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November 2014 • The PCB Design Magazine 37 the parasitics of the connecting vias and traces. The model, though it looks complicated, runs very fast in any SPICE tool in AC simulations. Note that since here we are interested in the capacitor's behavior above the series resonance frequency, dielectric losses are not included in the description. For an illustrating case that creates a series resonance frequency at 10MHz, the simulated impedance results are available in a spread- sheet [2] . The spreadsheet contains the AC sweep SPICE results at 200 frequency points, logarith- mically spaced from 1 MHz to 100 MHz, one decade below and above the series resonance. On two 3D charts you can see the current distri- bution inside the dielectric and in the capacitor plates. On both 3D plots the vertical axis shows current in amperes on a logarithmic scale, the VERTICAL RESONANCES IN CERAMIC CAPACITORS continues Figure 3: internal construction of a multi-layer ceramic capacitor. Figure 4: impedance magnitude on the top left chart. The current distribution is shown at 1 Mhz in the capacitor plates (lower left 3D chart) and in the dielectrics (lower right 3D chart). quiet power