*Key parameters are necessary to predict lifetime*

*Aluminum Electrolytic Capacitors (“elcaps”) are essential for the function of many electronic devices. Frequently, the lifetime of these devices is directly linked to the lifetime of the elcaps [9].*

*By Dr. Arne Albertsen, JIANGHAI EUROPE GmbH*

This article reviews the construction of elcaps and highlights related terms like ESR, ripple current, self-heating, chemical stability, and reliability. Two estimation tools for obtaining elcap lifetime approximations are illustrated.

### Construction of Elcaps

Aluminum electrolytic capacitors consist of a highly roughened anode foil covered by a thin dielectric layer and an exact-fitting cathode, the electrolyte liquid (Fig. 1).

The liquid electrolyte makes the construction of electrolytic capacitors special. The current flow is mediated by moving ions. Temperature rise decreases the viscosity and lowers the electrical resistance (ESR). The electrolyte’s boiling point limits the maximum permissible self-heating caused by the ripple current and ambient temperature. Electrolyte loss caused by electrochemical self-healing and drying out limit the lifetime of electrolytic capacitors [7].

### Equivalent Series Resistance ESR

The ESR (Equivalent Series Resistance) allows for an easy calculation of the thermal losses that occur during the operation of elcaps [1].

The ESR (Figure 2) is the sum of an approximately constant, a frequency dependent and a temperature dependent part [2]:

R_{o} designates the ohmic (foil, connecting tabs and solder terminals), R_{d} the frequency dependent (dielectric layer (Figure 3 (a) [3])), and R_{e} the temperature dependent resistance (electrolyte and spacer paper (Figure 3 (b))).

To obtain reliable designs, maximum rather than typical ESR-values should be used when selecting electrolytic capacitors.

### Ripple current

Usually, an a.c. or ripple voltage exists on top of a d.c. voltage and causes a ripple current and a self-heating of the elcap. As currents of any frequency contribute to the selfheating [8], RMS (root mean square) values of the rated ripple currents need to be considered:

*I _{a }*RMS value of the rated ripple currents

*I*RMS Values of ripple currents at frequencies

_{f1 }...I_{fn}*f1…fn*

Fcurrent correction factor at frequencies

F

_{f1}... F_{fn}^{ }*f1…fn*

where f_{0}= reference frequency of the nominal ripple current

The correction factors for the currents originate from the frequency dependency of ESR and are given in the datasheets.

### Self-heating of elcaps

During operation, the elcap’s temperature rises above ambient. In the steady state, the applied electrical power P_{el} matches the heat power P_{th} dissipated to the ambient.

*P _{el} = P_{th}*

The main cooling mechanisms for elcaps are radiation and convection. Heat conduction is usually very small. The capability to radiate heat depends on the elcap’s surface material. The visible sleeve color does not matter, though.

The contribution of convection to the total cooling effect can be improved by forced cooling [5].

The individual equivalent thermal resistances of each cooling mechanism may be lumped together into a single thermal resistance R_{th}.

The core temperature T_{c} can be expressed by:

The combined internal thermal resistances range in the order of

The measurement of the surface temperature T_{s} at the can bottom provides a good approximation of the core temperature T_{c} for radial and small snap-in elcaps (can diameters ≤ 25 mm). For larger can sizes, a direct measurement of the core temperature is recommended. Jianghai supplies elcaps with assembled thermocouples on request.

### Chemical Stability

Electrolyte systems are multi-compound mixtures, and their chemical stability is a must. A good indicator for chemical stability is the “shelf life” (Table 1, right column). As opposed to the regular storage of elcaps at moderate temperatures, the shelf life test is a demanding accelerated life test that subjects the test specimens to their upper category temperature without any voltage applied. A high shelf life figure is a good indicator for chemical stability, high purity of materials and advanced production quality. The results of this test are shown on the datasheets of all Jianghai series.

### Reliability and lifetime

The related concepts of reliability and lifetime provide answers to the questions of “How many elcaps may fail during the usage of my application?” and “How long will the elcaps survive in my application?”

The typical time course of reliability density for elcaps follows the socalled “bathtub curve” [6]. The failure rate (“FIT rate”) λ designates the number of failures per unit time (FIT = “Failures in Time” in

The bathtub curve in Figure 4 shows three distinct consecutive segments:

· The early failure period (decaying FIT rate λ)

· The period within the normal lifetime describes the occurrence of random failures (constant FIT rate λ)

· The final segment originates from wear-out and changes beyond acceptable limits at the end or after the end of the regular lifetime (increasing FIT rate λ)

Towards the end of the production process, all elcaps are subject to post-forming (similar to a “burn-in”). Early failures in the application are thus a rare exemption [1]. For the further proceeding, we consider the elcap is operated during the random failure period of the bathtub curve. The end of the lifetime is reached when certain parameters exceed pre-defined limits. It is common practice to allow a certain portion of species to be outside of these limits.

When comparing databooks of different elcap manufacturers, an inconsistent use of terms becomes obvious. The range of terminology comprises terms like "load life”, “useful life”, “endurance”, “life expectancy”, “operational life”, and “service life”. In addition to different limits that define the end of the lifetime, some manufacturers even use differing standards to allow for a certain amount of test items to be out of the specified range – this makes a comparison of the various lifetime values between suppliers very difficult. Today, there exist no valid uniform standards that could be used to obtain an exact definition of the terms and their meaning. Jianghai resolves to list all relevant definitions and test conditions in the datasheet (Table 1).

### Elcap lifetime diagram and lifetime model

To provide the users of their products with some tools for the lifetime estimation of elcaps, Jianghai has devised lifetime diagrams and a lifetime model. While the lifetime diagrams consider the most important parameters (temperature, ripple current) and show permissible combinations of these parameters graphically, the lifetime model also takes the influence of the actual operating voltage on lifetime into account. For each application, the results obtained by any tool need to be confirmed by the supplier. Jianghai lifetime diagrams (Figure 5) exclude combinations of ripple current and ambient temperatures that may lead to temperatures too close to or even exceeding the boiling point of the electrolyte. These load conditions may only be applied if confirmed by Jianghai.

The input of the lifetime model are some elcap type specific parameters from the datasheet along with application-specific parameters like ambient temperature, ripple current load and the actually applied voltage during operation [4]. In case of forced cooling the ripple current load capability needs to be adjusted accordingly.

### Example lifetime estimation

The following example is supposed to serve the illustration of a practical application of the lifetime diagram and of the lifetime model. Let a 105 °C elcap, type 390 µF, 400 V, 35x45 mm from the snap-in series CD_297_BB from Jianghai be operated at ambient T_{a} = 55 °C and a ripple current of 2.51 A_{rms }at 20 kHz. The actual operating voltage equals the rated voltage of 400 V, hence only ambient temperature and ripple current load enter the lifetime estimate. The cooling is supposedly done by free convection and radiation. The datasheet indicates a nominal ripple current of I_{R}= 1.27 A_{rms} at 120 Hz and 105 °C and a frequency correction factor of 1.4 for frequencies beyond 10 kHz and rated voltages 315 ~ 450 V. The lifetime ("useful life“) is specified to be L_{0}= 7,000 h at nominal load conditions.

The ratio of the actual, frequency-rated ripple and the nominal ripple current is computed as

From the lifetime diagram (Figure 5), we obtain an approximate value for the lifetime multiplier of 16 at the intersection of ambient temperature and ripple current ratio. The estimate for the “useful life” of the elcap in this application under the mentioned operating conditions is:

Alternatively, the lifetime can also be estimated by using the numerical lifetime model:

Inserting the values of

yields

The result of the numerical estimate matches the result obtained from the graphical solution that utilized the lifetime diagram.

**Summary**

Aluminum electrolytic capacitors often determine the lifetime of electronic devices. A thorough knowledge of some of the key parameters and aging concepts of these components are necessary to ensure the reliable design of electronic devices with a predictable lifetime. Typical electrical and thermal properties of elcaps as well as the definitions for reliability and lifetime are elucidated. Two methods are available for obtaining lifetime estimates: a graphical approach (lifetime diagram) and a numerical computation (lifetime model). The applicability of the models and their results depend on the specific product type and the particular application. Consultations with the supplier are key to get guidance throughout the design project and to confirm any estimates. A practical example shows how the methods presented here can be applied to obtain application specific elcap lifetime estimates.

**References:**

1) Both, J., Aluminium-Elektrolytkondensatoren, Teil 1 - Ripplestrom und Teil 2- Lebensdauerberechnung, BC Components, February 10, 2019.

2) Gasperi, M. L., A Method for Predicting the Expected Life of Bus Capacitors, IEEE Industry Applications Society, Annual Meeting, New Orleans, Louisiana, October 5-9, 1997.

3) Mirsky, G., Determining end-of-life, ESR, and lifetime calculations for electrolytic capacitors at higher temperatures, EDN, August 20, 2019.

4) Parler, S.G., Deriving Life Multipliers for Aluminum Electrolytic Capacitors, IEEE Power Electronics Society Newsletter, vol. 16, no.1, 11-12, February 2004.

5) Parler, S.G., Thermal Modeling of Aluminum Electrolytic Capacitors, IEEE Industry Applications Society Conference, October 1999.

6) Stiny, L., Handbuch passiver elektronischer Bauelemente, Franzis Verlag, Poing, 2007.

7) Thiesbürger, K.H., Der Elektrolytkondensator, Roederstein, Landshut, 1991.

8) van de Steeg, T., Selecting electrolytic capacitors for power supplies, DATAWEEK Electronics & Communications Technology, Issue February 28, 2019.

9) Venet, P., A. Lahyani, G. Grellet, and A. Ah-Jaco, Influence of aging on electrolytic capacitors function in static converters: Fault prediction method, Eur. Phys. J. AP 5, 71-83, 1999.