Equivalent circuit model of the capacitor
In the capacitor's equivalent circuit model, the simplest model comprises just a serial connection of the nominal capacitor, an equivalent series resistance and a parasitic series inductance. The ESR determines the lowest impedance reached at the capacitor's series resonance. Above this series resonance the capacitor's impedance will increase with frequency, thus behaving like an inductor. A more sophisticated model would also include the components Cp and Rp, connected in gray in figure 1. Modified equivalent circuits are also found in literature which show Cp and Rp in parallel to the whole serial connection of (desired) capacitor, ESR and parasitic inductance; it is merely a question of transforming the values of the respective inherent components. The parasitic inductance together with Cp leads to a parallel resonance that is frequently neglected, because such parallel resonance of typical SMD ceramic capacitors will only appear at several GHz.
Figure 1. Equivalent Circuit of a Capacitor
Figure 2. Equivalent Circuit of a Resistor
The series resonance of the capacitor is determined by its type (electrolytic, foil, ceramic), mechanical dimensions (axial, radial, SMD, size) and of course its value. The higher the capacitance of a certain capacitor type, the lower the series resonance frequency. Therefore it is advisable not just to place a single capacitor for decoupling purpose, but combine two or several caps to achieve broadband decoupling. For example, it is often recommended to pair a 10nF capacitor for lower frequencies with a 100pF cap for higher frequencies. The following will explore whether this is advisable. A very basic linear RF simulation tool is sufficient for demonstrating this; there are even freeware tools available for this purpose. Many manufacturers of ceramic capacitors supply S-Parameter files for their products and it is advisable to use them. Figure 3 shows the attenuation of the above two capacitors when placed in parallel from a 50Ω track to GND.
Figure 3. Attenuation of