Equivalent Series Resistance ESR

As discussed in Chapter 1, if a sinusoidal alternative current is applied on an ideal capacitor, the output voltage should be out of phase by 90° independent of the frequency. However, in a supercapacitor, the output voltage is normally out of phase fewer than 90°, suggesting that an equivalent series ohmic resistor is coupled. This ohmic component is defined as the equivalent series resistance (ESR). 

Equivalent circuit of supercapacitor in presence of equivalent series resistance. 

ESR is an important parameter in evaluating a supercapacitor s performance, in particular its power density, because the ESR restricts the rates at which the capacitance can be charged or discharged upon application of a given current or voltage. 

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Every eapaeitor has a small resistanee and induetanee in series with the spee-ified eapaeitanee of the eapaeitor. The equivalent series resistance (ESR) and equivalent series inductance (ESL) are parasitie elements eaused by the eon-struetion of the eapaeitor. Both tend to isolate the internal eapaeitanee from the signal on its terminals. Henee a eapaeitor will have its best eharaeteristies at de, but may behave more poorly at the switehing frequeney of the supply. 

The equivalent series resistance (ESR) and equivalent series inductance (ESL) of the output capacitor substantially control the output ripple. Use an output capacitor with low ESR and ESL. Surface mount Tantalums, surface mount polymer electrolytic and polymer electrolytic and polymer Tantalum, Sanyo OS-CON, or multilayer ceramic capacitors are recommended. Electrolytic capacitors are not... 

The actual SPICE model of this circuit is shown in Fig. 10.2. Note that there are two resistors in series with each of the capacitors, Rl and R2. These resistors model the approximate equivalent series resistance (ESR) of the tantalum capacitors in the circuit at the switching frequency. 

Rs (Figure 1.22a). The double layer capacitance is represented by the capacitance C, and Rs is the series resistance of the EDLC, also named the equivalent series resistance (ESR). This series resistance shows the nonideal behavior of the system. This resistance is the sum of various ohmic contributions that can be found in the system, such as the electrolyte resistance (ionic contribution), the contact resistance (between the carbon particles, at the current collector/carbon film interface), and the intrinsic resistance of the components (current collectors and carbon). Since the resistivity of the current collectors is low when A1 foils or grids are used, it is generally admitted that the main important contribution to the ESR is the electrolyte resistance (in the bulk and in the porosity of the electrode) and to a smaller extent the current collector/active film contact impedance [25,26], The Nyquist plot related to this simple RC circuit presented in Figure 1.22b shows a vertical line parallel to the imaginary axis. 

Equivalent series resistance (ESR) of the active material and of the construction, topology... 

For example, a real inductor has the basic property of inductance L, but it also has a certain non-zero dc resistance ( DCR ) term, mainly associated with the copper windings used. Similarly, any real capacitor has a capacitance C, but it also has a small equivalent series resistance ( ESR ). Each of these terms produces ohmic losses — that can all add up and become fairly significant. 

Theoretical filter performance is based on the assumption that we are using ideal components. However, real-life inductors are always accompanied by some winding resistance (DCR) and some inter-winding capacitance. Similarly, real capacitors have an equivalent series resistance (ESR) and an equivalent series inductance (ESL). 

As fully discussed in Chapter 2, the electrolyte has complex interactions with the electrode materials (active components) of electrochemical supercapacitors (ESs), which play an important role in the performance of ESs. Besides the active component of ESs, the compatibility or possible interaction between the electrolyte and inactive components such as current collectors, binders, and separators should also be considered. For example, the possible corrosion of current collectors in certain electrolytes could reduce the operative cell voltage and decrease the lifetime of ESs. Besides, the transfer of electrolyte ions across the separator could affect the equivalent series resistance (ESR) and the power performance of the ES. Therefore, the inactive components of ESs should be compatible with the electrolytes and electrode materials. 

FIGURE 10.10 PEDT as cathode material (grey = metal white = metal oxide dielectric black = PEDT layer), boosting performance of solid electrolytic capacitors by better conductivity, lower equivalent series resistance (ESR), better impregnation, and avoidance of ignition. 

Super-capacitors, which are capable of storing up to a hundred times more energy than traditional capacitors, act like batteries but without the handicap of equivalent series resistance (ESR). They are able to deliver high pulses of power with charge-up and discharge times which can be measured in seconds. Operating voltages tend to be between two and three volts. It is therefore necessary to... 

Nyquist impedance plot comparing ideal vertical impedance of capacitor (thin line) and that of supercapacitor (thick line). Equivalent series resistance (ESR) is derived from the intercept of the real impedance axis followed by the equivalent distributed resistance (EDR) of a porous electrode. Source Kotz, R. 2000. Electrochimica Acta, 45,2483-2498. With permission.)... 

Thus, this novel acid-alkaline hybrid capacitor has a larger voltage window and higher specific energy, when compared to that in a single electrolyte of either acid or alkaline. However, the maximum output power is still limited by the ionic interface/membrane that results in higher equivalent series resistance (ESR). Based on the bipolar membrane (BPM) we used, the ESR of acid-alkaline hybrid capacitor is around 4 times higher than that of either acidic or alkaline capacitor, in which no separator was used. 

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