Circuit for resistance measurements
A voltage divider as shown in the figure bellow is the simplest way to measure resistance.
Applying Kirchhoff’s laws we get
(3)
and
(4)
RLDR and ULDR are the resistance and voltage drop at the LDR. Rref and Uref are the resistance and voltage drop at a reference resistor. U0 is the supply voltage which we choose to be 5V. This gives
(5)
an equation to calculate RLDR from ULDR, which can be measured with the micro controller.
We need to find an equation to choose an optimal resistor Rref . We want a maximum change of ULDR for a certain detection range of RLDR. Therefore equation 5 is solved for ULDR giving
(6)
The change ∆ULDR of ULDR between a maximum value Rmax and a minimum value Rmin of RLDR is
(7)
which has a maximum for
(8)
We expect an Rmax of approximately 2 MΩ and an Rmin of approximately 1 MΩ. By using equation 8 as a guideline we choose Rref to be 1.5 MΩ.
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