## 2 Aluminum Electrolytic Capacitors (Al-Caps)  
Capacitors are generally classified into three main types: electrolytic, film, and ceramic. Each type can be further subdivided based on factors such as the dielectric material, construction, terminal connection, application, coating, and electrolyte that are used [14]. Among the capacitors used in PCs, aluminum electrolytic capacitors (al-caps) are widely used because they have high volumetric efficiency, are compact, are cheap, and are available in a wide range of capacitance values [22; 23]. However, their high dissipation factor and leakage current limit their maximum operating voltage to about 1 kV [24]. Al-caps consist of a wound element (Figure 1a) that is impregnated with an electrolyte, connected to the leads, and placed inside a metal can (Figure 1b). The element itself is composed of two aluminum foils, the anode and cathode foil, which are physically separated by paper separators soaked in electrolyte (Figure 1a). The foils are composed of high-purity aluminum and are etched with billions of microscopic tunnels, which significantly enhances their surface area [14; 22; 23]. Internally, an al-cap consists of two capacitors: the anode capacitor (an-al-cap) and the cathode capacitor (ca-al-cap). The an-al-cap comprises an anode foil (positive plate), a dielectric layer (designed to withstand the rated voltage), and the electrolyte (serving as the negative plate). The ca-al-cap, on the other hand, consists of the electrolyte (positive plate), a much thinner dielectric layer (supporting voltages below 0.5 V), and the cathode foil (negative plate) [14]. The electrolyte, which serves as the cathode for the an-al-cap, is an ion-conducting liquid that comes into contact with the dielectric layer, the aluminum oxide (Al\({}_{2}\)O\({}_{3}\)). Its main functions are to ensure firm adhesion to the surfaces of both foils, establish electrical  
Figure 1: Basic structure of an al-cap [22]: (**a**) the whole structure and (**b**) inside the can. continuity between the an-al-cap and ca-al-cap, and assist in repairing defects in the anode dielectric layer. The strong adhesion of the electrolyte to the aluminum foil maximizes the contact area, thereby increasing the al-cap capacitance. When defects form in the dielectric layer, the leakage current increases, triggering the electrolysis of the water in the electrolyte and generating hydrogen and oxygen. The released oxygen then reacts with the anode foil, regenerating Al2O3 in areas where the dielectric layer is thinner or damaged. The process described above is known as the self-healing mechanism, and it naturally changes the electrical characteristics of the al-cap. As the water content in the electrolyte decreases, the contact area with the dielectric layer is reduced, which leads to a drop in capacitance. Additionally, the reduction in the electrolyte impairs the electrical connection between the an-al-cap and the ca-al-cap, which results in an increase in the capacitor's internal resistance. Another important aspect to consider is the generation of gases, which increases the internal pressure within the can. To prevent rupture or explosion, the capacitor is equipped with a pressure-relief mechanism designed to safely release excess pressure. The equivalent circuit of an al-cap (Figure 2) can be modeled using three main components: an ideal capacitor (C), the equivalent series resistance (ESR), and the equivalent series inductance (ESL). The ESR accounts for various resistive elements within the capacitor, including terminal, tab, and foil resistances, as well as the paper-electrolyte and tunnel-electrolyte resistances. It also includes the parallel resistance associated with the leakage current. The ESL arises from the tab loop configuration, specifically the loop area formed by the terminals and tabs outside the active winding [14]. Failures in aluminum electrolytic capacitors (al-caps) can have several causes, but the two main mechanisms are the self-healing mechanism, described above, and electrolyte evaporation.