[sdiy] LM13600 Gain Question

[Magnus Danielson]

From: Scott Gravenhorst <music.maker at gte.net>
Subject: [sdiy] LM13600 Gain Question
Date: Fri, 23 Jan 2004 10:24:23 -0700
Message-ID: <200401231824.i0NIONK28361 at linux6.lan>

> I'm looking at the LM13600 data sheet and fig. 4 (stereo
> volume control) has a formula to calculate the gain given
> Iabc as:
> 
> Vout
> ---- = 940 X Iabc
> Vin
> 
> Why 940?

Look at page 6. Equation 5 there is the basic equation:

       q*I
          ABC        
I    = ------ V
 out    2kT    in

where CODATA-86 gives these values:

                       -19 
q = 1.60217733(49) * 10    C

                     -23
k = 1.380658(12) * 10    J/K

and let's assume we are running at about 27 degrees, that is

T = 300 K

Then this formula becomes

                       4 
        1.60217733 * 10
I    = ------------------ * I    * V
 out   2 * 1.380658 * 300    abc    in

giving

I    = 19.3407 * I    * V
 out              abc    in

We also notice that the references figure 2 has the following equations hidden
in it:

        0.5
V   = -------- V
 in   30 + 0.5  1

V    = 30k * I
 out          out

Resulting in 

                               0.5
V    = 30k * 19.3407 * I    * ---- * V
 out                    abc   30.5    1

Tossing these together I get

V    = 9511.82 * I    * V
 out              abc    1

I am off by a decade and maybe I just fluke it... but it seems to fit
together when I redo it.

That at least how I should do it more or less. Maybe they made the misstake,
I don't know. Hopefully you get a large enought hint by seeing the above
calculations. 

> Also, with a maximum Iabc of 2 ma. applied to one OTA, this
> circuit can achieve a maximum gain of only 1.88.  So through
> most of it's Iabc range, it's more of a voltage controlled
> attenuator.  Am I whacked here?

Change the output-resistor!

V    = R    * I
 out    out    out

Cheers,
Magnus - time to go home