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34 The PCB Design Magazine • February 2015 The density of multilayer ceramic capacitors (MLCC) has increased tremendously over the years. While 15 years ago a state-of-the-art X5R 10V 0402 (EIA) size capacitor might have had a maximum capacitance of 0.1 uF, today the same size capacitor may be available with 10 uF capacitance. This huge increase in density un- fortunately comes with a very ugly downside: the capacitance is now very sensitive to DC and AC bias across the part. MLCCs are manufactured with different types of ceramics. With a given case size, dielec- tric thickness and plate count, the capacitance is proportional to the dielectric constant of the ceramic: the higher the dielectric constant, the more capacitance we get from the same struc- ture. For low-loss, high-performance RF and mi- crowave applications Class 1 materials are used [1] . These provide very good and stable electrical characteristics, practically zero bias and temper- ature dependence, but their relative dielectric constant is below 100 and hence capacitance density is low. In a 0402-size package we may get 1000 pF with 50V rating. If we need more capacitance in a small package, we have to se- lect Class 2 (or Class 3) ceramics [2] , which are ferroelectric materials with a dielectric constant in the 200 to 14000 range. A typical two-terminal MLCC internal ge- ometry is shown in Figure 1. The two vertical metal terminals connect every other horizontal plate, creating a number of parallel-connected parallel-plate capacitor segments. The stack of capacitor plates fills the H total capacitor body height with an effective height of H e . The non- connected capacitor plates should not come out to the sidewall of the capacitor body, they are pulled back to create a small G gap. If, for now, we ignore these gaps and consider H=H e and G=0, each pair of adjacent capacitor plates creates a C u unit capacitance: where e 0 is the dielectric constant of vacu- um, or 8.85 pF/m, and e r is the relative dielec- tric constant of the ceramic material. In the ca- pacitor body altogether we have N plate pairs, where N (if we ignore the end effects) can be approximated with The total capacitance from the N pairs of capacitor plates gives us the following formula: In the above expression the LWH product is the volume of the capacitor body. For regular ceramic capacitors the H height typically does not exceed the W width; for a given case size feature coulmn by Istvan novak OrACle qUIET POWER Effects of DC Bias on Ceramic Capacitors Figure 1: Approximate internal geometry of MlCC.