Error calculations of Half Ohm

This is a follow up to my last post.

A test equipment is worth nothing if you don't know if you should trust it. Only way to trust it yourself of convince someone else to trust it is to calculate the error properly. So I will show a simple example of error calculations by calculating my Half Ohm error. The rules of thumb for error calculation are: To calculate error of adding and subtraction take the bigger error. To calculate error of multiplication or division - add errors. So if you have 1% and 10% resistor in series their resistances add up. So their combined error is 10%. To get voltage divider error you have to add errors of resistors and input voltage.

Meanwhile I learnt what are chopper/zero drift amplifiers. Before, most of the error was from op-amp input offset voltage, but zero drift amplifiers have about 1000 times smaller input offset voltage for the same money. From that point of view I changed all resistors to 0.1% ones and recalculated their values.

To calculate error of a circuit we have to first know the formula of the circuit. Simplified formula of my circuit is  (Vin*x/R1)*gain. So I have to calculate the error of each part and add them together. The first place where the voltage enters is voltage reference. The voltage reference is 0.5% precise. Next was the divider resistor, that is also 0.1%. So the total error is 0.5% + 0.1% = 0.6%.

Next error comes from the voltage divider. Output voltage is  Vin / (R1 + R2) * R2 where Vin = 1.24V, R1 is divider resistor and R2 is the resistance we are measuring. But because we presume that the output is linear, we can think that Vout = (Vin / R1) * R2. This is acceptable if the R1 is order of magnitudes higher value than R2. The error is the bigger the bigger is R1 resistance. So worst case scenario is when measuring biggest resistance. But on the other hand, the smaller the R1 the smaller error from op-amp input offset voltage. I calculated with some resistors in spreadsheet and settled with 620Ω resistor. It offers almost minimal combined error of 0.41% and the gain of the op-amp has to be exactly 500, what is easier to achieve than lets say, a gain of  403.225806451613.

Both of the resistors for the op-amp give additional 0.1% error. So the grand total worst case error will be 0.6% + 0.41% + 0.2% = 1.21%. And each Ohm of resistance in test probes will give additional 0.16% of error.