Equivalent series resistance

Tan 5 is a measure of dielectric loss in a capacitor unit and is represented by the ratio of equivalent series resistance and capacitive reactance of a capacitor unit at the rated voltage and frequency (Figure 9.7) i.e. 

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. 

Dielectric losses arise from the direct capacitive coupling of the coil and the sample. Areas of high dielectric loss are associated with the presence of axial electric fields, which exist half way along the length of the solenoid, for example. Dielectric losses can be modeled by the circuit given in Figure 2.5.3. The other major noise source arises from the coil itself, in the form of an equivalent series resistance, Rcoii. Exact calculations of noise in solenoidal coils at high frequencies and small diameters are complex, and involve considerations of the proximity and skin depth effects [23],... 

This means the equivalent series resistance of SC should notably be reduced in order to increase their specific power. Hence, as can be shown, the electrode resistivity should be reduced significantly - down to 0.5... 

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. 

T. N. Rudakov, J. H. Flexman, V. T. Mikhaltsevitch, P. A. Hayes, W. P. Chisholm, C. N. Aitken, and J. H. Feldman, Nuclear Quadrupole Resonance Scanner for Detecting Explosives in Mail, Has Low Equivalent Series Resistance Switch to Switch Capacitance of Tunable circuit Enclosed by Electromagnetic Shield, US Patent Application No. US2006012366-A1 (2006). 

In considering the practical application of capacitors, the equivalent series resistance (e.s.r.) is more significant since it carries the total current passed by the capacitor. 

Fig. 5.7 Frequency response of the equivalent series resistance rs and the impedance Z for a typical mica capacitor (C = 100 pF, L = 100 nFI, itel=l 2, tanc5 = 0.0002).

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... 

Entry Electrode Thickness (inch) Density (g/ml) Equivalent Series Resistance (ohm) Specific Capacitance (F/g) Knee Point Erequency (Hz) Pore Resistance (ohm)... 

Through this equation the Q-factor is also defined, which, in addition, can be used to specify the losses or quality (Q) of the capacitor. In Figure 1.49 the parallel and series equivalent circuits of a capacitor are shown, along with the frequency dependence of the impedance Z. Both the parallel and series circuit can be used synonymously, that is they describe an identical behavior. (The series circuit is normally preferred for high frequencies.) ESR stands for equivalent series resistance . The total impedance Z for the parallel circuit is ... 

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). 

Ochi, A., Mori, T., Nakanishi, M., Utsumi, K., Abe, S., and Yoshimoto, T., Y5V multilayer ceramic capacitors with high specific capacitance and low-equivalent series resistance, lEEE-CHMT, 8, 572 (1991). 

---