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NOVEMBER 2018 I DESIGN007 MAGAZINE 63 in the second pass of simulations. Based on the measured dielectric thickness and mea- sured capacitance, the dielectric constant and dielectric loss numbers were also updated. Fig- ure 6 shows the representative cross-section photos, and Table 2 details the nominal and actual simulation parameters. For the open-edge test boards, three different simulators were used: a simple analytical solu- tion based on loss-less cavity models imple- mented in Excel macros [3] , a causal SPICE grid model solved by Berkeley SPICE [1] , and a hybrid solver (Cadence Sigrity PowerSI) [4] . You can see the correlation for the 4-mil lam- inate in open-edge test boards in Figures 7 and 8. The impedance magnitude correlation is quite good. Even the lossless analytical formu- las (black trace labeled "Excel") capture cor- rectly the capacitive downslope, overall induc- tive upslope, as well as the antiresonance peak frequencies. What it cannot capture properly are the loss-related items: magnitudes of the Figure 7: Impedance magnitude correlation of the 4-mil laminate data at the corner (L) and center (R). Table 2: Nominal and actual simulation parameters. Figure 6: Cross-sections of the test board with four different laminate thickness: (L to R) 4, 1, 0.5, and 0.35 mils. Only the upper half of the stackup is shown. The DUT laminate is towards the bottom of the photos.

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