For this way of calibration there must be a linear response of measuring tool on change of meassured variable and two samples with known value of measured variable (eg. ion concentration).
Thats all we need. Because linear characteristic is a line in two dimensional space (plane). And the line in 2-D space can be described definitely by two points (calibration samples). And position of point in 2-D is defined by two coordinates. The first coordinate is a response of measuring tool and the second one is value of measured variable.
Measuring tool need to know the equation of this line for correct meassuring. It is:
In this case y is the value of measured variable and x is meassuring tool response a and b are constants which we need to assign.
We have got this two equations for two unknown:
Now it's up to our decision, how do we solve the equation.
We want to calibrate our EC metr. At first we need two samples with known conductivity (eg. EC(1)=2, EC(2)=6)
From equations 1 and 2 we express a by subtracting them
y1,y2 are concentrations of our samples(2,6)
Now we need to know the response of meassurig tool to our samples. We get 65 for EC=2 and 256 for EC=6
We substitute into our equations:
and we get a, which is slope of the line. Sustituting a into one of equations we get exact position of the line.
So the equation for our meassuring tool is:
EC=0,0209*meassuring tool response+0,6496