Difference between revisions of "Minimig Video d/a resistor ladder"
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:[http://en.wikipedia.org/wiki/Preferred_number#Capacitors_and_resistors Wikipedia: Preferred number] | :[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] | :[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 |
Revision as of 21:54, 22 August 2007
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 = 0.6917V (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:
The original 4000Ω 2000Ω 1000Ω 560Ω resistors, Gives this curve for desired vs actual signal:
Note the dent in the middle of the curve!
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
The modification with 4220Ω 2100Ω 1050Ω 523Ω resistors, Gives this curve for desired vs actual signal:
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
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); } #-----------------------------------------------------------------------------
Gnuplot command: gnuplot> plot "dac_sim.txt" using ($1):($2) smooth csplines