Trace Resistance

Bouler, CO (September 2024) - This experiment compares the 2-wire and 4-wire resistance measurement techniques on Digital Multimeters along with the failure characteristics of 6-mil traces under excessive current. The key takeaways are that the 4-wire technique is significantly more accurate for measuring small resistances than the 2-wire technique, and that even small traces can handle a significant amount of current, but using best practices for trace width keeps the circuit from overheating and failing catastrophically.

To estimate the resistance of the various traces, the relationship between the sheet resistance of 1 oz copper is used with the length and width of the traces. Here, 1 oz copper indicates the weight (W) of the copper when spread over a one square foot area (A); this along with the density of copper (ρ) can be used to calculate the thickness (t) of the copper as shown in Equation 1.

Using the fact that the ratio between best-case bulk resistivity (also ρ) and material thickness will never change, the resistance (R) of a trace can be expressed in terms of the number of squares of the trace width (w) along its length (L) as shown in Equation 2.

Here, Rsq indicates the resistance through a square of the trace that is trace width by trace width in size with n indicating the number of squares that make up the trace in question. For a 6-mil wide trace, Rsq can be calculated as shown in Equation 3.

This value allows the thickness of the trace to be ignored, since it is already incorporated into the value, and to instead treat the traces as a 2-dimensional series of squares, each with 0.5mΩ of resistance. The estimated resistance of each trace seen in Figure 1, along with the experimental data collected for them, are summarized in Table 1.

Data collection was done using both the 4-wire setup depicted in Figure 1, and for the 2-wire technique which is the simpler method that does not involve supplying current through the component. As expected, the 4-wire technique provided result much closer to the estimated values because it can isolate the resistance measurement from the cable and contact resistances present in the 2-wire technique. The disparity between the 4-wire measurements and the estimate can be explained through variations in manufacturing, rounding during estimation, and using best-case material properties. The estimate is slightly conservative but outperforms measuring using the 2-wire technique.

Next, the characteristics of a 6-mil trace under various loads was observed by slowly increasing the current through the trace. As the current increases the expectation is that the resistance will also rise, as measured by the voltage drop over the trace, since there is a thermal component to the resistance of copper. The experiment was completed twice and started with running 1A through the trace to validate the maximum recommended current for this size trace did not qualitatively create any increase in the trace temperature. The first indication that the trace was heating up came at approximately 2.5A when the trace felt warm. At 3A the trace was noticeably hot to the touch. At 4A the trace was showing signs of thermal run away as indicated by the fact that the measured voltage drop with 4A running through the trace continuously increased. Finally, at 4.8A the trace began to smoke. Observing the trace for several seconds, it glowed red as it continued to heat up. In Figure 1, the trace on the right was allowed to run until the trace was broken so it shows more sign of damage than the trace on the left which had current cut shortly after it started smoking.

This experiment shows the benefits of using the 4-wire method for measuring small resistances, the accuracy of the squares technique when estimating trace resistances and validated the recommended maximum current for traces: 1A for 6-mil traces and 3A for 20-mil traces. This simultaneously shows that small traces can handle more current than it seems and the importance of staying within the recommended limits. Additionally, the temperature component of resistance was observed along with an instance of thermal run away which further motivates the need for adhering to best practices.