﻿ Product Information: Aluminum Electrolytic Capacitor Technical Notes/Capacitor, Power Supply Units RUBYCON CORPORATION

# Aluminum Electrolytic Capacitor Technical Notes

## 3. Basic Performance

### 3-1 Capacitance and Energy Storage

Capacitance of a capacitor is generally expressed with the following formula (Equation 1). On aluminum electrolytic capacitor, "S " is effective surface area of anode foil enlarged to 60 to 150 times of the projected area through etching process. "d " corresponds to the thickness of dielectric (13 to 15 angstroms per volt). Relative permittivity "εr " of aluminum oxide film is about 8.5.
Actual aluminum electrolytic capacitor are composed of anode foil and cathode foil as shown in Fig. 1, and cathode foil also has natural oxide film or oxide film formed with a low forming voltage and has capacitance. Therefore, product capacity Cp of the aluminum electrolytic capacitor is calculated as shown in Equation 2, considering that capacitance of anode foil Ca and capacitance of cathode foil Cc are connected in series. Electric charges Q (Coulomb) stored in capacitor when the voltage V (volts) is applied between the terminals are expressed as follows (Equation 3). The work W (Joule) made by the charge Q is expressed as shown in Equation 4. ### 3-2 Tangent of Loss Angle (tan δ) DF and ESR

When a sinusoidal alternating voltage is applied to an ideal capacitor, the current advances by π/2 in phase. In the case of a practical capacitor, however, advance in phase is (π/2-δ ), which is smaller than π/2 . "δ " is referred to as Loss Angle (Fig. 8). Fig. 8 Loss Angle

Tangent of this loss angle (tanδ) is used to show magnitude of the loss, the smaller this value, the higher the performance and the closer to and ideal capacitor. In addition, this loss angle is generally used as an index showing magnitude of dielectric loss. This dielectric loss (tanδ) is shown in the complex plane in Figure 9 and is defined as Equation 5.  Fig. 9 tanδ

One of the reasons why loss angle arises is electric resistance of materials used in electrolytic capacitor, including the intrinsic resistance of foil, resistance of electrolyte and resistance of terminals.
Another reason is due to the dielectric relaxation phenomenon. When voltage applied to the capacitor changes, polarization of dielectric does not immediately reach equilibrium state, so current response is delayed and a loss (dielectric loss) occurs. Dielectric loss (tanδ) has a specific value for each dielectric material. Resistance component due to dielectric loss becomes tanδ/2πfC from Equation 5 and it will be inversely proportional to frequency. Therefore, resistance component of the capacitor has a frequency dependence, and resistance increases as frequency decreases.
Figure 10 shows the equivalent circuit of aluminum electrolytic capacitor. R is called the equivalent series resistance (ESR), which corresponds to resistance when the resistance described above is represented as series equivalent circuit of Fig. 10. Fig. 10 Schematic diagram of equivalent circuit

### 3-3 Leakage Current

When a voltage is applied to the aluminum electrolytic capacitor, a large current (charge current) determined by the capacitance and series resistance of the capacitor flows first, but the current gradually decreases. It eventually converges to a constant current (leakage current) due to disappearing the influence of absorption current. (Fig. 11) Fig 11 Leakage current change after voltage application

Factors of this slight leakage current include the presence of defects in the dielectric layer (aluminum oxide), destruction of the dielectric layer due to impurities and the like, and reparation by electrolyte components. Intrinsically, leakage current means this convergent current, but since it takes long time to converge, for the purpose of convenience, the current after 1 to 5 minutes (specify time for each product) from applying the rated voltage in the 20ºC environment is specified as leakage current in the product catalog.

### 3-4 Impedance

Impedance ( Z ) is the factor that impedes the flow of current when an alternating voltage is applied to the capacitor, which is expressed as Z = 1/jωC + jωL + R and its magnitude is shown in Equation 6. Fig. 12 is the schematic illustration of impedance and ESR, where Xc is predominant in low frequency range, ESR around the resonance point, and XL in high frequency range. Fig. 12 Schematic illustration of impedance and ESR Frequency Characteristics

### 3-5 Temperature Characteristics

Each characteristic of aluminum electrolytic capacitor has a temperature dependence, and especially in low temperature range, large decrease in capacitance and increase in impedance and tangent of loss angle (tanδ) may be seen due to increase in resistance of electrolyte. Leakage current increases as temperature increases. Fig. 13 to 15 show capacitance and impedance, tangent of loss angle (tanδ) and leakage current change with temperature. Fig. 13 Temperature Characteristics of capacitance change and impedance ratio (based on 20 ºC) Fig. 14 Temperature Characteristics of tangent of loss angle (tanδ) Fig. 15 Temperature Characteristics of leakage current

### 3-6 Frequency Characteristics

Characteristics of aluminum electrolytic capacitor are also frequency dependent. Capacitance reduce as measuring frequency increases. The change of impedance and ESR is described in 3-4 (Fig. 12). However the rate of the change is not constant, the presumed reasons are as follows:
1) Condition of etched surface of aluminum foil
2) Property of aluminum oxide layer as dielectric
3) Property of electrolyte
4) Construction of capacitor
Frequency-response curves of capacitance is shown in Fig. 16. Fig. 16 Frequency-response curves of capacitance

### 3-7 Load and Storage Characteristic

When an aluminum electrolytic capacitor is applied with a DC voltage or a DC voltage with superimposed ripple current for a long time, capacitance will reduce and the tangent of loss angle will increase. Specifications are provided for these changes in individual characteristic  to judge practical life of capacitor. When aluminum electrolytic capacitor is stored for a long time without electric charge, capacitance will also reduce and the tangent of loss angle will also increase. Changes in capacitance and the tangent of loss angle are primarily caused due to loss of electrolyte through dissipation and decomposition, which are accelerated in a high temperature atmosphere.
In load life testing, leakage current generally stays low because aluminum oxide layer used as dielectric is always repaired by the DC voltage applied, consuming electrolyte. On the contrary, in shelf life test, leakage current may increase because the repairing of aluminum oxide layer does not occur until voltage is applied.
Changes in characteristics in the rated voltage load test (Life test) and the no-load storage test (Shelf test) at 105ºC are shown in Figures 17 to 19. Fig. 17 Changes in capacitance with time at 105ºC Fig. 18 Changes in tangent of loss angle (tanδ) with time at 105ºC Fig. 19 Changes in leakage current with time at 105ºC (only life)

1938-1, Nishi-Minowa Ina City, Nagano 399-4593 Japan TEL:0265-72-7111 FAX:0265-73-2914