Calculating dynamic resistance using voltage and current values (U1, I1; U2, I2; U3, I3)

Yes, I am wondering, after all, in the problem Ud = 10uV is probably given, tiny, because tiny but always, and since there are other data, and the Id current can be calculated from it?

Paweł Es. wrote:

Yes, I am wondering, there is still in the problem Ud = 10uV ...

only that it has the mark Um and it's not clear what the tension is ...
Of course, you can always count (by first determining the value of I. d ).



Quarz

This is probably a fast-changing (at least in terms of the marking) voltage ;)

Quote:

19 Sep 2007 22:18 Re: Dynamic resistance


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Again from the beginning, because I am asking a few people and the results are amazing:
Task - Calculate the dynamic resistance of the diode:
Data:
T = 450K
Is = 10to-8
Ud = 10uV
Wanted:
Rd =?

in the above entry changed "name" to Ud.

Let's wait what the author of the thread will say, because he is probably not entirely sure himself

Hello, you are right, I don't know if Um or Ud is specifically in this task? in my notes I have written yes and yes, my friends have the same, so I have already lost my mind, but to be precise, at the beginning of the task I have Um - although I do not know what it is, now it suits me better for Ud - thanks to Quarz's hints, so let it remain Ud

@Quarz
how from this:

you got:
- what happened to?
and as for the calculation
- I don't understand it anymore?

Shel wrote:

[...]
so let Ud be

@Quarz
how from this:

you got:
- what happened to?

see there: 20 Sep 2007 15:40 Re: Dynamic resistance
Here e it is the basis of natural logarithms; e = 2.71828 ...
That is:
Id = (10 ^ (- 8)) o (2.71828 ^ (0.00001 / 0.03878) -1) = 2.57897955311170E-0012, this I counted on my desktop calculator.
The lower significant figures here differ from the previous calculations that I made with MathCAD, but there the value e it is taken probably with 15 significant places, and also a value UT here it has only four significant places.

Shel wrote:

and as for the calculation
- I don't understand it anymore?

Below is the calculation of the values Rd for the previously calculated current value Id :
Rd = 0.03878 / (10 ^ (- 8) + 2.57913 o 10 ^ (- 12)) = 3.87700007128062E + 0006, fits?

Here, in my calculations with the calculator, the expression: E + 0006 = 10 ^ (+ 0006) = 1,000,000

greetings

@Quarz
I looped again, can you still help me?
So my point is that at the very beginning you wrote that the dynamic resistance of the diode:
Rd = du (i) / di
then after the transformations you wrote Rd = UT / (Is + Id)
and now I have no idea how one relates to the other, I mean it from the mathematical point of view, because I have serious problems with integrals?
@ Paul Es.
Looking through my wise books, I also do not understand where this pattern came from:

I found, but something like this:

Hello,

Shel wrote:

@Quarz

I looped again, can you still help me?
So my point is that at the very beginning you wrote that the dynamic resistance of the diode:
Rd = du (i) / di

then after the transformations you wrote Rd = UT / (Is + Id)

the first relationship is the formula generic to the derivative of a function voltage u (i) , where independent variable is the diode current and and after calculating this derivative (for the function: u (i) = UT o ln (i / Is + 1) ) We get functions Rd (i) .
However, the dependence:
Rd = UT / (Is + Id) it's counted derivative value du (i) / di in point where for the independent variable and substituted Is that is, it has been counted dynamic resistance value for i = Is :
Rd (i = Is) = UT / (Is + Id) that's it.

Shel wrote:

... and now I have no idea how one relates to the other, I mean it from the mathematical point of view, because I have serious problems with integrals?

But that's not my concern anymore, a mathematical apparatus (at an appropriate level) you need to know ...
And they are not integrals , just derivatives of functionsone variable , and this is already in the high school math curriculum ( derivative of one variable function, definition, geometric interpretation, derivative calculation for elementary functions ).
Exponential function f (x) = e ^ x [ e raised to power x ], where e is the basis of natural logarithms, e = 2,71828 ... [ e = 1/0! + 1/1! + 1/2! + 1/3! + ... 1 / n! + ...] belongs to elementary functions.

greetings

I'm sorry for writing it here, but I think it's a pity to start a new topic because I would only like to ask one question

To calculate the dynamic resistance of the diode at e.g. 10mA, the derivative rd = dU / dI should be calculated. According to my lecturer, this derivative is equal to r = kT / q * Ifp. Where k is Boltzmann's constant T - temperature q-charge and Ip our current at point. I also found out that the value of the expression kT \ q is often written as 26 [mV]. Therefore, I wanted to ask whether rd can be calculated as 26 [mV] / 10mA. If you can count this way, then for several different diodes with different parameters, the dynamic resistance at the 10 mA point will be the same?

Not really, because the 26mV is for a specific temperature, and this may change depending on the outside temperature, but also on the self-heating of the junction as a result of the current flow (at higher current values).

It will be different for different diodes, because the characteristics of real junctions differ from the mathematical one and each diode has a slightly different one, even if you take two copies of the same type. Various imperfections of the production process will come out here (e.g. the accuracy of the doping of semiconductors in the layers)

In addition, it must be taken into account that in the diode, apart from the connector itself, there is a series resistance resulting from the properties of the material itself and the leads from the terminals to the connector itself (they can be technically differently solved and usually it is not visible). At low currents, these resistances can be ignored and you can only see the influence of the junction itself, but at higher currents, this resistance will be visible on the characteristic curve.