Equivalent series inductance

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. 

Answer Yes, but only to some extent. The overall ESL (equivalent series inductance) and ESR are reduced,... 

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... 

But any real-world component also comes along with various reactive parasitics. For example an inductor can have a significant parasitic capacitance across its terminals — associated with electrostatic effects between the layers of its windings. A capacitor can also have an equivalent series inductance ( ESL ) — coming from the small inductances associated with its leads, foil, and terminations. Similarly, a mosfet also has various parasitics — for example the unseen capacitances present between each of its terminals (within the package). In fact, these mosfet parasitics play a major part in determining the limits of its switching speed (transition times). 

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). 

There is an equivalence between the differential equations describing a mechanical system which oscillates with damped simple harmonic motion and driven by a sinusoidal force, and the series L, C, R arm of the circuit driven by a sinusoidal e.m.f. The inductance Li is equivalent to the mass (inertia) of the mechanical system, the capacitance C to the mechanical stiffness and the resistance Ri accounts for the energy losses Cc is the electrical capacitance of the specimen. Fig. 6.3(b) is the equivalent series circuit representing the impedance of the parallel circuit. 

FIGURE 11.9 Basic capacitor electrical equivalent circuit comprising a capacitance, a series inductance, a series resistance, and a parallel resistance. This simple model can fit a DLC behavior in first approximation for a given frequency. 

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. 

Real capacitors are equivalent to a series resonant circuit as shown in Figure 9.53. The model is valid for both interdigital and plate capacitors. The selfresonance effect is caused by parasitic series inductance of the electrodes and connections such as conductor traces or vias. The series resistance of tiie electrode metal R and the dielectric losses (expressed by the parallel resistor Rp) in the tape or high-K material are contributing to the capacitor loss. To simplify the model, both parts can be combined in the equivalent series resistance R . 

In applications where really high temperatures of up to 200 C may be encountered, Cornell Dubilier offers mica and Teflon (PTFE) electrolyte metal clad versions in silver-plated metal cases. These designs, which feature ultra-low inductance terminations and heat spreading when operating at high power, assure low ESR (Equivalent Series Resistance) to greater than 1 GHz, and high ripple current capabilities with stability in subminiature sizes. 

When a capacitor circuit is compensated through a series reaetor. either to suppress the system harmonics or to limit the switching inrush currents (Section 23.11) or both, it will require suitable adjustment in its voltage and capacitive ratings, fhe series reactor will dampen the switching currents but consume an inductively reactive power and offset an equivalent amount of capacitive kVAr. and require compensation. The following example w ill elucidate this. 

In the parallel configuration, the same potential difference occurs across each and every element with the total current being the algebraic sum of the current flowing through each individual circuit element. Table 2-35 summarizes the equivalent resistance, conductance, capacitance, and inductance of series-parallel configurations of resistors, capacitors, and inductors. 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

Figure 12.4 depicts a typical admittance parametric plot for the quartz crystal resonator. Note that the effect of the static capacitance C0 in the parallel branch is to shift the admittance circle upward by resonance frequency top which now depends on C0, in addition to the series resonance frequency to, = 2irfa. Changes in the resonance frequency are related to changes in the equivalent inductance L and broadening of the admittance curve near resonance (decrease in the circle diameter l/R in Fig. 12.4) are related to equivalent resistance R. 

The second meaning of the word circuit is related to electrochemical impedance spectroscopy. A key point in this spectroscopy is the fact that any -> electrochemical cell can be represented by an equivalent electrical circuit that consists of electronic (resistances, capacitances, and inductances) and mathematical components. The equivalent circuit is a model that more or less correctly reflects the reality of the cell examined. At minimum, the equivalent circuit should contain a capacitor of - capacity Ca representing the -> double layer, the - impedance of the faradaic process Zf, and the uncompensated - resistance Ru (see -> IRU potential drop). The electronic components in the equivalent circuit can be arranged in series (series circuit) and parallel (parallel circuit). An equivalent circuit representing an electrochemical - half-cell or an -> electrode and an uncomplicated electrode process (-> Randles circuit) is shown below. Ic and If in the figure are the -> capacitive current and the -+ faradaic current, respectively. 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

To separate the contribution of the anode from that of the cathode, Wagner et al. provided a more general equivalent circuit, as shown in Figure 6.33. The anode, the cathode, and the membrane resistance were in series. A parasitic inductance due to the mutual induction effect was also included. The cathode impedance was given by charge-transfer resistance (Rct0i) and constant phase element (CPE) in... 

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