Editing Minimig Video d/a resistor ladder

Model:<br>
[[Image:Minimig_dac_resistor_ladder_model.png|thumb| none |150px|D/A resistor ladder electrical model]]<br><!-- http://en.wikipedia.org/wiki/Wikipedia:Extended_image_syntax -->

Equations:<br>
:Defining constants:
::U_vga = 0.7 V
::R_vga = 75 Ω
::U_vcc = 3.3 V

::Total resistance = 1/(1/4000+1/2000+1/1000+1/560)+75 = 357.8282.. Ω
::Common current through resistor ladder plus vga impedance (75Ω) = 3.3V / 357.8282.. = 0.009222 A
::Current * [[Video Graphics Array|VGA]] impedance = 0.6917V  (specification says 0.7 p-p)
::Output voltage = 75 * (3.3/(1/(1/4000+1/2000+1/1000+1/560)+75)) = 0.6917V

:Simplification:
::U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V

:Base resistor value = (1/8+1/4+1/2+1/1)/(1/((R_vga*U_vcc)/U_vga-R_vga)) = 522.3214Ω

:Deviation summary:
::0523/523 = 1.0000
::1050/523 = 2.0076
::2100/523 = 4.0153
::4220/523 = 8.0688

:As can be seen no more than 1% is useful with digikey resistors. Resistor combinations will add tolerances and use valuable pcb space.
:Maximum output voltage if VGA impedance is 75Ω is: (75*3.3)/(1/(1/4220+1/2100+1/1050+1/523)+75) = 0.6981 V

Useful links:<br>
:[http://en.wikipedia.org/wiki/Resistor Wikipedia: Resistor]
:[http://en.wikipedia.org/wiki/Preferred_number#Capacitors_and_resistors Wikipedia: Preferred number]
:[http://www.digikey.com/scripts/DkSearch/dksus.dll?Cat=65538;keywords=resistor Digikey: Resistors]

[[Image:Minimig_v1.0_video_dac_resistor_ladder_simulation_original.png|thumb| right |250px|Value vs output signal originaly]]<br>
The original 4000Ω 2000Ω 1000Ω 560Ω resistors, Gives this curve for desired vs actual signal:<br>
Note the dent in the middle of the curve!<br>
<pre>
0 0.000002
1 0.060736
2 0.119277
3 0.175740
4 0.230233
5 0.282857
6 0.333708
7 0.382873
8 0.389764
9 0.437103
10 0.482927
11 0.527307
12 0.570310
13 0.612000
14 0.652436
15 0.691673
</pre>

[[Image:Minimig_v1.0_video_dac_resistor_ladder_simulation_modified.png|thumb| right |250px|Value vs output signal modified]]<br>
The modification with 4220Ω 2100Ω 1050Ω 523Ω resistors, Gives this curve for desired vs actual signal:<br>
<pre>
0 0.000002
1 0.057625
2 0.113793
3 0.167545
4 0.220000
5 0.270256
6 0.319355
7 0.366446
8 0.413880
9 0.458053
10 0.501297
11 0.542855
12 0.583575
13 0.622742
14 0.661153
15 0.698131
</pre>

Simulation program (perl):<br>
<pre>
#!/usr/bin/perl
#
# Created:  2007-08-23 05:25.32
# Purpose:  Minimig Video D/A resistor ladder simulation
#-----------------------------------------------------------------------------
$map[$n++]=0;
$map[$n++]=8;
$map[$n++]=4;
$map[$n++]=12;
$map[$n++]=2;
$map[$n++]=10;
$map[$n++]=6;
$map[$n++]=14;
$map[$n++]=1;
$map[$n++]=9;
$map[$n++]=5;
$map[$n++]=13;
$map[$n++]=3;
$map[$n++]=11;
$map[$n++]=7;
$map[$n++]=15;

for($v=0; $v<=15; $v++) {
  $d=$map[$v];

  $d3 = ($d & 8)?1:0;
  $d2 = ($d & 4)?1:0;
  $d1 = ($d & 2)?1:0;
  $d0 = ($d & 1)?1:0;

  if(  !($d3==0 && $d2==0 && $d1==0 && $d0==0)   ) {
    $r_dac=1/( 
#      ${d3}/4000+ ${d2}/2000+ ${d1}/1000+ ${d0}/560
      ${d3}/4220+ ${d2}/2100+ ${d1}/1050+ ${d0}/523
      );
    } else { $r_dac=100*1000*1000; }

  $u = (75*3.3)/($r_dac+75);

  printf("%d %f\n",$v,$u);
  }

#-----------------------------------------------------------------------------
</pre>

Gnuplot command: gnuplot> plot "dac_sim.txt"  using ($1):($2) smooth csplines