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68 DESIGN007 MAGAZINE I NOVEMBER 2018 100 MHz, all traces curve up, which is where you see slight differences because the series resonance frequency varies a little with lami- nate thickness. Remember that the uptick of extracted capacitance is not real—it is just a side-effect of the approaching series resonance, which happens at slightly different frequencies with different laminate thicknesses. The main takeaway from Figure 16 is that the static capacitance of power-ground lami- nates is inversely proportional to the laminate thickness. With thinner laminates, you get more capacitance, which is the reason why thin laminates are sometimes called buried capacitance. However, while the plane capaci- tance itself may be sufficient for bypassing for nanopower circuits, in medium- and high- power circuits, the lower inductance and reso- nance peaks greatly help. To see clearly how the inductance of laminates depends on dielec- tric thickness, I look at the data on shorted- edge test boards next. The measurement setup for the shorted-edge test boards is similar to the open-edge boards, but I must reduce the low-frequency error caused by the cable-braid resistance. This is not an issue when you measure open-edge boards because their impedance at low frequencies is much higher than the cable-braid resistance. With shorted-edge boards, you have to mea- sure in milliohms or less impedance at low fre- quencies—which is practically the resistance of plane loops—and cable braid resistances in the same order of magnitude because it would create too much error. There are different ways of reducing this error. Here, I used common- mode toroids on the measurement cable. Fig- ure 17 shows this setup. For shorted-edge test boards, the simula- tions were done with PowerSI. Figures 18 and 19 demonstrate the correlation for the 4-mil laminate shorted-edge boards. Up to about 1 MHz, the impedance magnitude is flat, because I measured the resistance of shorted planes. Above 1 MHz, the impedance slopes upwards, indicating a combination of increas- ing skin resistance and inductive reactance. The impedance magnitude plots at the center have resonance peaks and valleys at high fre- Figure 17: Setup for measuring shorted-edge boards. Note the grey high-permeability toroids on each of the cables. Figure 18: Impedance magnitude correlation of the 4-mil laminate data at the corner (L) and center (R).