# An Ideal Diode Equation problem with Temperature

Discussion in 'Homework Help' started by KC8RWR, May 14, 2013.

1. ### KC8RWR Thread Starter New Member

May 14, 2013
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Hello,

I am currently working my way through an old EE textbook by myself. I'm not actually in any class so I don't have a professor or T/A to turn to with questions.

Anyway, I am stuck on a problem where the book gives a diode, temperature, voltage and current. I need to determine what voltage would be required to maintain that same current as the temperature is changed.

The answer I am getting does not match the one in the back of the book. Also, I don't think my answer makes sense because I get a higher voltage required at a higher temperature. My understanding is that most diodes work the other way around.

I attached my work as a pdf because I already had it typed up and when I tried just pasting it I lost all of the subscript and superscript formatting. At least for now it is also reachable at http://unforgettability.net/files/random/prob2.37.html.

Thanks in advance for any help!

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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The diode reverse saturation current isn't constant with temperature. In fact, I understand the diode forward drop is more dependent on the temperature variation in Is than it is upon the temperature dependence of Vt.

Last edited: May 15, 2013
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3. ### KC8RWR Thread Starter New Member

May 14, 2013
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@T_N_K

Thanks! But.. if you look at part 3 under 'What I Have Tried' in either the pdf I attached or page I linked to (they are identical) you will see I already accounted for that.

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
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So I guess it depends then on the fudge factor for Is.

I have a note that suggests

$I_s_{(T_j)}=I_s_{(T_o)}\exp(k(T_j-T_o))$

where k is typically 0.14 for Silicon junction.

Hence the Is fudge factor from 10°C to 40°C would be exp(0.14*30)=66.7 which is way different to your factor of about 8

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5. ### KC8RWR Thread Starter New Member

May 14, 2013
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Hmmm... I can't try it out right now but I will tomorrow. Thanks!

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Curiously, I have just noted a document that asserts (on one page) the temperature dependence of Is as: doubling for every 10°C rise in junction temp. Then in the same document on another page, the assertion is made that Is doubles for every 5°C rise in Tjunc. Go figure that one out.

A more definitive paper might be of interest. See attachment - particularly equation 2-17 which according to the author:

"..can be interpreted to be the average temperature rate at which the diode voltage must change to preserve constant diode current over the temperature range ..."

The "beauty" / convenience of this function is that one is relieved of the mathematical task of calculating the specific value of Is at any condition. It then only remains to find Vt for each condition and make the substitutions. The uncertainty factor is the particular value of parameter P which may have a significant range [2 to 5 for Si devices] depending on the particular diode "construction".

• ###### LS3PNJunctionDiode.pdf
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Last edited: May 15, 2013
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7. ### KC8RWR Thread Starter New Member

May 14, 2013
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Yeah, I've found a lot of different calculations for Is vs temperature by searching Google. Doubling every 10C seems to be the more common one but beyond that, it is the one in my textbook so I would expect to get the textbook's answer by using it even if another formula may or may not be more accurate.

I think part of the reason there seems to be so many answers for the question of how Is changes with temperature is that it is really only a question about an idealy 'typical' diode. Real diodes may not follow any of the formulas exactly. Does that sound right?

Maybe this means I just shouldn't get hung up on this question and should move on. Still though, I would like to think that I can calculate this correctly if I do have the correct Is for a given diode. Even if I don't I would expect that there is some value to using a calculation with an 'ideal' Is, that it would at least give me answers in the correct ballpark.

I wonder if maybe I am doing something wrong in how I solved for V or if maybe I shouldn't be using the ideal diode equation this way and should have used something else to calculate V although I can't think of anything in the chapter that would do it.

8. ### t_n_k AAC Fanatic!

Mar 6, 2009
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It would seem pretty clear that the book answers were not based on the analysis you provided or the author used different fudge factors.

Based on a doubling of Is for every 10°C rise in junction temp your results are quite logical.

I see no reason why your method is invalid - the only issue being the resulting answers are counter intuitive to what one would find in a real diode. Again it comes back to the model one uses and the parameters chosen which enable the model to fit the real world situation.