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JUNE 2019 I PCB007 MAGAZINE 57 per thickness, the average, minimum, and max- imum resistance values for each test coupon were graphed based on the copper thickness for each aspect ratio (Figure 4). A second-degree polynomial trendline was added to the data and strongly correlated for each of the given aspect ratios (R 2 = 0.996 (15:1), 0.993 (20:1), 0.995 (25:1), and 0.999 (30:1)). Given a known resis- tance Y and solving for X would determine the copper thickness; conv ersely, given a known copper thickness and solving for Y would deter - mine the resistance measurement. These trendlines would accurately predict the four-wire resistance measurements if there were only plated through-holes at these pre- cise aspect ratios to consider. But what if cop- per thickness needed to be determined on a via at an aspect ratio that fell outside of this range or was within the range but not one of the test- ed aspect ratios? Then, it would be necessary to extrapolate from the data to generate the curves to predict at these other aspect ratios. To do this, the second-degree polynomial trendlines that were created for each aspect ra- tio (Table 1) were reviewed and the quadratic Table 1: Resistance trendline equations by aspect ratio. Figure 3: Resistance measurements (0.020" drill and 15:1 aspect ratio). Figure 4: Resistance measurements for 25:1 aspect ratio (average, minimum, and maximum).