Difference between revisions of "Minimig Video d/a resistor ladder"
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− | :Equations: | + | == Electrical model == |
− | ::Total resistance = 1/(1/4000+1/2000+1/1000+1/560)+75 | + | [[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 --> |
− | ::Common current through resistor ladder plus vga impedance ( | + | |
− | ::Current * | + | == Equations == |
− | ::Output voltage = 75 * (3.3/(1/(1/4000+1/2000+1/1000+1/560)+75)) = 0. | + | :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 = 0.6917 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: | :Simplification: | ||
− | :U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V | + | ::U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | :Deviation | + | :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 | ::1050/523 = 2.0076 | ||
::2100/523 = 4.0153 | ::2100/523 = 4.0153 | ||
::4220/523 = 8.0688 | ::4220/523 = 8.0688 | ||
− | |||
− | |||
− | :[http://en.wikipedia.org/wiki/Resistor | + | :As can be seen no more than 1% is useful with digikey resistors. Resistor combinations will add tolerances and use valuable pcb space. |
− | :[http://en.wikipedia.org/wiki/Preferred_number#Capacitors_and_resistors | + | :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 |
− | :[http://www.digikey.com/scripts/DkSearch/dksus.dll?Cat=65538;keywords=resistor digikey: | + | |
+ | == Useful links == | ||
+ | :[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] | ||
+ | :[http://en.wikipedia.org/wiki/Resistor#Thick_and_thin_film Wikipedia: Thin vs Thickfilm resistor] | ||
+ | ::In essence Thin = More expensive, but without nasty temperature coefficient. | ||
+ | |||
+ | Digikey ordering:<br> | ||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! 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 == | ||
+ | [[Image:Minimig_v1.0_video_dac_resistor_ladder_simulation_original.png|thumb| right |250px|Value vs output amplitude originaly]]<br> | ||
+ | The original 4000Ω 2000Ω 1000Ω 560Ω resistors, Gives this curve for the desired vs actual amplitude:<br> | ||
+ | Note the dent in the middle of the curve!<br> | ||
+ | <!-- awk '{print "|-\n| "$1" || "$2}' da_org.txt --> | ||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! 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 == | ||
+ | [[Image:Minimig_v1.0_video_dac_resistor_ladder_simulation_modified.png|thumb| right |250px|Value vs output amplitude modified]]<br> | ||
+ | The modification with 4220Ω 2100Ω 1050Ω 523Ω resistors, Gives this curve for the desired vs actual amplitude:<br> | ||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! 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: | ||
+ | :<pre>gnuplot> plot "dac_sim.txt" using ($1):($2) smooth csplines</pre> | ||
+ | |||
+ | == Simulation script == | ||
+ | <br> | ||
+ | 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> |
Latest revision as of 18:50, 28 August 2007
Contents
Electrical model[edit]
Equations[edit]
- 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[edit]
- 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[edit]
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[edit]
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[edit]
Gnuplot command:
gnuplot> plot "dac_sim.txt" using ($1):($2) smooth csplines
Simulation script[edit]
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); } #-----------------------------------------------------------------------------