JSFHDetermining the Value of the Current Limiting Resistor -
A Maple Simulation
L. Van Warren MS CS, AE
WDV
May 3, 2009
<Text-field style="Heading 1" layout="Heading 1"><Font executable="true" size="14">Preamble:</Font></Text-field>Whenever we start a document in Maple, we want the machine in a known state:
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%;Consider the simple case of Ohm's Law, which relates current (i), voltage(v) and resistance(R):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEoT2htc0xhd0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSomY29sb25lcTtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSJpRidGL0YyLUY2Ni1RIj1GJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKLUkmbWZyYWNHRiQ2KC1GIzYjLUYsNiVRInZGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1GIzYjLUYsNiVRIlJGJ0ZaRmZuLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Ziby8lKWJldmVsbGVkR0YxLUY2Ni1RIjtGJ0YyRjkvRjxGZW5GPUY/RkFGQ0ZFL0ZIUSYwLjBlbUYnRkotSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGYnAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2JVEmc29sdmVGJ0ZaRmZuLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JUYuRlpGZm4tRjY2LVEiLEYnRjJGOUZqb0Y9Rj9GQUZDRkVGW3AvRktRLDAuMzMzMzMzM2VtRidGam5GMkZnbw==print(); # input placeholderA current limiting resistor splits R into two parts LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJExFREYnRjJGNUYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9GNlEnbm9ybWFsRic= for the LED resistance and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRKUxpbWl0aW5nRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw== for the limiting resistance.
We will denote the maximum permissible LED current by 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqU29sdXRpb24wRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEmc29sdmVGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUShPaG1zTGF3RidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictSSVtc3ViR0YkNiUtRiw2JVEiUkYnRi9GMi1GIzYjLUYsNiVRJExFREYnRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjktRjY2LVEiO0YnRjlGO0ZnbkZARkJGREZGRkhGaG5GTS1GLDYjUSFGJw==print(); # input placeholderSubstituting the values used in the simulation we compute the equivalent resistance of the LED: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print(); # input placeholderHaving computed equivalent resistance used by the simulation we now solve the equation for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJkxJTUlURidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==.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(); # input placeholderThe nearest resistance in the standard values table at www.elexp.com/t_eia.htm is 100 ohms.
We want to know the current that will result in the LED and that is:
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print(); # input placeholderIn practice a higher resistance would be used to insure a longer life of the LED.
We can derate the part by setting LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJG1heEYnL0YzUSZmYWxzZUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y/to 15 mA. It is critical to keep our units straight, or Ohm's law fails!
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(); # input placeholderWhich is our new resistance that makes the LED dimmer, but gives it longer life.
To use this approach for multiple LED's in series we must modeling their series resistance. In this case Ohm's law becomes: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print(); # input placeholderwhere LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the number of LED's in series and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJExFREYnRjJGNUYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic= is the effective internal resistance of the LED.
If n is unavailable, one can compute the total resistance by measuring the current with a known applied voltage and a convervatively valued (large value) series resistor, so the LED segment or array is not damaged.print(); # input placeholder%;