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18 PCB007 MAGAZINE I DECEMBER 2024 and R x (R par ) is included in the potential mea- surement part of the circuit and therefore, can affect the accuracy of the result. To overcome this, a second pair of resistors R′ 1 and R′ 2 form a second pair of arms of the bridge (hence 'double bridge') and are connected to the inner potential terminals of R s and R x (identified as P 2 and P′ 2 in the diagram). e detector D is connected between the junction of R 1 and R 2 and the junction of R′ 1 and R′ 2 . 1 e balance equation of this bridge is given by the equation: (Equation 1) In a practical bridge circuit, the ratio of R′ 1 to R′ 2 is arranged to be the same as the ratio of R 1 to R 2 (and in most designs, R 1 = R′ 1 and R 2 = R′ 2 ). As a result, the last term of the above equation becomes zero and the balance equa- tion becomes: (Equation 2) Becomes (Equation 3) Rearranging to make R x the subject: R x = R 2 • R s R 1 e parasitic resistance R par has been elimi- nated from the balance equation and its pres- ence does not affect the measurement result. is equation is the same as for the function- ally equivalent Wheatstone bridge. In practical use, the magnitude of supply B can be arranged to provide current through R s and R x at or close to the rated operating currents of the smaller-rated resistor. is contributes to smaller errors in measurement. ese types of anomalies will go undetected and ultimately result in a field failure, as it may take some time for the anomaly to deteriorate under heat or stress. The Kelvin Bridge Although 4-Wire Kelvin testing is nothing new, it has not been used significantly in vali- dating printed circuits until more recent times. Four-wire Kelvin or high-resolution resistance testing came about through the innovation of William ompson (1824—1907) also known as Lord Kelvin. He was instrumental in the for- mation of the first and second laws of thermo- dynamics. e absolute temperature scale is expressed in Kelvin units (Kelvin Scale) in his honor due to his work determining the exact temperature in Celsius and Fahrenheit of the value of Absolute Zero. However, more specific to our discussion is his development of the Kelvin bridge for which 4-Wire Kelvin testing is based. e operation of the Kelvin bridge is very similar to the Wheatstone bridge but uses two additional resistors. Resistors R 1 and R 2 are connected to the outside potential terminals of the four-terminal known or standard resis- tor R s and the unknown resistor R x (identified as P 1 and P′ 1 in Figure 1). e resistors R s , R x , R 1 and R 2 are essentially a Wheatstone bridge. In this arrangement, the parasitic resistance of the upper part of R s and the lower part of R x is outside of the potential measuring part of the bridge and therefore are not included in the measurement. However, the link between R s Figure 1: Kelvin bridge.