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

I have a question "How to calculate the dynamic resistance ??" For points: U1 = 3V I1 = 0.21A
U2 = 5V I2 = 0.425A
U3 = 6V I3 = 0.5A

I think so:


Rd = dU / dI??U / ?I

on the first segment = 3V / 0.21A = 14.285?
the other = (5V-3V) / (0.425A-0.21A) = 9.3?
the third = (6V-5V) / (0.5A-0.425A) = 13?

Thank you

but from what it seems to me it is the calculated static resistance, because from what I read, the dynamic resistance is counted from the indications of the AC meters in the appropriate system, where the diode is powered simultaneously with direct and alternating current, and what I see are the results for such measurements are different, it turned out that as the voltage drops, the current increases.

Hello,

lordac wrote:

I think so:

Rd = dU / dI??U / ?I

on the first segment = 3V / 0.21A = 14.285?
the other = (5V-3V) / (0.425A-0.21A) = 9.3?
the third = (6V-5V) / (0.5A-0.425A) = 13?

the method and geometric interpretation of the derivative at the point presented here contradicts the definition of the limit of the difference quotient ...
At the "input" we have numbers; one and two-digit, and on the "output" as many as five digits!
So, buddy lordac how many significant digits in this result: 14.285? are some numbers?
It is not even worth mentioning that it is a static resistance instead of a dynamic one ...
It should not be forgotten that from the definition of the derivative it follows that its value at a point is the quotient of the appropriate sides of a right triangle, but of a triangle built on the tangent to the curve at a given point!
On the other hand, the uncertainty (error of the result) of this quotient is determined by the uncertainty of its components, i.e. the margin of error of the divisor and the divisor, and what is this error in the discussed case?
After all, the author of the topic did not present us a graph of this curve (current-voltage characteristic of a two-way point) for which the derivative (value of dynamic resistance) at a given point is to be calculated.
Aren't the given pairs of numbers (values; voltage and current) the points from this curve (current-voltage characteristic)?
I personally have a lot of doubts here and I am asking the author of the topic to explain them ... :D

greetings

boys, thank you for your willingness to help but the topic is no longer relevant (see date
And it is correct, without a graph, it is impossible to calculate the dynamic resistance - now I know it but i don't even know where i got this chart ;-)

The topic is no longer valid

Hello, I will join the topic because I have a final task to calculate, which I am not sure until the end, but maybe you can help me:

"Calculate the dynamic resistance:
data T = 450 K
Is = 10 to the power of -8

and it was given Um, perhaps 10 uV, but it had nothing to do with the task

because Rd = Ut / Is "

How is it calculated?

can you present the whole content of the task ?? and show a graph if there is any.

There was no graph, and the content is only the above, but I will not cut my head

Or maybe you know what element this dynamic resistance should be?
Diodes ??? Toilet seat thermocouples ??? ???

Heh, of course it is about the dynamic resistance of the didode.

Hello,

Shel wrote:

Heh, of course it is about the dynamic resistance di ( d ) odes.

ooo ... that's something specific.

Shel wrote:

"Calculate the dynamic resistance:
data T = 450 K
Is = 10 to the power of -8

and it was given Um, perhaps 10 uV, but it had nothing to do with the task

because Rd = Ut / Is not true ! [ perm. Quarz ] "

dynamic resistance is derivative of voltage versus current , that is:
Rd = d u (i) / d and on current - voltage characteristics forward biased diode, i.e. in the first quadrant of the rectangular coordinate system at - and but this characteristic is not thermal voltage Ut and saturation current Is .
Look for the abovementioned characteristic described analytically, and then you only need to differentiate it and substitute the current value into this relationship to get the derivative value for a given forward current value AND , i.e. the value of dynamic resistance Rd .

greetings

Found something like this, but still can't figure out the task.


Since the resistance of the blocking region is very high, about 107 times higher than the breakdown and conduction resistance, a two-segment approximation of the diode characteristic is often used, e.g. to determine the conduction power losses.

For this model in the conduction state, one can write:
Uf = Uf (To) + Ifrf
where:
Uf - voltage of the diode switch-on threshold,
rf - dynamic resistance of the diode,

Diode dynamic resistance definition:
In the reverse state, the diode is represented by a linear resistor Rr, and in conduction by a series circuit consisting of a voltage source modeling the voltage of the diode turn-on threshold and a dynamic resistance rf. Thus, for voltages and the conduction state, the voltage is described by the formula for the two-segment model.

Look for the Shockley pattern - it should come in handy

The changes in the intensity of the ideal pn junction as a function of the bias voltage are described by Shockley's formula:

where: Is - junction saturation current,

U - bias voltage,
T - temperature [K], S- joint surface,
Dp, Dn - hole and electron diffusion constants, Ln, Lp - electron and hole diffusion paths
Boltzmann constant k = 8.62 o 10-5 eV / K elementary charge q = 1.6 o 10-19 C

Added after 35 [seconds]:

but I still don't know how to use it in the task?

In the evening (when I return from work) I will do this task for you.

Hello,

Shel wrote:

The changes in the intensity of the ideal pn junction as a function of the bias voltage are described by Shockley's formula:

where: Is - junction saturation current,

U - polarization voltage,
T - temperature [K], S- joint surface,
Dp, Dn - hole and electron diffusion constants, Ln, Lp - electron and hole diffusion paths
Boltzmann constant k = 8.62 o 10-5 eV / K elementary charge q = 1.6 o 10-19 C

Added after 35 [seconds]:

but I still don't know how ( with ) noun live in the task?

the formulas are correct (Shockley's formula), only that you have the forward current relationship given here AND from forward voltage AT , that is I (u) therefore, simply, you should Shockley's formula transform and take advantage of my first hint.
You can also find a derivative the inverse function d AND/ d AT and then transform, but for that function it will be more complicated than finding the inverse first U (I) and only then differentiation U (I) .

greetings

PS Boltzmann's constant k better to use with legal SI units, i.e. k = 1.3806505 o 10 ^ (- 23) J / ° K .

Hello, the topic has stopped, and I still do not know how to properly solve the above-mentioned task, but maybe someone will help me?

Hello,

Shel wrote:

Hello, the topic has stopped, and I still do not know how to properly solve the above-mentioned task, but maybe someone will help me?

can you read with understanding? Do you know calculus and what is a single variable function?
After all, I have already written a hint there: Sep 13, 2007 11:34 am Post subject: Re: Dynamic resistance

What else would you like to calculate this simple derivative?

greetings

You have the formula for the diode current as a function of the voltage on it:


$$Id=Is*(e^{\frac{Ud}{U_T}}-1)$$

From this you find the formula Ud = f (Id) that is


$$Ud=U_T*ln(\frac{Id}{Is}+1)$$

where

$$U_T=\frac{kT}{q}\approx 86\mu V*T$$

T - temperature in degrees Kelvin

from the formula for Ud you calculate the derivative

$$\frac{dU_d}{dI_d}$$

you substitute the values of UT (from the formula for UT that is 42.14mV) and Id and you get the value of Rd

First you need to draw a graph based on the formulas you got from Paweł ES.
Later, you select the point from the graph where you want to test the dynamic resistance
Then you draw some interval near that point on the X axis and corresponding one on the Y axis
On the X axis you count the increment (you subtract the smaller value from the greater value) and you already have dU similarly on the Y axis
And then Rd = dU / dI

Hello,

sesil wrote:

First you need to draw a graph based on the formulas you got from Paweł ES.
Later, you select the point from the graph where you want to test the dynamic resistance
Then you draw some interval near that point on the X axis and corresponding one on the Y axis
On the X axis you count the increment (you subtract the smaller value from the greater value) and you already have dU similarly on the Y axis
And then Rd = dU / dI

this is a very inaccurate description. It is necessary, first of all, to build tr rectangular triangle on tangent to the curve at a given point and from the length of the triangle's legs, calculate the quotient: ?U / ?I = Rd .
This is an approximate calculation derivative value at point based on derivative geometric interpretation .
The dependence of the current AND from voltage ( Shockley's formula ) AT or also inverse function , i.e. the dependence of voltage on current is given in the manner analytical , so there is nothing to prevent this derivative from being counted (exactly) in this way.
Then substitute the value of the current to obtain the value of this dynamic resistance for the given value of the current.

Regards

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 =?

According to @Paul_ Es., We have:

I transform it as follows to extract Ud:

we also have data:


now we count Rd:

but I still lack data, ie what about this Id?

Shel wrote:

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 =?
[...]
now we count Rd:

but I still lack data, ie what about this Id?

only that you computed this derivative wrong (or I don't understand this - simplify it) ... check.
On the other hand, to get the number, i.e. the value of the derivative for a given current value Id , you just have to substitute the forward current of the diode Id , and you already know the other quantities in this derivative.

greetings

otherwise I won't write it down, the fractions are wrongly placed
@Quarz
you can correct me from this integral, because I am not an ace of integration, I only write what my colleagues explained to me ...

Shel wrote:

otherwise I won't write it down, the fractions are wrongly placed
@Quarz
you can correct me from this integral, because I am not an ace of integration, I only write what my colleagues explained to me ...

but to simplify a two-story fraction, you can? You will then see what you will receive ...

greetings

Nothing works for me anymore, I'm already blown away from this science today - shit ...

You're exaggerating ...

Rd = UT / (Is + Id) easy what?

Now you need to know the value Id to find the value of dynamic resistance at a given point, or calculate it as a function Rd (Id) .

greetings

Quarz wrote:

You're exaggerating ...

Rd = UT / (Is + Id) easy what?

Now you need to know the value Id to find the value of dynamic resistance at a given point, or calculate it as a function Rd (Id) .

greetings

Exactly, this simplification did not give me much, because I still have one more unknown Id

Quote:

or count it as a function Rd (Id)

I don't know that either, all the time relying on the data in the task?

Hello,
maybe these charts will "lighten" this issue for you:



Notice that the charts are made of semi-log scale (one of the axes has a linear scale, and the other has a logarithmic scale), and this is due to the spread of size changes and with a linear scale, a significant part of the graph (due to the resolution of the drawing) would not be properly shown.

Don't forget that derivative of a function of a given independent variable is also function (only another one) this variable .
To obtain the value of a function for a given value of the argument (independent variable), then this value of the argument should be known, and if the value of the argument is not known, only the dependence graph prepared on the basis of the analytical record of this function remains.

Of course occurring here physical quantities have their units (which I have not written here in order not to obscure the record), and which are legal and basic units of the binding System of Units SI .

greetings