Capacitor Effective Frequency

Every capacitor has a narrow frequency band where it is most effective as a decoupling capacitor. This band is centered at the capacitor’s self-resonant frequency F_RSELF. The effective frequency bands of some capacitors are wider than others. A capacitor’s ESR determines the capacitor’s quality (Q) factor, and the Q factor can determine the width of the effective frequency band:

•Tantalum capacitors generally have a very wide effective band.

•Ceramic chip capacitors with a lower ESR, generally have a very narrow effective frequency band.

An ideal capacitor only has a capacitive characteristic, whereas real non-ideal capacitors also have a parasitic inductance (ESL) and a parasitic resistance (ESR). These parasitics work in series to form an RLC circuit (This Figure). The RLC circuit’s resonant frequency is the capacitor’s self-resonant frequency.

To determine the RLC circuit’s resonant frequency, use Equation 11-1:

Equation 11-1      

Another method of determining the self-resonant frequency is to find the minimum point in the impedance curve of the equivalent RLC circuit. The impedance curve can be computed or generated in SPICE using a frequency sweep. See the Simulation Methods section for other ways to compute an impedance curve.

It is important to distinguish between the capacitor's self-resonant frequency and the mounted capacitor’s effective resonant frequency when the capacitor is part of the system, F_RIS . This corresponds to the resonant frequency of the capacitor with its parasitic inductance, plus the inductance of the vias, planes, and connecting traces between the capacitor and the FPGA.

The capacitor’s self-resonant frequency, F_RSELF , (capacitor data sheet value) is much higher than its effective mounted resonant frequency in the system, F_RIS . Because the mounted capacitor's performance is most important, the mounted resonant frequency is used when evaluating a capacitor as part of the greater PDS.

Mounted parasitic inductance is a combination of the capacitor's own parasitic inductance and the inductance of: PCB lands, connecting traces, vias, and power planes. Vias traverse a full PCB stackup to the device when capacitors are mounted on the PCB backside. For a board with a finished thickness of 1.524 mm (60 mils), these vias contribute approximately 300 pH to 1,500 pH, (the capacitor’s mounting parasitic inductance, L_MOUNT) depending on the spacing between vias. Wider-spaced vias and vias in thicker boards have higher inductance.

To determine the capacitor’s total parasitic inductance in the system, L_IS , the capacitor's parasitic inductance, L_SELF, is added to the mounting’s parasitic inductance, L_MOUNT :

Equation 11-2      L_IS = L_SELF + L_MOUNT

For example, using X7R Ceramic Chip capacitor in 0402 body size:

C = 0.01 mF (selected by user)

L_SELF = 0.9 nH (capacitor data sheet parameter)

F_RSELF = 53 MHz (capacitor data sheet parameter)

L_MOUNT = 0.8 nH (based on PCB mounting geometry)

To determine the effective in-system parasitic inductance (L_IS), add the via parasitics:

Equation 11-3      L_IS = L_SELF + L_MOUNT = 0.9 nH + 0.8 nH
L_IS = 1.7 nH

The values from the example are used to determine the mounted capacitor resonant frequency (F_RIS). Using Equation 11-4:

Equation 11-4      

 

Equation 11-5      

 

F_RSELF  is 53 MHz, but F_RIS is lower at 38 MHz. The addition of mounting inductances shifts the effective-frequency band down.

A decoupling capacitor is most effective at the narrow-frequency band around its resonant frequency, and thus, the resonant frequency must be reviewed when choosing a capacitor collection to build up a decoupling network. This being said, capacitors can be effective at frequencies considerably higher and lower than their resonant frequency. Recall that capacitors of differing values in the same package share the same inductance curve. As shown in This Figure, for any given frequency along the inductive portion of the curve, the capacitors are equally effective.