# rhinoman

Member Since: September 3, 2010

Country: United States

• I am doing it with simple math and a beowulf cluster of computers(you can do it with a pc but it will take a long time). The math is as follows:

where “a” is the left most resistor and “h” the farthest on the right. Ground or - is on the left and Vcc or + is on the right. So my previous result would read like this

GND –> 560(a) –> pin1 –> 8200(b) –> pin2 –> 18000© –> pin3(this pin is connected to an analog pin of a micro controller) –> 910(d) –> pin4 –> 9100(e) –> pin5 –> 15000(f) –> pin6 –> 5100(g) –> pin7 –> 51(h) –> Vcc where “–>” is a connection between the two.

button 1: 1024 * ( a + b ) / ( a + b + d + e + f + g + h ) button 2: 1024 * ( a + c ) / ( a + c + d + e + f + g + h ) button 3: 1024 * ( a + b ) / ( a + b + f + g + h )
button 4: 1024 * ( a + b + c ) / ( a + b + c + h ) button 5: 1024 * ( a ) / ( a + h ) button 6: 1024 * ( a + b + c ) / ( a + b + c + d + e + h ) button 7: 1024 * ( a + b + c ) / ( a + b + c + g + h ) button 8: 1024 * ( a ) / ( a + g + h ) button 9: 1024 * ( a + b + c ) / ( a + b + c + d + e + g + h ) button 10: 1024 * ( a + b + c ) / ( a + b + c + e + f + g + h ) button 11: 1024 * ( a ) / ( a + e + f + g + h ) button 12: 1024 * ( a + b + c ) / ( a + b + c + d + f + g + h )

For further study do a google search on “Voltage resistor ladder” or “voltage resistor divider”

• Doing further analysis with a larger number of values has yielded some slightly better results. The best being

560 8200 18000 910 9100 15000 5100 51

This result has a minimum spread of 80!

This test was based on the following 98 resistor values:

1 2 3 3.9 5.1 6.2 8.2 9.1 10 11 12 13 15 16 18 20 22 24 27 30 33 36 39 43 47 51 56 62 68 75 82 91 100 110 120 130 150 160 180 200 220 240 270 300 330 360 390 430 470 510 560 620 680 750 820 910 1000 1100 1200 1300 1500 1600 1800 2000 2200 2400 2700 3000 3200 3300 3600 3900 4300 4700 5100 5600 6200 6600 7500 8200 9100 10000 11000 12000 13000 15000 16000 18000 20000 22000 24000 27000 30000 33000 36000 39000 43000 47000

• After a hundred trillion plus calculations(348 checks ~ 1.7 trillion * 80 calculations per check) I was able to find even better results. The theoretical maximum minimum spread is ~85 digital levels. With using only 34 resistor values ( I could have used many more values say 40 or 50 but I feel that the result would have been similar and took another day or more to calculate I was able to find 2 results with a minimum spread of ~78 digital levels. The resistor values are:

1) 390 3900 9100 510 5100 8200 2700 39

2) 390 3900 9100 560 5100 8200 2700 39

you can multiply these values by 10 or 100 and get the same result. The 34 resistor values I used were as follows:

39 47 51 68 82 100 150 180 220 270 300 390 470 510 560 680 820 1000 1200 1500 1800 2200 2700 3000 3300 3900 4700 5100 5600 6800 8200 9100 10000 12000

• My optimal combination is as follows

GND-220-P1-3300-P2-10000-P3/TAP-220-P4-3000-P5-5100-P6-1800-P7-300-Vs

The minimum difference is ~7.1% which equates to about 73 digital levels at a min.

No public wish lists :(

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