LM13700 as Voltage controlled resistor wrong values

[nhouza]

Hello. I'm having trouble to figure out why my calculations don't match the measurements when I hook up a LM13700 as Voltage controlled resistor.
Similar issue for both configurations: single ended or floating.

as for [url=https://www.ti.com/lit/ds/symlink/lm13700.pdf]https://www.ti.com/lit/ds/symlink/lm13700.pdf] [url]https://www.ti.com/lit/ds/symlink/lm13700.pdf]https://www.ti.com/lit/ds/symlink/lm13700.pdf]https://www.ti.com/lit/ds/symlink/lm13700.pdf] [url]https://www.ti.com/lit/ds/symlink/lm13700.pdf[/url]LM13700 Datasheet (fig.28, Floating Voltage-Controlled Resistor)


THEORY:
the formula given is Rx= (2 * R)(gm * RA) , where gm is 19.2 * Ibias
In my calculations,
Ibias is max 0.42 mA
Ra is 1K
R is 100K
The Rx resulting should be 24.8 K and for descreasing Ibias, Rx goes up.

PRACTICE: By following the circuit ,
i feed max 0.42 mA at Pin 1 and 16 of the LM13700 and i set up a simple voltage divider to test it in practice as follows.


Vin is 5.19 V, R1 is replaced with the LM13700 and r2 is 100k.

Following the theoric calculations, i should expect Vout =4.16.

But what i can measure in practice is 3.36V though.

Do you have any suspects if I'm doing something wrong or hints to give?

I take for granted that Ibias of 0.42 mA that i split between pin 1 and 16 of the OTA, has to be used as it is in the Formula ( and so i don't have to use 0.42mA/2)

Thanks a lot for any advice or help.

[moffy]

The spice model for the LM13700 can be downloaded from: https://www.ti.com/product/LM13700#design-development if you import it in LTSpice it will give you a cross check on your calculations and measurements.

[nhouza]

Thanks for the hint.

Then I have done a simulation for the first time with LTspice. So, please excuse me if I mistake something.

This should be easier to understand than my monologue above.

I attach the files for this simulation if you are interested (i guess they are enough to run it).

It looks to me is that my practical measurments match the LTspice simulation since i get 3.2V at the output (almost 3.34 that i measured).



So, I'm wondering what I'm doing wrong in my theorical calculations.

I'm missing a very stupid point somewhere but I can't figure it out.

[moffy]

Nice job on your simulation.
For the resistance calculation: Rx = 2*R/(gm*Ra) with R=100k, Ra=1k and gm = 19.2Iabc or gm= 19.2*210u
so Rx = 200/0.004032 = 49.6k which is consistent with the results you are getting. You are getting roughly 2/3 of the 5.19v across the 100k resistor when Iabc = 210u or 420u/2.

[nhouza]

That's it!  TI datasheet's formula means Iabc to be halved prior to stick that into the formula.
I thought about that at the beginning but i thought that would have been stated on the datasheet. That particular one looks quite tricky to me.

from the very most precise calculations i can do, from the simulation I still measure 3.491V instead of 3.469V expected from the theoric calculations. This is of course a ''good enough'' but is quite irritating since should be pure math and both Ltpisce and formulas exclude components tolerance.

I also discovered that the  first spice model that i used (found here https://github.com/deanm1278/LM13700-spice-model ) is not quite well performing.
The original TI is the most accurate (and it makes sense).
Both simulations attached.

thanks a lot @moffy

[moffy]

Glad to be of help.