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| − | == Electrical model ==
| + | :Equations: |
| − | [[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 -->
| + | ::Total resistance = 1/(1/4000+1/2000+1/1000+1/560)+75 |
| − | | + | ::Common current through resistor ladder plus vga impedance (75 ohm) = 3.3V / 357.8282.. |
| − | == Equations ==
| + | ::Current * vga impedance = 0.6917V (specification says 0.7 p-p) |
| − | :Defining constants:
| + | ::Output voltage = 75 * (3.3/(1/(1/4000+1/2000+1/1000+1/560)+75)) = 0.6917V |
| − | ::U_vga = 0.7 V
| + | :Simplification: |
| − | ::R_vga = 75 Ω
| + | :U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V |
| − | ::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: | + | :U_vga = 0.7 Volt |
| − | ::U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V | + | :R_vga = 75 ohm |
| | + | :U_vcc = 3.3 Volt |
| | + | : |
| | + | :Base constant = (1/8+1/4+1/2+1/1)/(1/((R_vga*U_vcc)/U_vga-R_vga)) = 522.3214 ohm |
| | | | |
| − | :Base resistor value = (1/8+1/4+1/2+1/1)/(1/((R_vga*U_vcc)/U_vga-R_vga)) = 522.3214Ω
| + | :Deviation |
| − |
| + | :: 523/523 = 1.0000 |
| − | :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 |
| | + | : |
| | + | :As can be seen no more than 1% is useful with digikey resistors. |
| | | | |
| − | :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/Resistor wikipedia: Resistor] |
| − | :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://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] |
| − | == 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"
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| − | |-
| |
| − | ! Value !! Order number (digikey.com)
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| − | |-
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| − | | 523 || RR12P523DCT-ND
| |
| − | |-
| |
| − | | 1.05K || RG20P1.05KBCT-ND
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| − | |-
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| − | | 2.1K || RR12P2.1KDCT-ND
| |
| − | |-
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| − | | 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"
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| − | |-
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| − | ! Value !! Amplitude [V]
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| − | |-
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| − | | 0 || 0.000002
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| − | |-
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| − | | 1 || 0.060736
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| − | |-
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| − | | 2 || 0.119277
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| − | |-
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| − | | 3 || 0.175740
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| − | |-
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| − | | 4 || 0.230233
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| − | |-
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| − | | 5 || 0.282857
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| − | |-
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| − | | 6 || 0.333708
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| − | |-
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| − | | 7 || 0.382873
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| − | |-
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| − | | 8 || 0.389764
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| − | |-
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| − | | 9 || 0.437103
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| − | |-
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| − | | 10 || 0.482927
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| − | |-
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| − | | 11 || 0.527307
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| − | |-
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| − | | 12 || 0.570310
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| − | |-
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| − | | 13 || 0.612000
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| − | |-
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| − | | 14 || 0.652436
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| − | |-
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| − | | 15 || 0.691673
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| − | |}
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| − | | |
| − | == Value-vs-Amplitude Modified ==
| |
| − | [[Image:Minimig_v1.0_video_dac_resistor_ladder_simulation_modified.png|thumb| right |250px|Value vs output amplitude modified]]<br>
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| − | The modification with 4220Ω 2100Ω 1050Ω 523Ω resistors, Gives this curve for the desired vs actual amplitude:<br>
| |
| − | {| class="wikitable"
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| − | |-
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| − | ! Value !! Amplitude [V]
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| − | |-
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| − | | 0 || 0.000002
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| − | |-
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| − | | 1 || 0.057625
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| − | |-
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| − | | 2 || 0.113793
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| − | |-
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| − | | 3 || 0.167545
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| − | |-
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| − | | 4 || 0.220000
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| − | |-
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| − | | 5 || 0.270256
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| − | |-
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| − | | 6 || 0.319355
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| − | |-
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| − | | 7 || 0.366446
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| − | |-
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| − | | 8 || 0.413880
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| − | |-
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| − | | 9 || 0.458053
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| − | |-
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| − | | 10 || 0.501297
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| − | |-
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| − | | 11 || 0.542855
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| − | |-
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| − | | 12 || 0.583575
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| − | |-
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| − | | 13 || 0.622742
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| − | |-
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| − | | 14 || 0.661153
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| − | |-
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| − | | 15 || 0.698131
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| − | |}
| |
| − | | |
| − | == Gnuplot ==
| |
| − | Gnuplot command:
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| − | :<pre>gnuplot> plot "dac_sim.txt" using ($1):($2) smooth csplines</pre>
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| − | | |
| − | == 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;
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| − | $map[$n++]=8;
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| − | $map[$n++]=4;
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| − | $map[$n++]=12;
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| − | $map[$n++]=2;
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| − | $map[$n++]=10;
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| − | $map[$n++]=6;
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| − | $map[$n++]=14;
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| − | $map[$n++]=1;
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| − | $map[$n++]=9;
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| − | $map[$n++]=5;
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| − | $map[$n++]=13;
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| − | $map[$n++]=3;
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| − | $map[$n++]=11;
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| − | $map[$n++]=7;
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| − | $map[$n++]=15;
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| − | | |
| − | for($v=0; $v<=15; $v++) {
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| − | $d=$map[$v];
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| − | | |
| − | $d3 = ($d & 8)?1:0;
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| − | $d2 = ($d & 4)?1:0;
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| − | $d1 = ($d & 2)?1:0;
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| − | $d0 = ($d & 1)?1:0;
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| − | | |
| − | if( !($d3==0 && $d2==0 && $d1==0 && $d0==0) ) {
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| − | $r_dac=1/(
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| − | # ${d3}/4000+ ${d2}/2000+ ${d1}/1000+ ${d0}/560
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| − | ${d3}/4220+ ${d2}/2100+ ${d1}/1050+ ${d0}/523
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| − | );
| |
| − | } else { $r_dac=100*1000*1000; }
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| − | | |
| − | $u = (75*3.3)/($r_dac+75);
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| − | | |
| − | printf("%d %f\n",$v,$u);
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| − | }
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| − | | |
| − | #-----------------------------------------------------------------------------
| |
| − | </pre>
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