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34 The PCB Design Magazine • November 2014 Ceramic capacitors are very popular in pow- er distribution networks (PDN). They are small, cheap and come in a very wide range of avail- able values. Typical ceramic capacitors also have low losses, at least compared to similar-valued electrolytic or tantalum capacitors. Because of their small size, we might think that structural resonances inside the ceramic capacitors do not exist in the frequency range where we usually care for the PDN. The unexpected fact is that the better PDN we try to make, the higher the chances that structural resonances inside ce- ramic capacitors do show up. This column tells you why and how. Figure 1 shows measured data [1] on a small 0508 reverse-geometry 10uF capacitor. There are several interesting aspects of these plots that are explained in the paper found in [1] . Here, we focus only on one strange-looking detail: the double-hump resonance we see on the imped- ance magnitude and impedance real part curves somewhere in the 3 to 10 MHz frequency range. The test setup made sure that as much as possi- ble the measurement result represented only the capacitor: The little fixture used for the measure- ment was separately characterized and showed no resonance in that frequency range. The biggest linear dimension of this ca- pacitor is 80 mils, or 2 mm. The wavelength of 10MHz in free space is 30 meters; this is so much bigger than the linear dimensions of the capaci- tor that any resonance at such low frequency is really surprising, even if we factor in the high dielectric constant of the ceramic material. To understand what happens, we have to create a detailed electrical model of the capacitor, for instance a two-dimensional bedspring matrix, shown in Figure 2. QuIET POWER column by Istvan Novak oraCle Vertical Resonances in Ceramic Capacitors Figure 1: Measured data from [1] .