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Quiet Power: Vertical Resonances in Ceramic Capacitors

Ceramic capacitors are very popular in power distribution networks (PDN). They are small, cheap and come in a very wide range of available 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 ceramic capacitors do show up. This column tells you why and how.

Figure 1 shows measured data on a small 0508 reverse-geometry 10 uF capacitor. There are several interesting aspects of these plots that are explained in the paper found in. Here, we focus only on one strange-looking detail: the double-hump resonance we see on the impedance magnitude and impedance real part curves somewhere in the 3 to 10 MHz frequency range. The test setup made sure that as much as possible the measurement result represented only the capacitor: The little fixture used for the measurement was separately characterized and showed no resonance in that frequency range.

The biggest linear dimension of this capacitor 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 capacitor 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.

Ceramic capacitors we use for power distribution bypassing have multiple metal plates interdigitated and embedded in a high dielectric constant ceramic material. As shown in Figure 3, the capacitor plates connect alternating to vertical metalized terminals at the two ends of the capacitor body. High-density ceramic capacitors can have hundreds of these capacitors plates. Between adjacent capacitor plates, which are connected to the opposite terminals, there are thin ceramic layers. Many of these sections are connected in parallel by the vertical terminals, conveniently increasing the total capacitance and reducing the inductance as well as the series resistance of the part. Without cross sectioning we don’t know how many conductive plates a particular capacitor actually has, but to model the resonances we see in the measured data, it is really irrelevant. Read the full column here.Editor's Note: This column originally appeared in the November 2014 issue of The PCB Design Magazine.