Difference between revisions of "Minimig Video d/a resistor ladder"

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(defined constants)
(cleanup)
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:Equations:
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Model:<br>
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::Total resistance = 1/(1/4000+1/2000+1/1000+1/560)+75
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[[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 -->
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::Common current through resistor ladder plus vga impedance (75 ohm) = 3.3V / 357.8282..
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::Current * vga impedance = 0.6917V  (specification says 0.7 p-p)
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Equations:<br>
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:Defining constants:
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::U_vga = 0.7 V
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::R_vga = 75 Ω
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::U_vcc = 3.3 V
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::Total resistance = 1/(1/4000+1/2000+1/1000+1/560)+75 = 357.8282.. Ω
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::Common current through resistor ladder plus vga impedance (75Ω) = 3.3V / 357.8282.. = 0.009222 A
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::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
 
::Output voltage = 75 * (3.3/(1/(1/4000+1/2000+1/1000+1/560)+75)) = 0.6917V
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:Simplification:
 
:Simplification:
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:U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V
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::U = (75*3.3)/(1/(1/4000+1/2000+1/1000+1/560)+75) = 0.6917V
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:
 
  
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:U_vga = 0.7 Volt
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:Base resistor value = (1/8+1/4+1/2+1/1)/(1/((R_vga*U_vcc)/U_vga-R_vga)) = 522.3214Ω
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:R_vga = 75 ohm
 
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:U_vcc = 3.3 Volt
 
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:
 
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:Base constant = (1/8+1/4+1/2+1/1)/(1/((R_vga*U_vcc)/U_vga-R_vga)) = 522.3214 ohm
 
  
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:Deviation
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:Deviation summary:
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:: 523/523 = 1.0000
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::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
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:
 
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:As can be seen no more than 1% is useful with digikey resistors.
 
  
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:[http://en.wikipedia.org/wiki/Resistor wikipedia: Resistor]
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:As can be seen no more than 1% is useful with digikey resistors. Resistor combinations will add tolerances and use valuable pcb space.
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:[http://en.wikipedia.org/wiki/Preferred_number#Capacitors_and_resistors wikipedia: Preferred number]
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: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
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:[http://www.digikey.com/scripts/DkSearch/dksus.dll?Cat=65538;keywords=resistor digikey: Resistors]
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 +
Useful links:<br>
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:[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]

Revision as of 18:35, 22 August 2007

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 = 0.6917V (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:

Wikipedia: Resistor
Wikipedia: Preferred number
Digikey: Resistors
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