Equivalent circuit analysis of aluminum electrolytic capacitor

In order to analyze the electrical characteristics of aluminum electrolytic capacitor, especially the relationship between capacitance C, loss tangent tgδ, impedance Z, temperature T, and frequency ƒ, and this relationship has a close and complex dependence on the structure of the aluminum electrolytic capacitor itself, it is necessary to use an equivalent circuit to analyze it.

1 Series and parallel equivalent circuits of capacitor dielectrics

In order to understand the equivalent circuit of aluminum electrolytic capacitor, we must first understand the relationship between the series circuit and parallel circuit of capacitor dielectrics. The dielectric of aluminum electrolytic capacitor is Al₂O₃ film. According to dielectric theory, dielectric polarization will occur under the action of an electric field, which contributes to the dielectric permittivity ε. When it forms a capacitor, there is capacitance C. Similarly, there is loss in the dielectric and it is represented by loss resistance. If the above-mentioned effect of capacitor dielectrics is to be represented, it can be represented by parallel or series equivalent circuits, as shown in Figure 1.

Figure 1 Series-parallel equivalent circuit of capacitor dielectric and current-voltage vector diagram

It should be pointed out that the resistance representing loss has different meanings in the two equivalent circuits, and its numerical values are also completely different. In the parallel equivalent circuit of Figure 1(a), the resistance representing dielectric loss can be regarded as a conductive resistance, and the R value should be very large, while in the series equivalent circuit of Figure 1(b), it is actually represented as a dielectric energy loss resistance, so the r value should be very small. From the current-voltage vector diagram in Figure 1, it can be concluded that:

Parallel circuit:

(1)

Series circuit:

(2)

The relationship between R and C_R in the parallel circuit and r and C_r in the series circuit can be obtained from the complex impedance formula in the electrical principle. Since both circuit forms represent the polarization form of the same medium at the same time, the impedance of the parallel circuit must be equal to the impedance of the series circuit.

The complex impedance Z_Parallelof the parallel circuit is:

The complex impedance Z_Serial for a series circuit is:

According to the complex function relationship, the real and real parts, imaginary and imaginary parts on both sides of the equation should be equal, then it can be calculated:

（3）

（4）

If tgδ≪0.1 tg²δ≪0.01, then the above two equations can be simplified to:

2 Equivalent circuit of aluminum electrolytic capacitor

After understanding the special structure of aluminum electrolytic capacitor and the equivalent circuit of capacitor dielectric, the equivalent circuit of aluminum electrolytic capacitor can be further analyzed.

For foil-wound aluminum electrolytic capacitor, the working electrolyte actually acts as the cathode. In order to avoid direct contact between the anode foil and the cathode foil, which causes the two electrodes to be conductive, an electrolytic paper is sandwiched between the two electrode foils, which can adsorb a certain amount of working electrolyte. Since the electrolytic paper itself is an organic cellulose dielectric material, it also uses the anode foil and the cathode foil as two metal plates to form another additional capacitor, which is called the backing capacitor C_paper, and is in series with the capacitor of the aluminum anodized film in structure. In addition, the electrolytic paper adsorbing the electrolyte also has dielectric loss. In this way, the equivalent circuit of the aluminum electrolytic capacitor can be represented by Figure 2. For the convenience of calculation, it is simplified in the following order: