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Question: Why use Kelvin connections for Sense resistor?
We use Kelvin connections at the Sense resistor to minimize any additional resistance added by copper connections power to sense resistor and sense resistor to the LED load. At low current, the error is minimal due to additional voltage added to the voltage across the Sense resistor. As current increases, the voltage drop increases across that small piece of copper inside the Kelvin current sense connections. The increase in voltage will cause current measurement errors.
For example, the current sense resistor is 0.100-ohms; this is 0.1V measured for 1A current flow through the sense resistor. Now add an incorrectly used Kelvin connection where the additional copper inside the Kelvin sense connections adds additional 0.020-ohms in the current measurement section. This is now 1A through 0.120-ohms for a voltage measurement of 0.120V. An error of 20 percent when all design calculations expect 0.100V measured across the current sense resistance.