Capacitor equation

CCD detector designers try to increase the signal-to-noise ratio of an amplifier in two ways (1) increase the responsivity, or (2) decrease the random current fluctuation between source and drain. The responsivity can be increased by decreasing the amplifier size. Decreasing the amplifier size decreases the capacitance of the MOSFET. The responsivity of a MOSFET obeys the capacitor equation which relates voltage, V, to the charge Q on capacitance C V = QIC. 

As the capacity of the two electrodes is different, even in a symmetric capacitor, Equation 8.1 indicates that the value of C is determined by the electrode with the smallest capacity value. Moreover, the later electrode operates in a larger potential window than the other one, which consequently reduces the voltage range of the device. This drawback can be circumvented by balancing the respective masses of the electrodes or by using, for each electrode, different materials working in their optimal potential range. 

Hence a potential (bias) dependent capacitance Cscl can be defined with use of the simple capacitor equation Csd/A = ere0/dsci. (As the E field is completely shielded... 

To analyze what happens in Figure 1-6 we must first learn the capacitor equation — analogous to the inductor equation derived previously. If the duality principle is correct,... 

We know intuitively (and also from the capacitor equation) what happens to a capacitor when we attempt to suddenly discharge it (by means of the parallel switch). Therefore, we can now easily guess what happens when we suddenly try to discharge the inductor (i.e. force its current to zero by means of the series switch). 

In 1879, von Helmholtz proposed that all of the counterions are lined up parallel to the charged surface at a distance of about one molecular diameter (Figure 10.5). The electrical potential decreases rapidly to zero within a very short distance from the charged surface in this model. Such a model treated the electrical doublelayer as a parallel-plate condenser, and the calculations of potential decay were based on simple capacitor equations. However, thermal motion leads to the ions being diffused in the vicinity of the surface, and this was not taken into account in the Helmholtz model. 

This method relies on the fact that detectors often respond like a charging capacitor - Equation 10.12. This is such a convenient and common assumption that we often forget that it is an assumption - we just use it as our model. That behavior is shown in Figure 10.10. 

Pij is the potential difference between atoms i and j. If there are n atoms, there are n — 1 independent equations of the type (13a) (one equation is redundant since the total charge of the compound is zero), and if there are m bonds, there are w — n + 1 independent equations of type (13b). The electric potential is related to the charge on the capacitor by the capacitor equation Fy = PyCy. All that is required to solve the resulting set of equations is the capacitance, Cy, of each of the m different bonds. The principle of maximum symmetry (1) implies that the values of Cy will all be equal, and in practice this is found to be the case for equilibrium structures. Two types of constraint break this symmetry anisotropies in the electronic structure of the ion, e.g., lone pairs and Jahn-Teller distortions discussed in Sect. 7, and steric stresses, e.g., atoms in cavities that are too large, such as the hydrogen atom in hydrogen bonds, as discussed in Sect. 8. In this section, we consider only those structures in which these constraints are absent. 

Although the relationship between the channel charge and gate bias can be compHcated, it can be simply approximated as a capacitor stmcture. In this simplification the foUowiag equation holds, where q is the electron charge,... 

Capacitors. Ceramic materials suitable for capacitor (charge storage) use are also dependent on the dielectric properties of the material. Frequently the goal of ceramic capacitors is to achieve maximum capacitance in minimum volume. The defining equation for capacitance is given by ... 

Based on the system studies carried out and Table 23.1, it has been assessed that in actual operation, effective current through a capacitor circuit may increase up to 1.3 limes its rated cunent, /,., i.e. = 1.3 /, to account for all the harmonic effects (V, - Jf. equation (23.4)). A capacitor unit is thus designed for at least M)9r continuous overload capacity (Section 25.6). Its switching and protective devices are selected along similar lines. 

The above discharge is also possible through only an extra resistance in each capacitor switching circuit. Using equations (25.5) and (25.6),... 

Then the unbalance voltage for a grounded system, on a failure of any one unit (assuming the capacitor units to have external type fuses), according to equation (26.f)... 

In the voltage method the normal voltage is applied across the capacitor terminals and line current, /, is measured. The value of capacitance, C, can be determined from the equations provided in Section 23.5.2. In the bridge method... 

Erom C-1.1 the equation for capacitance of a parallel plate capacitor (plate area A, separation d) s ... 

The values for the output filter capacitors are to be determined by using Equation 3.36. 

Calculating the real power loss created by the ESR of the capacitor is given in Equation 4.4. 

The zero attributed to the output filter capacitor is still present in the control-to-output characteristics. Its location is found in Section B.2.1 and Equation B.9. 

Then find the value of the feedback capacitor C. The designer knows the value of the input resistor (R). It is the upper resistor in the voltage divider responsible for the voltage feedback to the error amplifier. One then performs Equation B.15. 

A capacitor, previously called a condenser, stores electrical energy based on the relationship between voltage (V) and stored charge (Q) in coulombs as shown in the equation C = QU. One farad of capacitance is a coulomb per volt of stored charge. The voltage limit of a capacitor is determined by the breakdown potential of the dielectric material. 

Capacitors are often combined in series or parallel, with the resulting circuit capacitance calculated as depicted in Figure 4. An important relationship is the time constant of a capacitor. The time constant is based on the product of the resistance and capacitance and is known as the RC time constant. A capacitor in a dc circuit will charge or discharge 63.2 percent in one RC time constant. The time dependence of a capacitor is shown in the equations. 

The sphere-plane capacitor model gives a useful approximate expression for the function f(Rlz). Equation [13] shows that in the region 0 < z/R < I, which is typical in SPFM imaging, / can be approximated by a 1/z dependence. The planar lever adds a nearly constant term. Thus for the range 0 < z < f , we have the following approximate function... 

In 1873, Gabriel Lippmann (1845-1921 Nobel prize, 1908) performed extensive experiments of the electrocapiUary behavior of mercury and established his equation describing the potential dependence of the surface tension of mercury in solutions. In 1853, H. Helmholtz, analyzing electrokinetic phenomena, introduced the notion of a capacitor-like electric double layer on the surface of electrodes. These publications... 

The above relationships were derived for low electrode coverages by the adsorbed substance, where a linear adsorption isotherm could be used. Higher electrode coverages are connected with a marked change in the surface charge. The two-parallel capacitor model proposed by Frumkin and described by the equation... 

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