We have a liquid conductivity sensor/meter that can be configured to output its sensor value encoded onto a 4-20 mA current loop. The meter has options of outputting the 4-20mA loop as a linear scale or a logarithmic scale. We need the logarithmic scale so we can get finer resolution at the low end, but still have a wide full range.
When configuring the meter for logarithmic mode, it asked for the following inputs, and I show what we input:
Sensor Min : 0.02 uS/cm
Sensor Max : 2.00 mS/cm
Number of Decades: 4 (wasn't quite sure what to put here)
My question is: based off of these settings, what is the forumula to convert mA back into siemens/cm? I contacted the manufacturer for help, but none of their tech support seemed to have a concrete formula. One of their engineers was able to replicate our meter settings and "simulate" some readings, just to see what the current would measure. This was his table:
1) 4 mA = 0.02 µS/cm
2) 6 mA = 0.625 µS/cm
3) 8 mA = 2.00 µS/cm
4) 10 mA = 6.5 µS/cm
5) 12 mA = 20 µS/cm
6) 14 mA = 66 µS/cm
7) 16 mA = 200 µS/cm
8) 18 mA = 660 µS/cm
9) 20 mA = 2000 µS/cm
Based on these numbers, this is my best guess at a formula:
uS = 10^((mA-const)/4)
const = 20 - 4 *log10(uS_max)
uS_max = 2000
But this doesn't give me exactly the same values. The lower end of the scale is also a little bit wonky, because this equation relies on there being a sensor decade every 4 milliamps, but that breaks down at the lower end.
Can anyone help figure out what the conversion formula is?
The sensor is a Mettler Toledo InPro-7000 VP. The meter (the one in which generates the current loop) is the Mettler Toledo M300 (the older version, with buttons instead of the touchscreen).