What are impedance/
ESR frequency characteristics in capacitors?


Category: Capacitor Room
The basics of capacitors are explained in this technical column.
Today's column describes frequency characteristics of the amount of impedance |Z| and equivalent series resistance (ESR) in capacitors.
  Understanding frequency characteristics of capacitors enables you to determine, for example, the noise suppression capabilities or the voltage fluctuation control capabilities of a power supply line. Frequency characteristics are therefore important parameters that are essential for circuit design. This column describes two types of frequency characteristics: impedance |Z| and ESR.

1.Frequency characteristics of capacitors
  The impedance Z of an ideal capacitor (Fig. 1) is shown by formula (1), where ω is the angular frequency and C is the electrostatic capacitance of the capacitor.

Figure 1. Ideal capacitor

  From formula (1), the amount of impedance |Z| decreases inversely with the frequency, as shown in Figure 2. In an ideal capacitor, there is no loss and the equivalent series resistance (ESR) is zero.

Figure 2. Frequency characteristics of an ideal capacitor

  In actual capacitors (Fig. 3), however, there is some resistance (ESR) from loss due to dielectric substances, electrodes or other components in addition to the capacity component C and some parasitic inductance (ESL) due to electrodes, leads and other components. As a result, the frequency characteristics of |Z| form a V-shaped curve (or U-shaped curve depending on the type of capacitor) as shown in Figure 4, and ESR also shows frequency characteristics for values equivalent to loss.

Figure 3. An actual capacitor

Figure 4. An example of |Z|/ESR frequency characteristics of an actual capacitor

  The reason why |Z| and ESR form curves like those shown in Figure 4 can be explained as follows. 

  Low-frequency region: |Z| in regions with a low frequency decreases inversely with frequency, similar to the ideal capacitor. ESR shows a value equivalent to dielectric loss from delay of polarization in the dielectric substance.
  Near the resonance point: As the frequency rises, ESR resulting from parasitic inductance, electrode resistivity and other factors causes |Z| behavior to stray from that of an ideal capacitor (red broken line) and reach a minimum value. The frequency at which |Z| is the minimum value is called the self-resonant frequency, and at this time, |Z|=ESR. Once the self-resonant frequency is exceeded, the element characteristic changes from capacitor to inductor, and |Z| starts to increase. The region below the self-resonant frequency is called the capacitive region and the region above is called the inductive region.
  ESR is affected by loss caused by the electrode in addition to dielectric loss.
  High-frequency region: In frequency zones even higher than the resonance point, |Z| characteristics are determined by parasitic inductance (L). |Z| in the high-frequency region approaches formula (2) and increases proportionately with frequency.
  As for ESR, electrode skin effects, proximity effects and other effects begin to appear.

  The above was an explanation of frequency characteristics of an actual capacitor. The main point to remember is that, as frequency rises, ESR and ESL cannot be ignored. As there is an increasing number of applications in which capacitors are used at high frequencies, ESR and ESL become an important parameter that shows capacitor performance, in addition to electrostatic capacitance values.