Effect of Tunnel Pits Radius Variation on the Electric Characteristics of Aluminum Electrolytic Capacitor
Authors: Mukaiyama Daisaku , Yamamoto Masayoshi 
Published: February 2020

Introduction

The electric characteristics of aluminum electrolytic capacitors had been analyzed by the transmission line model which was proposed in Broadbent investigation (1). The anode foil pits are considered as cylindrical holes and the pit impedance is estimated by eq. [1]. The pit impedance depends on the pit geometry, in particular, radius and length. The pits are manufactured to have the same length as much as possible to keep the foil strong as shown in Fig. 1. Therefore, the pit length variation is neglected in this paper. The distribution of the pit radius of etched foils is not in accordance with a normal distribution, but instead with a log normal distribution, as shown in Fig. 2. In this paper, the effect of the pit radius distribution on the impedance of aluminum electrolytic capacitors is calculated by Monte Carlo method. Furthermore, we discuss the resistance of paper and electrolyte system which is expected to be enlarged by the high current density near the narrow opening of pits. Lastly, a new complex relative permittivity εr expression of the anodized film based on the response function (2) is applied to this calculation.

Experiments

The specifications of the test capacitors are as follow: “400V / 280μF / D25mm X L40mm”. These capacitors were fabricated with the following raw materials. Anode foil: 120HB15S-580V (HEC), Cathode foil: 50CK (JCC), Spacer Paper: PE4-30 (NKK), Electrolyte: resistivity 600Ωcm at 30oC (an organic acid ammonium salt in a solvent mainly containing ethylene glycol). The impedance parameters, |Z|, Capacitance, ESR (equivalent series resistance), tanδ were measured for 3 pieces of the test capacitors, in a frequency range from 20Hz to 1MHz with respect to temperatures from -40oC to 105oC.

Modeling

The pit radius distribution of anode foils is supposed to be a log normal distribution. In this discussion, the pit radius is defined as rpit, the average pit radius is rpit_mu and the standard deviation of the pit radius is σpit. The symbols are defined in the “List of symbols”. Fig.3 shows the concept of the “basic structure” of aluminum electrolytic capacitor system. The pit impedance is given by eq. [1]. Where, the dielectric permittivity of anode foil is given by eq. [2] and [3] (2). And the impedance of the dielectric of the anode foil bulk (flat) part is given by eq. [4]. The random sequence of rpit is provided numerically by the Box and Müller method considering the parameters rpit_mu and σpit, and the averaged pit impedance zpit_av can be obtained. The anode foil capacitance per unit macroscopic area is expressed as the function of the pit number density npit from zpit_av and zbulk shown in eq. [4]. Therefore, the npit is determined from the anode foil capacitance measurement data. Then, the radius rb of the “basic structure” can be given by eq. [5], and the resistance enhancement factors of the paper and electrolyte system are given by eq. [6] to [12]. These equations are derived by applying the analytical calculation results to the three resistors circuit model shown in Fig.4. The cathode impedance per macroscopic area is estimated by the typical impedance calculation. The aforementioned calculations and Monte Carlo calculation for rpit give: (i) zbasic_av : the average impedance of the “basic structure” shown in Fig.3. (ii) zc: the impedance per unit foil length between the anode foil metal layer and the cathode metal layer. The transmission resistance rtrans per unit foil length is estimated according to ohm law with taking the skin-effect into account, and the equations will be presented in the final manuscript. Once zc and rtrans are determined, the impedance of the capacitor winding element is calculated with the anode foil length and the lead tabs location (3). The resistance of lead tabs is unneglectable, and it can be obtained from the same formula of rtrans. The parasitic inductance mainly comes from the current loop which is formed by the lead tabs and terminals and we set it as 12nH in this calculation (4).

Results

The calculation results of capacitance versus frequency with respect to temperatures are shown in Fig.5. The calculation results show good agreement with the measurement data over a broad range of temperature and frequency.

Reference:

R. H. Broadbent, Electrochem. Technol., 6, 163 (1968)

D. Mukaiyama, “Dielectric Characteristics Analysis of Aluminum Electrolytic Capacitors Based on Linear Response Theory”, Abstract of the 235th ECS meeting ( to be submitted ).

R. M. Peekema and J. P. Beesley, Electrochem. Technol., 6, 166 (1968)

S. G. Parler, IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 929–935, 2003.

Figure 1