

In the normal operating range the voltage is generated by the cell. That voltage is then divided between R_s and the load. Hence the junction voltage will be higher than the output voltage. The reverse will be true if the current is being driven by an external voltage, as in a dark cell measurment.
__________________
� � � � Tom Gutman

[g1lai]

>In the normal operating range
>the voltage is generated by
>the cell. That voltage is
>then divided between Rs and
>the load. Hence the junction
>voltage will be higher than
>the output voltage. The
>reverse will be true if the
>current is being driven by an
>external voltage, as in a dark
>cell measurment.

Correct. I was confused before. Here is how I determine the sign of Rs.

(1) Source voltage (Vd) is always positive;
(2) Measured current (Id) is always the same sign as Isc in the range from 0 to Voc.
(3) Once the signs of I and V are determined, there is only one possibility of junction potential Vd+I*Rs, either greater or lower than sourcing voltage Vd. A simple way to do this is to plug in a large Rs value (5 or -5) in your trial solution and see which sign makes sense from I-V profile.

As such, we may say that 1-diode Lambert W model generates negative Rs which does not seem to make sense. The series resistance of the cell is around 0.5ohm. The 2 diode model fitting results in Rs=0.36ohm which is more reasonable.

My solar cell sample is directly from PV production line with high efficiency and lower series resistance. The attached pdf present some technique to extract parameters from dark I-V. They also used 2 diode model.

Thanks.

[ptc-1368288]

>As such, we may say that 1-diode Lambert W model generates negative Rs which does not seem to make sense.<<br> ____________________________

Lambert does not generate negative Rs, it solves in "scalar maths", which scalar maths are unitless and dimensionless. Sign convention is something that comes after the "scalar solution" and that is very common in applied maths, at least when constructing diagram that have branches that are in the Laplace domain (just for example). In fact, the diagram construct bears the [-] in front of Rs, and Lambert concludes by itself in total ignorance of what the draftsman could have drawn incorrect. What I'm saying is that Lambert solves in the "math scalar domain". Take the example of a quadratic scalar solution that has two roots where only one is valid (per say the real one)... or a solution valid in a certain portion of the plane. Lambert solves for a set of "scalar coincidences that must equate numerically". The diagram is a short form of a grid network, if you would have to solve via matrix solving, the sign convention is most important otherwise no solution or incorrect solution would result. What I'm saying again in other words is that the model is scalar rather than physical, even if you are confined to used instruments that are not scalar or don't operate in the scalar domain.

The last PDF is very interesting, will read again.

jmG

[TomGutman]

I just choose signs based on consistency and logic. I start with the diagram from your first reference. Since I consider the cell as the source of the current, I take the positive direction of I_ph to be upwards (that is consistent with the convention in that paper, but reversed from your data). I then take that current as divided between the various sinks -- the two diodes, the shunt resistance, and the load. Thus the positive current for each of those is taken as downward (from top to bottom). In the normal operating range the result is that the current and voltage for the load are both positive, resulting in a net power consumption in the load.

I have been able to tweak the two diode solution to work in MC14. With some interesting results. The solve block based solution in MC13 appears to be anomalous. It is anomalously fast (faster than the ODE based solution), and the results differ from the other three results (which agree with each other). In MC14 the solve blcok solution is much slower, but the result agree with the ODE based solution. The ODE based solution is a bit slower, but ends up still faster than the solve block solution.

I don't see much relevance of the attached paper. On several grounds. For starters, it uses dark cell measurements (avoiding the estimation of I_ph), which is not what you have. It also ignores the shunt resistance (assumes infinite R_s), whereas you claim a significant shunt current (and the model results support that). While there is some talk of a two diode solution, the math is based on a one diode solution. Their approach seems to depend on working in a range where only one diode carries appreciable current. And the whole approach is similar to the others, an attempt to make various assumptions to simplify the problem and to estimate parameters based on attributes of the curve. I suppose that is reasonable if your main tool is a graphing calculator so that graphs are all you can reasonably get. But not when you have the power to fit the actual complete model.
__________________
� � � � Tom Gutman

[PhilipOakley]

The problem of sign convention is likely to be due
to differing viewpoints.

The first is that of a regular rectifier, for which
the convention has the diode looking like a positive
resistance (forward voltage generates forward
current..)

The other viewpoint is as the power source, and we
all like to believe that such devices supplying
current (like a battery would), so in that quadrant
of operation we want, again, positive I & V values,
but that conflicts with the first viewpoint, but we
don't notice 'cos we are 'happy'! - typical human
ability to believe two contradictory things at the
same time.

Philip Oakley

[TomGutman]

>>The problem of sign convention is likely to be due to differing viewpoints.<<

Of course. That's why it's a matter of convention and needs to be explicitly stated. And why care needs to be taken when comparing data or equations from different sources. The data or equations are based on a specific arbitrary choice, and one needs to know what that choice was to interpret the results.
__________________
� � � � Tom Gutman

[ptc-1368288]

There is more than that Philip,

All models (linked) are wrong. No "generator" of any kind can exist w/o internal resistance, which resistance is in series right after the diode symbol but not shown. In the case of semiconductors, there is a backward current ... then the shunt resistance is correct. The applicability of the series resistance past the shunt junction, view it a the completion of a one leg bridge system under load.

From a wrong model, easy to math it wrong !
The two diodes solar cell from Bruno [1984 ?], done in mathcad is right. I won't refer to it to avoid more confusion. Each solar cell technology has its own model ... about DE's , Oh !

Jean

[g1lai]

On 7/15/2009 10:28:36 PM, jmG wrote:
>There is more than that
>Philip,
>
>All models (linked) are wrong.
>No "generator" of any kind can
>exist w/o internal resistance,
>which resistance is in series
>right after the diode symbol
>but not shown. In the case of
>semiconductors, there is a
>backward current ... then the
>shunt resistance is correct.
>The applicability of the
>series resistance past the
>shunt junction, view it a the
>completion of a one leg bridge
>system under load.
>
>From a wrong model, easy to
>math it wrong !
>The two diodes solar cell from
>Bruno [1984 ?], done in
>mathcad is right. I won't
>refer to it to avoid more
>confusion. Each solar cell
>technology has its own model
>... about DE's , Oh !
>
>Jean

Thanks for all input. I have better understanding of solar cells.

(1) Principle of PV effect (PVCDROM, Ch 4.5). Under illumination, there are excess electrons in N-type side and excess holes in P-type side that functions as a "battery". The "internal resistance" of this battery is the diode itself and/or parasitic resistance. In the equivalent circuit, this battery is represented by a current source Iph, a diode, and/or parasitic resistance. This makes sense for me.

(2) I-V measurement is always performed using a SourceMeter. An external sourcing voltage is applied to the 2 terminals of solar cell, and the current is recorded. For the SourceMeter, positive current is designated as that current flowing OUT of the SourceMeter instrument.
The negative sign of the current just indicates that the current is flowing INTO the SourceMeter instrument.

(3) In my worksheet, the current is always negative in the 0-Voc range. This indicates the current flow from the "battery" into SourceMeter.

(4) Thus the bias at the terminals is smaller than that at the junction (Page 172 of the book)

http://books.google.com/books?id=s5NN34HLWO8C&printsec=frontcover&dq=the+physics+of+solar+cells&ei=jaFeSpWqO5DUyQTvlYnDBQ

(5) Phillp's viewpoints are actually related to different paths of current flow during operation. (1) External path: excess electrons in N-type side migrate through external circuit (such as SourceMeter) to P-type side --- It forms the first term of Eq1 (V=0); and (2) Internal path: excess electrons in N-type side diffuse into P-type side when an external voltage is applied --- this is the second term of Eq1. As sourcing voltage increases, more and more electrons diffuse across the PN junction due to the lowering barrier. As such, less and less current flows into the SourceMeter as is shown in the I-V curve.

[ptc-1368288]

http://collab.mathsoft.com/~Mathcad2000/read?126002,16

You seem to have fixed your model on EQ1, solved by Lambert W0 (the principal branch). The question is about your Mathcad version if it does accept the initialisation for that branch wrt the range of the W argument as I have demonstrated. If it does work in your mathcad version, you can then generalise your project, end it there. If your version does not accept Lambert W, you won't be able to fit other similar data sets and the question is, for you you to reply :

1. Does this work sheet works for you ?
If YES = project done
If NO = is it because your version does not initialise Lambert ?
If so, the matter would resolve by a short series approximating W(x) in the project range. But you have to reply by an image showing where it turns red c/w the error message of your version.

If this work sheet work fine in your Mathcad version, then you might have more questions that you can add at the end of the sheet. This point here governs and resumes all your visits in this collab as you have indicated testing solar cells from different supply and maybe of different technology, at this point here: if you don't get a fit from your model, it would indicate either out of spec product or wrong model. If such would be the case, the matter then will spread into supplementary statistical analysis.

jmG

[g1lai]

On 7/16/2009 9:09:05 AM, jmG wrote:
>http://collab.mathsoft.com/~Ma
>thcad2000/read?126002,16
>
>You seem to have fixed your
>model on EQ1, solved by
>Lambert W0 (the principal
>branch). The question is about
>your Mathcad version if it
>does accept the initialisation
>for that branch wrt the range
>of the W argument as I have
>demonstrated. If it does work
>in your mathcad version, you
>can then generalise your
>project, end it there. If your
>version does not accept
>Lambert W, you won't be able
>to fit other similar data sets
>and the question is, for you
>you to reply :
>
>1. Does this work sheet works
>for you ?
>If YES = project done
>If NO = is it because your
>version does not initialise
>Lambert ?
>If so, the matter would
>resolve by a short series
>approximating W(x) in the
>project range. But you have to
>reply by an image showing
>where it turns red c/w the
>error message of your version.
>
>If this work sheet work fine
>in your Mathcad version, then
>you might have more questions
>that you can add at the end of
>the sheet. This point here
>governs and resumes all your
>visits in this collab as you
>have indicated testing solar
>cells from different supply
>and maybe of different
>technology, at this point
>here: if you don't get a fit
>from your model, it would
>indicate either out of spec
>product or wrong model. If
>such would be the case, the
>matter then will spread into
>supplementary statistical
>analysis.
>
>jmG
>

Thanks for your worksheet. It is very good.

(1) I do see the something turns red in MC14. My friend has MC13 and will try on his PC later. The image is attached and the message is "no solution was found"

(2) The rest of the worksheet looks good in my PC. It seems the expression of f(V,Iph,I0,Rs,Rsh,n) is copied from the MC11 solution instead of generated by my MC14.

(3) A major concern is that the sign of Rsh and Rs should be positive. However, 1-diode model fitting always end up with -Rs for my worksheet.

(4) 2-diode model fitting ends up with positive Rs. However, it will take ~10min for 1 worksheet.

BTW, I am not quite clear why repeating "@ this point, you can isolate the project and do more works" twice, and re-define W(a) function in your worksheet.

1lai

[ptc-1368288]

On 7/16/2009 10:22:37 AM, g1lai wrote:
>On 7/16/2009 9:09:05 AM, jmG wrote:
>>http://collab.mathsoft.com/~Ma
>>thcad2000/read?126002,16
>>....................................
>Thanks for your worksheet. It is very
>good.
>
>(1) I do see the something turns red in
>MC14. My friend has MC13 and will try on
>his PC later. The image is attached and
>the message is "no solution was found"
>
>(2) The rest of the worksheet looks good
>in my PC. It seems the expression of
>f(V,Iph,I0,Rs,Rsh,n) is copied from the
>MC11 solution instead of generated by my
>MC14.
>
>(3) A major concern is that the sign of
>Rsh and Rs should be positive. However,
>1-diode model fitting always end up with
>-Rs for my worksheet.
>
>(4) 2-diode model fitting ends up with
>positive Rs. However, it will take
>~10min for 1 worksheet.
>
>BTW, I am not quite clear why repeating
>"@ this point, you can isolate the
>project and do more works" twice, and
>re-define W(a) function in your
>worksheet.
>
>1lai
________________________________

The red part of your work sheet is red for two reasons... double red !!!
It is red but functional in 11, as it is copied and then explicited in terms of the arguments. It is red in your version because your version is symbolic MuPad and does not solves at all, as Tom explained. But if the remaining of the sheet works and if you see all graphs then you are OK.

There are many ways to exploit the Mathcad/Maple symbolic engine in 11 and lower versions. Here is attached some details that might help. The best or preferred use of the symbolic depends upon the project. In your project the matter is to get an explicit solution as a function, in this case the Lambert W.

jmG

[g1lai]

On 7/12/2009 3:50:54 PM, Tom_Gutman wrote:
>You can try applying the
>paper's methodology. I
>haven't worked it through. It
>seems to do a fair bit of
>eyeball estimates based on the
>plots.
>
>But I'm still not happy with
>the sign conventions. The
>paper treats the current from
>the cell as positive, you
>consider it negative. Does
>your cell have different
>polarity from theirs, or are
>you just using a different
>sign convention?
>
>If I change the sign of the
>current to match the form
>shown in the paper, I can get
>a very good fit, with a finite
>Rsh. But ... it insists on a
>negative Rs. I can force Rs
>positive, but then it comes
>out essentially zero, and the
>fit is decidedly poorer both
>in terms of the size of the
>error and the structure of the
>residuals.
>
>It would be interesting if you
>could get the raw data for the
>examples in the paper, and
>then compare results.
>__________________
>� � � � Tom Gutman


OK, since V+abs(I*Rs) should be always greater than V, it seems that the Lambert W function generates a solution with V-abs(I*Rs).

[ptc-1368288]

On 7/12/2009 11:51:52 AM, g1lai wrote:
...
>Yes, the program is great. I
>assume that Rsh can be derived
>independently (as suggested in
>the paper) and can also get
>reasonable fitting.
_______________________________

It's always (or almost always) possible to solve in Mathcad, so that you get either an analytical expansion or in many case the solution as function. You were asking for solving I (current), I did both: yours (Wiki) & Jim.
Put your demand on work sheet and by same token start a work sheet with the diagram so that the readers get interested, thus assuring continuity in collaboration and project value.

jmG

[ptc-1368288]

... that's what I meant: generalise so that the project turns technical as applied and academic. Make your case and if it fails pass in the collab.

jmG

[g1lai]

>It's always (or almost always) possible
>to solve in Mathcad, so that you get
>either an analytical expansion or in
>many case the solution as function. You
>were asking for solving I (current), I
>did both: yours (Wiki) & Jim.

OK, it seems to be MathCAD14's problem. I was no able to see your solutions.

[g1lai]

On 7/12/2009 5:20:01 AM, Tom_Gutman wrote:
>As it turns out the equation
>in the paper is solvable in
>terms of the Lambert W
>function.

It is hard for me to understand all terms in Lambert W function. But your solution does not seem to be exactly the same as jmG's (I can read both work sheets in MC13). Did you make any assumption?

[TomGutman]

WYSIWYG. The keywords and modifiers are there in the expression. You can see them. No assumptions, but some collects to simplify the result. As to understanding the terms, I have not made any attempt to do so. Mathcad came up with a solution, I tweaked the form a bit with keywords to reduce the size of the expression, and that's it. I trust Mathcad to have gotten it right and that the resulting function is equivalent to the original function.

MuPad is a much weaker symbolic system and so MC14 is unable to solve this equation. I did this sheet in MC11, my preferred version when I just want to get something done.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 7/13/2009 12:59:55 AM, g1lai wrote:
>On 7/12/2009 5:20:01 AM, Tom_Gutman
>wrote:
>>As it turns out the equation
>>in the paper is solvable in
>>terms of the Lambert W
>>function.
>
>It is hard for me to understand all
>terms in Lambert W function. But your
>solution does not seem to be exactly the
>same as jmG's (I can read both work
>sheets in MC13). Did you make any
>assumption?
____________________________________

At least 3 collabs read your project, and collaborate. You, you don't as far as the project description and the diagram mostly. Your project is interesting wrt the Mathcad elegant solution and its generalisation, and mostly wrt the "collaboration mining" for similar or even same again project. You don't retur the part that fails in your version, who can do what about it. I'm about sure that Tom's version takes into account the mutual conviviality between my 11 and your 13 Mathcad version. If your are talking about RHS function solution, there are items to be defined, as per the experimental diagram and the applicable physical constants. So, just complete the necessary introduction of the measured and the given data.

At tread 55, your project is still floating.
1. You wanted to solve for I (current), you have but does not work.
2. You wanted to solve for RHS, you have but does not work.
3. What else do you want to solve that won't work ?
4. How can collab solve w/o the necessary "ins".
5. Who cares if your diagram is the same as a paper in reference ? Just confirm in the work sheet by same diagram. If you think the equation(s) from the paper are correct, then reproduce and simply source so that the work sheet stands by itself. Lot many papers vanish in the blue. A Mathcad work sheet shouldn't be a paper of paper. Up to this point, that's what it is. If Lambert does not work in 13, that is dramatic but you can still invoke the W(x) Lambert from the explicit Tom's function.

In simple words, I neither follow what you are talking about, neither what you are looking for. Hours can't sum up indefinitely only from the collaborator's side.

jmG

[g1lai]

On 7/13/2009 2:26:32 AM, jmG wrote:
>At least 3 collabs read your project,
>and collaborate. You, you don't as far
>as the project description and the
>diagram mostly. Your project is
>interesting wrt the Mathcad elegant
>solution and its generalisation, and
>mostly wrt the "collaboration mining"
>for similar or even same again project.
>You don't retur the part that fails in
>your version, who can do what about it.
>I'm about sure that Tom's version takes
>into account the mutual conviviality
>between my 11 and your 13 Mathcad
>version. If your are talking about RHS
>function solution, there are items to be
>defined, as per the experimental diagram
>and the applicable physical constants.
>So, just complete the necessary
>introduction of the measured and the
>given data.
>
>At tread 55, your project is still
>floating.
>1. You wanted to solve for I (current),
>you have but does not work.
>2. You wanted to solve for RHS, you have
>but does not work.
>3. What else do you want to solve that
>won't work ?
>4. How can collab solve w/o the
>necessary "ins".
>5. Who cares if your diagram is the same
>as a paper in reference ? Just confirm
>in the work sheet by same diagram. If
>you think the equation(s) from the paper
>are correct, then reproduce and simply
>source so that the work sheet stands by
>itself. Lot many papers vanish in the
>blue. A Mathcad work sheet shouldn't be
>a paper of paper. Up to this point,
>that's what it is. If Lambert does not
>work in 13, that is dramatic but you can
>still invoke the W(x) Lambert from the
>explicit Tom's function.
>
>In simple words, I neither follow what
>you are talking about, neither what you
>are looking for. Hours can't sum up
>indefinitely only from the
>collaborator's side.
>
>jmG

What I am looking for: derive Rs, Rsh and n from I-V characteristic (See the description of problem in my worksheet).

There could be different types of answers: either quick answer (for high-school students) or a few weeks/months' answer (for engineers), depending on how much we understand the physics and math. I think I know much better what and how much Math can do for this special case. In summary,

(1) I cannot use the approach to throw many experimental data;
(2) Jim's solution is nice for math rather than physics;
(3) The Lambert solution is amazing. However, it may still need to be tweaked to generate reasonable results.

I understand I am asking more and more professional question which seems to be crazy. So this thread can be closed at any time.

[ptc-1368288]

On 7/13/2009 9:45:50 AM, g1lai wrote:
.......
>What I am looking for: derive Rs, Rsh
>and n from I-V characteristic (See the
>description of problem in my worksheet).

==> That's new ! and if you expect collab completing or doing the project entirely ... fine but you didn't make it clear this way.

>There could be different types of
>answers: either quick answer (for
>high-school students) or a few
>weeks/months' answer (for engineers),
>depending on how much we understand the
>physics and math. I think I know much
>better what and how much Math can do for
>this special case. In summary,

==> There will be NO long or short answer or college type answer or Engineer answer ... only Mathcad answer.


>(1) I cannot use the approach to throw
>many experimental data;

==> If you can't collect all what the physical model needs, then the project ends there. You have to have more experimental parameters and constants than just the I-V data .

>(2) Jim's solution is nice for math
>rather than physics;

==> Jim's model solution started making sense to your original work sheet.

>(3) The Lambert solution is amazing.
>However, it may still need to be tweaked
>to generate reasonable results.

==> What ! tweak Lambert ... Lambert solves exactly the physical model. For your specific data set, the solution is via the seeded root InverseFunction.

>I understand I am asking more and more
>professional question which seems to be
>crazy. So this thread can be closed at
>any time.

==> Up to you if you want to close the thread. But at this stage it would rather look weird. All what you are asking comes out the "Mathcad tool box" . It's just that you don't understand what you have to do to complete the project in terms of experimental supplementary informations.

jmG