When looking at the frequency characteristics graph for capacitance, the capacitance value suddenly disappears after a certain frequency is reached. Does this mean that there is no more capacitance?
  • Kondensatoren
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  • Keramik-Vielschichtkondensatoren (MLCC)


Fig. 1

Fig. 1

Capacitance values cannot be measured directly. This is why ESR (equivalent series resistance) and Xs (synthetic impedance) are measured and the capacitance values are then calculated with an approximation formula.
Approximation formula

Approximation formula

This approximation formula works until the self-resonant frequency is almost reached, but cannot be used in the frequency region where the self-resonant frequency is reached or exceeded. This is why it looks like the capacitance has suddenly disappeared on the graph. Do not worry as this does not mean that there is no more capacitance.
Figure 2 shows a standard equivalent circuit of a multilayer ceramic capacitor (“MLCC”). And the impedance of the equivalent circuit is shown in Formula 1.
Figure 3 shows an example of C1608JB0J106M frequency and impedance characteristics.
Fig. 2

Fig. 2


Zs: Total impedance
ESR: Equivalent series resistance
ESL: Equivalent series inductance
Xs: Synthetic impedance
Synthetic impedance is inductance components (2πf・ESL) *1 combined with capacitance components (1/(2πf・C)) *2
j: √-1

Fig. 3 |Z|/f characteristics of C1608JB0J106M

Fig. 3 |Z|/f characteristics of C1608JB0J106M

With an ideal capacitor, impedance decreases as frequency rises. However, as shown in Figure 2, in an actual MLCC, in addition to the capacitance component, there is an inductance component and resistance component. Because this inductance component becomes dominant when self-resonant frequency is exceeded, the impedance increases with the frequency, as shown in Figure 3.
The approximation formula of Xs≒-1/(2π*f*C) works when frequency is sufficiently lower than the resonant frequency because the capacitance component (*2) is much greater and the inductance component can be disregarded because it is so small (the region on the left side in Figure 3). The capacitance value is calculated backward from this formula. In other words, C=-1/(2πf*Xs). However, at self-resonant frequencies and above, impedance 2π*f*ESL (*1) from inductance components is dominant with total impedance Zs, the C=-1/(2πf*Xs)formula cannot be used, and capacitance cannot be calculated. This is why there are sudden changes in values and the apparent disappearance of capacitance in frequencies near self-resonant frequencies and above.

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