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I Would like to come up with the capacitance between an infinite sheet and a finite area rectangle as a function of distance. I looked into my old E&M book, it did not consider edge effects I need to include those.
Here is the situation. I just spent the day working with a capacitive sensor. One plate is a rectangle ~(1X5 cm) the other is a 8" Si Wafer. The sensor measures the distance to the wafer with error less then 100 [itex] \mu m [/itex] . To calibrate this sensor the software collects 5000 data points as the sensor is moved from contact to 8mm away, it is then fit to a 4th order polynomial.
All very good, but through the day I noticed that the software was rounding and numbers, well not really rounding them, my thought was that they must be using single precision variables. I still not understand why or how 2 would be come 1.999999 ?
The kicker came when they used Matlab to come up with the "5th" order polynomial. The coefficient of the 3rd order was on the order of 10-14 the fourth was order 10-18 the fifth seemed to be set at 0.
I do not under stand how software which cannot handle integers can meaningfully compute that polynomial.
Soooo... I want to know what theory says..
Thanks for any help you can provide.
Here is the situation. I just spent the day working with a capacitive sensor. One plate is a rectangle ~(1X5 cm) the other is a 8" Si Wafer. The sensor measures the distance to the wafer with error less then 100 [itex] \mu m [/itex] . To calibrate this sensor the software collects 5000 data points as the sensor is moved from contact to 8mm away, it is then fit to a 4th order polynomial.
All very good, but through the day I noticed that the software was rounding and numbers, well not really rounding them, my thought was that they must be using single precision variables. I still not understand why or how 2 would be come 1.999999 ?
The kicker came when they used Matlab to come up with the "5th" order polynomial. The coefficient of the 3rd order was on the order of 10-14 the fourth was order 10-18 the fifth seemed to be set at 0.
I do not under stand how software which cannot handle integers can meaningfully compute that polynomial.
Soooo... I want to know what theory says..
Thanks for any help you can provide.
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