Relationship between capacitance frequency and parasitic parameters

When the frequency is high, the capacitance is no longer treated as a lumped parameter, and the influence of parasitic parameters cannot be ignored. Parasitic parameters include Rs, equivalent series resistance (ESR) and Ls equivalent series inductance (ESL).

The actual equivalent circuit of the capacitor is shown in Figure 1, where C is the static capacitance and 1Rp is the leakage resistance, also known as the insulation resistance. The larger the value (usually above GΩ level), the smaller the leakage, the more reliable the performance. Since Pp is usually large (above GΩ level), it can be ignored in practical applications. Cda and Rda are dielectric absorption capacitors and dielectric absorption resistors, respectively. Dielectric absorption is an internal charge distribution with hysteresis properties that restores a portion of the charge in a capacitor that is open after rapid discharge.

ESR and ESL have the greatest influence on the high-frequency characteristics of the capacitor, so the series RLC simplified model shown in Figure 1(b) is often used to calculate the resonant frequency and equivalent impedance:

â–² Figure 1 Decoupling Capacitor Model

The frequency domain impedance diagram of the capacitor series RLC model is shown in Figure 2. The capacitor appears capacitive below the resonant frequency; it is inductive above the resonant frequency, and the decoupling effect of the capacitor is gradually weakened. It is also found that the equivalent impedance of the capacitor decreases first and then increases with increasing frequency, and the minimum equivalent impedance is the ESR occurring at the series resonant frequency.

â–² Figure 2 Frequency domain impedance map of capacitor series RLC model

It can be concluded from the resonant frequency formula (4-8) that the magnitude of the capacitance and the change of the ESL value will affect the resonant frequency of the capacitor , as shown in Figure 3. Since the impedance of the capacitor at the resonance point is the lowest, the design should use the capacitor with fR and the actual operating frequency as much as possible. In an environment where the operating frequency varies widely, it is possible to consider both a large capacitor with a small fR and a small capacitor with a large fR.

â–² Figure 3 The effect of capacitance and ESL changes on capacitor frequency characteristics