For many purposes, real capacitors can be represented using a relatively simple lumped element model, consisting of an ideal capacitor with several additional components.
Equivalent series resistance (represented by Resr in the model) describes losses associated with moving charge through a capacitor. The resistance of the electrode and lead materials is a contributing factor, and losses occurring within the dielectric material itself also occur and are often dominant. The relevance of ESR to capacitor selection is twofold: 1) it influences the AC response of the capacitor, and 2) it imposes limits on the amount of AC current that can be permitted to flow through the capacitor, due to thermal limitations. Current flow through a capacitor’s ESR results in I2R losses just like any other resistor, causing a temperature increase within the capacitor that contributes to diminished device longevity.
ESR is influenced by device type and construction, and also by temperature and test frequency to varying degrees. In many cases, the ESR of a capacitor is not directly given in a datasheet, but rather communicated in terms of a summary figure such as Q, dissipation factor (DF), or Tan δ. All are quotients of a capacitor’s ESR and capacitive reactance (XC ) expressed differently. Tan δ and dissipation factor are calculated as ESR/XC, and are essentially the same figure, though it should be noted that dissipation factor is usually expressed as a percentage, rather than as a simple dimensionless factor. Q is simply the reciprocal of Tan δ, or XC/ESR.
Equivalent series inductance arises from the partial self-inductance of the device leads, coils formed due to the geometry of the device leads within the circuit, etc. In the lumped-model approximation, ESL is represented by an ideal inductor (Lesl) in series with the ideal capacitor (Cnom) representing the device’s nominal capacitance value. The relevance of ESL to capacitor selection is primarily its effect on AC response. As the lumped model suggests, real-world capacitors behave like series-connected LCR circuits. As the frequency of an applied AC voltage increases, the inductive reactance of the ESL increases to a point at which it is equal to the capacitive reactance of the device and the capacitor behaves as a resistor. At frequencies above this point, the capacitor is effectively an inductor.
Leakage is modeled as a relatively large-value resistor in parallel with the ideal capacitor in the lumped model. It arises from the fact that the dielectric materials used within the capacitor are not perfect insulators, and allow some amount of DC current to pass through the capacitor when a constant voltage is applied. Relevance of leakage to capacitor selection is application dependent; it can be a power consumption issue in micro-power applications, an error source in precision analog applications, or a reliability/thermal management issue in power applications.
Polarization is a non-ideal property of most electrolytic capacitors, which rely on a dielectric formed through electrochemical action. Applying a voltage to such a capacitor with incorrect polarity causes a reversal of the electrochemical process used to create the capacitor’s dielectric layer. This process of electrochemically destroying the dielectric layer results in higher-than-specified leakage currents, which are exacerbated as the thinning dielectric layer begins to break down under the stress of the application voltage.
Since leakage current results in internal heating and increases in temperature cause increases in leakage current, a cascading effect occurs that can result in rather spectacular catastrophic failures when the source impedance of the (mis)applied voltage is low.
Non-polarized electrolytic capacitors (which effectively are two polarized capacitors placed back-to-back) are available for use in applications where the polarity of applied voltage is unknown or may be occasionally reversed, though their use requires a measure of caution.
Dielectric absorption, also referred to as “soakage,” refers to energy storage within a capacitor’s dielectric that is absorbed and released on a longer time scale than would be predicted by the device’s nominal capacitance and ESR. In the lumped-element model, it can be represented as a series connection of a resistor and capacitor (or multiple instances thereof) in parallel with a device’s nominal capacitance.
Practically, this means that a capacitor held at DC potential for some length of time and then briefly discharged will appear to recharge itself to some degree. In a different example, the discharge through a resistor of a capacitor held at a DC potential for a while will be well-modeled by the usual exponential equation during the rapidly-changing portion of the discharge curve. During the “long tail” portion of the curve however, the capacitor will deliver a current higher than that predicted by the usual R-C discharge equation.
The phenomenon can be problematic in precision analog circuits, but poses a potentially lethal safety hazard in the context of high-voltage, high capacitance devices such as those used in many power factor correction or DC bus filtering applications. Many types of capacitors used for such applications currently and historically are some of the most prone to energy storage by dielectric absorption, with some being capable of “self-charging” to perhaps a fifth of the voltage previously applied. With larger devices, the energy & voltage present at the terminals due to this process can be sufficient to cause injury directly (burns or cardiac arrest are two possibilities) or indirectly as a result of involuntary reactions to electric shock.
Dependence of ____ on _____
In the first blank, insert any device parameter of interest; capacitance, ESR, ESL, leakage, lifetime, etc. In the second insert most any application parameter; temperature, voltage, frequency, time, etc. There’s a relationship between the two, and it’s dependent on device type and construction. Some of the relationships aren’t particularly strong and are usually negligible, while others are stronger and less negligible than an 800-pound gorilla on meth. Consequently, the existence and relevance of such relationships should be considered when making device selections.
Some capacitor types exhibit significant variations in their characteristics that occur on time scales much longer than most electrical signals of interest, rather like the way a Krispy Kreme® doughnut changes in character with time after leaving the fryer. This can pose problems from design, manufacturing, or calibration perspectives; a device that tests OK when it’s fresh out of the reflow oven might not meet spec after a week, for example.
Recall that the equation for the capacitance between two parallel plates is a strong function of electrode separation/dielectric thickness; if the distance between the plates is changed (such as by application of a mechanical force) the capacitance changes also. If the capacitance changes but the amount of stored charge remains constant, the voltage across the capacitor’s terminals varies in inverse proportion to the change in capacitance.
The result is that capacitors provide a transduction mechanism between the mechanical and electrical realms, commonly called a microphonic effect for its similarity to/application in audio microphones of the sort used in stage performances, portable electronics, etc. The effect is fantastically useful for these applications, but can also be problematic when it results in unintended coupling of mechanical signals into an electrical circuit, becoming a noise source or worse yet, an unintended feedback path.
The transduction mechanism is also bi-directional; application of voltage across a capacitor’s terminals results in mechanical forces being applied to the electrodes that can in turn couple mechanically into the surrounding environment, as audible noise for example. Though present in all capacitors due to electrostatic forces (the phenomenon behind “static cling”) it’s most pronounced in devices that incorporate piezoelectric dielectric materials. Such materials develop an electric charge in response to mechanical strain and, going the other direction, deform mechanically when subjected to an electric field. Because the piezo effect tends to generate significantly more mechanical force per volt applied than electrostatic forces do, the coupling between the electrical and mechanical realms is much stronger in capacitors that incorporate piezoelectric materials.