Minimig Video d/a resistor ladder

Electrical model

D/A resistor ladder electrical model

Equations

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 * VGA impedance = 0.6917 V (specification says max 0.7V p-p)

Output voltage = 75 * (3.3/(1/(1/4000+1/2000+1/1000+1/560)+75)) = 0.6917 V

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

Wikipedia: Resistor

Wikipedia: Preferred number

Digikey: Resistors

Wikipedia: Thin vs Thickfilm resistor

In essence Thin = More expensive, but without nasty temperature coefficient.

Digikey ordering:

Value	Order number (digikey.com)
523	RR12P523DCT-ND
1.05K	RG20P1.05KBCT-ND
2.1K	RR12P2.1KDCT-ND
4.22K	RR12P4.22KBCT-ND

Value-vs-Amplitude Originaly

Value vs output amplitude originaly

The original 4000Ω 2000Ω 1000Ω 560Ω resistors, Gives this curve for the desired vs actual amplitude:
Note the dent in the middle of the curve!

Value	Amplitude [V]
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

Value-vs-Amplitude Modified

Value vs output amplitude modified

The modification with 4220Ω 2100Ω 1050Ω 523Ω resistors, Gives this curve for the desired vs actual amplitude:

Value	Amplitude [V]
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

Gnuplot

Gnuplot command:

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

Simulation script

Simulation program (perl):

#!/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);
  }

#-----------------------------------------------------------------------------