Effective series resistance

The electrical characteristics of the cell and electrode will comprise both capacitative and resistive components, but for simplicity the former may be neglected and the system can be represented by resistances in series (Fig. 19.36 > and c). The resistance simulates the effective series resistance of the auxiliary electrode A.E. and cell solution, whilst the potential developed across by the flow of current between the working electrode W.E. and A.E. simulates the controlled potential W.E. with respect to R.E. 

They are several concerns when designing an EMI filter. The parameters of the EMI filter examined in this book reflect these concerns. If the EMI filter is to be used on a converter, the input impedance of the converter must be greater than the output impedance of the filter at all frequencies. It is good practice to allow 6 dB of margin for this parameter. If the output impedance of the filter gets too close to the input impedance of the converter, there can be problems with the stability of the converter. It may be important to note here that this output impedance is sensitive to the effective series resistance (ESR) of the output capacitors. For the hardware data taken for this unit, tantalum capacitors, which have unspecified ESR, were used. The ESR of a similar capacitor was measured for the simulations. 

In the buck however, note that though the output diode needs to be positioned close to the IC/switch, the output capacitor is not critical (its current is smoothened by the inductor). If we place a ceramic capacitor in parallel to the output capacitor, it is only for the purpose of decreasing high-frequency noise and ripple at the output even further. But it is really not mandatory, and can cause severe loop instability, particularly with voltage mode control, especially if the effective series resistance (ESR) of the output capacitor section becomes too low (less than 100 inQ typically). 

Now we turn our attention to a real power supply to see for ourselves where all the buzz is really coming from. First consider what would happen if the input bulk capacitor of the power supply had been a perfect capacitor i.e. with zero effective series resistance (ESR) (ignoring all other capacitor parasitics too). Then any possible differential noise source inside the power supply would be completely bypassed by this capacitor. Clearly, the reason this does not happen is the non-zero ESR of the bulk capacitor. 

The series resistance (i.e., the limiting impedance value at very high frequencies) is very small for the SC. In a practical experimental setup, the impedance of the viable skin will in fact overrule this component. The value of this effective series resistance is typically in the range of 100—500 Q. 

It can be seen that the semicircle due to the charge transfer on electrode/elec-trolyte boundary is followed by a 45° line, characteristic for diffusion, which changes to a vertical line due to the limited diffusion length and reflective boundary. The effective series resistance observed by applying dc current to this circuit for a prolonged time is just a sum of R and Rd. The relative importance of charge transfer and diffusion for the performance of this particular power source is simply quantified as the ratio between R and Rd, in the above example it is 0.1 Ohm and 0.2 Ohm. Thus for this case, the diffusion is twice as important for the dc performance than is the charge transfer. 

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],... 

They also assumed that there was an effective diffusion coefficient Den) which was dependent on a series resistance relationship R) involving the alloying elements such that... 

In practice, poor charge mobility, energetic disorder, carrier trapping, and physical aberrations comphcate device characterization. The effects of these nonidealities are often modeled according to an equivalent circuit shown in Fig. 12. Incorporating all specific series resistive elements as R, and all specific parallel resistances as R, one obtains the expression... 

Gentner (Ref 33)studied the spark initiation of Composition B and LA. This work is particularly important because it treated the partition of energy among the elements of the circuit, and gap in a quantitative manner, fie showed that only 10% of the energy stored in the discharge capacitor actually was delivered to the spark gap when a series resistance was put in the circuit. Litchfield et al (Ref 29) studied the spark initiation of organic vapors and emphasized the effects of gap length. and... 

Figures 11.3 and 11.4 show the frequency spectra of 2600F, 0.5mQ BCAP0010 DLC capacitance and series resistance for three different polarization voltages. It is interesting to observe the low-capacitance value when there is no voltage polarization. This phenomenon should be studied as a function of the electrode thickness. If ionic depletion was the cause, a thick electrode should display a more pronounce effect.

Increasing the temperature will have the main effect to reduce the electrolyte viscosity and to improve the accessibility of the surface for the ions. The ions, thanks to their higher mobility in the warm solvent, will be able to reach deeper carbon area in a shorter time. The increased accessible surface area results in a reduced DLC series resistance and in an increased capacitance with the temperature. Figures 11.5 and 11.6 show the measured and simulated frequency spectra of the BCAP0010 DLC capacitance and series resistance for different temperatures. 

Experiments show that in high quality Si solar cells the superposition principle is valid to a good approximation. In CdS/Cu2S, amorphous Si [139] and in polymer solar cells some of these approximations are grossly violated. As an example consider the effect of series resistance. In the presence of the series resistance Rs the dark current is given by,... 

The approximate temperature distribution in a multiple-effect evaporator is under the control of the designer, but once built, the evaporator establishes its own equilibrium. Basically, the effects are a number of series resistances to heat transfer, each resistance being approximately proportional to The total available temperature... 

Energy Considerations and Spark Characteristics. Many effects listed under items 1 to 7 play important roles in spark initiation because they affect the aimt and rate of energy transfer from the storage capacitor to the spark gap. The energy delivery. can be detd in part by observations made on the electrical circuit. MSW carried out these measurements for a number of tests and provided some analytical treatment of their circuits. The only. quantitative result which. can be drawn from their work is that only about 15% of the stored energy was actually delivered to the spark gap when a series resistance greater than 1000 ohms was placed in the circuit (Ref 35,p 13)... 

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