Because the precise current measurement was known for each current step, it is possible to determine what the INA190 output for each trace should be using a current trace resistance calculator to calculate the theoretically ideal resistance for each trace of given width and length. Temperature data obtained at the 0 A current step was interpreted as the ambient temperature and was factored into this theoretically-ideal resistance value. Traces are assumed to be 1 oz copper thickness. Analyzing the deviation from this expected value can give insight into the feasibility of using copper as a shunt resistor. Figure 2-1 shows the plots of these discrepancies for all measured traces at room temperature (uncontrolled temperature environment) for the three-inch measurement. These plots were almost identical for the one- and two-inch locations and are omitted here. Table 2-1 shows the average error for each trace. These errors excluded the percent error value for 0 A, as this current level was so small that some traces had percent errors near 20000%, due in part to the offset error of the INA190. Board 1 and Board 2 in Table 2-1 refer to different iterations of the same revision, as each revision consisted of three boards, each with the same layout.

The only trace width without significant error was the 1750-mil trace. It should be noted that at low current levels (less than 1 A), the 1750 mil had positive error, but from there to 50-A errors became negative. All other traces had very large errors that were; however, remarkably consistent. Also, discrepancies between measurements made on board 1 and board 2 were noted, as shown with the two instances of the 100 mil bottom tap off data points. Finally, measurements made at the center of the trace were different from those made at the bottom. However, this effect is not predictable. Some were better approximations, but some were worse. The 100-mil trace showed the largest difference, with 6.36% difference in error. The 1750-mil trace was also a better approximation at the center tap off.

To determine the cause of the large error, one of the boards was cut in half and analyzed by a Scanning Electron Microscope (SEM). SEM analysis of the trace cross-section showed that trace thickness was much larger than the assumed 1 oz/ft² copper that was ordered. One of the trace cross-sections is shown in Figure 2-2, and the actual trace thicknesses are displayed in Table 2-2.

As shown in Table 2-2, some traces were almost twice as thick as was expected compared to the ideal 1 oz (34.8 µm). A thicker trace decreases the resistance, explaining why some of the trace percent errors were in the –40% to –50% range.

Contacting the PCB manufacturer revealed the reason that the smaller copper traces were so much thicker than expected. Due to the process of plating copper on the outer layer of a PCB, patterns with less surrounding copper will be thicker in general. Thus, for the 100- and 200-mil traces, since they are relatively isolated from other copper patterns, the thickness is large. The 1750-mil trace, however, is large enough to reduce the impact of this effect and is much closer to what is expected. This is borne out by examining standards released by the Association Connecting Electronics Industries (IPC). IPC standards mandate a minimum copper trace thickness, but they do not specify the maximum. Essentially, this means that any trace used as a current shunt will always be less than the expected resistance, with a more prominent effect occurring for smaller trace widths. The relevant IPC standard is shown in Figure 2-3. (Table reproduced with permission from IPC).

The fact that trace width can vary even on the same board makes it difficult to determine whether or not the square shaped trace affects the trace resistance, although this comparison was reexamined in the second revision as detailed in Section 3.

Using the data from Table 2-2, the estimates of trace resistance were modified to attempt to better match the experimental results. Instead of 1-oz copper, the thickness was set as the entry in Table 2-2. Also, since previous resistance measurements assumed 25°C ambient temperature, the new temperature was set to be whatever temperature the TMP235 read at the 0-A current step. Table 2-3 shows the adjusted results.

After the adjustment process, the traces decreased significantly in error with the exception of the 1750-mil trace which experienced a substantial increase in error. The differences between center and bottom tap off points as noted in Table 2-1 are also much less pronounced and, in the case of the 1750-mil trace, are even reversed.

Because copper traces experience heating as current passes through, the extrapolated resistance of the copper traces were recorded with respect to the current passing through them. Potential for error exists in the fact that, throughout the measurement process, the trace might have continued to heat up as noted in Section 1. The impact of additional trace heating during the temperature equalization process would have most likely resulted in a difference of around 0.5 mΩ at the very maximum, based on observations made in the later tests. Plots of how trace resistance changes with current are shown in Figure 2-4. Temperature data is unavailable for the 8-mil traces.

These plots demonstrate that for low current values, the trace resistance exhibits nonlinear behavior, but after a certain point the resistance changes more or less linearly with current. This is most likely due to the INA190 offset error which has a larger impact when the output is smaller. The point at which a trace begins to behave linearly is dependent on the size of the trace, as the 100-mil trace entered this region around 0.1 A, the 200-mil trace around 0.2 A, and the 1750-mil trace around 2.5 A. This is important information to keep in mind, as it demonstrates that simply running current through the trace affects the resistance. Any application of a copper trace must take into account the fact the time needed for the trace resistance to stabilize in this manner.

Finally, the temperature sensor attached to the board gave indication of how the trace temperature changed as the current increased. A strong upward trend was expected and for the most part obtained. For smaller traces, full contact with the sensor could not be ensured, and the temperature results may be skewed by the surrounding PCB. However, temperature data was not recorded until the trace temperature as recorded by the sensor had ceased increasing, so these values should theoretically represent a stable reading after all change has taken place. Plots of the trace temperature are shown in Figure 2-5.

Maximum current values were chosen to cause approximately 20°C of temperature rise from the ambient. This was not the case for many of the plots in Figure 2-5. Similar trace widths did, however, experience similar temperature rises. It is most likely the case that this lack of expected temperature rise is the result of the manufacturing tolerances discussed previously and otherwise is not significant, as the temperature rise calculations involved several assumptions and also rounding error.