Inductance calculation

F. W. Grover, Inductance Calculations. Dover Publications, Mineola, 2004. 

The variations in the probability of damage induction calculated with RADACK are well reflected in the variation of frank SSBs and damaged bases (as expressed by ALS) for different forms of DNA B-DNA (Fig. 12.5), Z-DNA (Tartier et al. 1994 Fig. 12.6) and for a DNA quadruplex (Tartier et al. 1998). The yield of OH-induced frank SSBs of various topoisomers of DNA minicircles is the same (Culard et al. 1994). It has been concluded that the accessibility of H4 is already sufficient in the relaxed topoisomer that an increase in accessibility in the T-2 topoisomer would be without effect. 

Grover, F.W. 1946. Inductance Calculations. Van Nostrand, U.S. Department of Commerce, Princeton, N.J. Henney, K., ed. 1959. Radio Engineering Handbook, 5th ed. McGraw-Hill, New York. 

Grover E (1962) Inductance Calculations Working Formulas and Tables. Dover, New York. Yang Z, Liu W, Basham E (2007) Inductor modeling in wireless links for implantable electronics. IEEE Trans Magn 43 3851-3860, Oct. 2007. 

In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

Eddy currents and the magnetic flux that is associated to them are proportional to the radial distance of the coil center. The magnetic flux is proportional to the probe induction and consequently to the passing current. The theoretic calculation of this induction is given by the following equation ... 

In Fig. 2a, we compare the modulus of the normal component of the magnetic induction B (r) provided by the sensor and the one calculated by the model. Because of the excitation s shape, the magnetic induction B° (r) is rotation invariant. So, we only represent the field along a radii. It s obvious that the sensor does not give only the normal component B = but probably provides a combination, may be linear, of... 

In Fig. 3a,b are shown respectively the modulus of the measured magnetic induction and the computed one. In Fig. 3c,d we compare the modulus and the Lissajous curves on a line j/ = 0. The results show a good agreement between simulated data and experimental data for the modulus. We can see a difference between the two curves in Fig. 3d this one can issue from the Born approximation. These results would be improved if we take into account the angle of inclination of the sensor. This work, which is one of our future developpements, makes necessary to calculate the radial component of the magnetic field due to the presence of flaw. This implies the calculation of a new Green s function. 

The measure of the inductance variation observed during of the movement of the product in the solenoid generator allows to calculate directly the surface of the straight section of the defect of greater lengtli that the solenoid. More, tlie variation of the resistance allows to determine the height of the defect. 

The inductance variation measure with a defect long than the coil length permit to calculate the defect surface. 

The determined eddy-eurrent parameter is the inductance of the eomplex impedance measured by impedance analyzer at j=100 kHz. Therefore the impulse response function from chapter 4.2.1. is used for calculation. The depth of the cracks is big in comparison to coil size. For presentation the measured and pre-calculated data are related to their maxima (in air). The path X is related to the winding diameter dy of the coil. 

Knowles P J and Meath W J 1987 A separable method for the calculation of dispersion and induction... 

The two ways of learning - deductive and inductive - have already been mentioned. Quite a few properties of chemical compounds can be calculated explicitly. Foremost of these are quantum mechanical methods. However, molecular mechanics methods and even simple empirical methods can often achieve quite high accuracy in the calculation of properties. These deductive methods are discussed in Chapter 7. 

Inductive methods for establishing a correlation between chemical compounds and their properties are the theme of Chapter 9. In many cases, the structure of chemical compounds has to be pre-processed in order to make it amenable to inductive learning methods. This is usually achieved by means of structure descriptors, methods for the calculation of which are outlined in Chapter 8. 

Let us illustrate this with the example of the bromination of monosubstituted benzene derivatives. Observations on the product distributions and relative reaction rates compared with unsubstituted benzene led chemists to conceive the notion of inductive and resonance effects that made it possible to explain" the experimental observations. On an even more quantitative basis, linear free energy relationships of the form of the Hammett equation allowed the estimation of relative rates. It has to be emphasized that inductive and resonance effects were conceived, not from theoretical calculations, but as constructs to order observations. The explanation" is built on analogy, not on any theoretical method. 

Previous studies with a variety of datasets had shown the importance of charge distribution, of inductive effect), of r-electronegativity, resonance effect), and of effective polarizability, aeffi polarizability effect) for details on these methods see Section 7.1). All four of these descriptors on all three carbon atoms were calculated. However, in the final study, a reduced set of descriptors, shown in Table 3-4, was chosen that was obtained both by statistical methods and by chemical intuition. 

The underlying principle of the PEOE method is that the electronic polarization within the tr-bond skeleton as measured by the inductive effect is attenuated with each intervening o -bond. The electronic polarization within /r-bond systems as measured by the resonance or mesomeric effect, on the other hand, extends across an entire nr-system without any attenuation. The simple model of an electron in a box expresses this fact. Thus, in calculating the charge distribution in conjugated i -systems an approach different from the PEOE method has to be taken. 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

Mt 1.7 T (1.7 X 10 G) unless otherwise noted. Data in parentheses calculated on basis of loss (60 Hz)/loss (50 Hz) = 1.34 typical of high induction... 

The alternative of lower cost r-f systems, ie, induction and r-f heating systems at 40 MH2 and below, should be considered (96) (see also Furnaces, electric). More extensive discussions of the economic aspects of microwave systems and payback calculations are available (97,98). 

Dynamometer method (for medium-sized motors, say up to 500 h.p.). The output of an induction motor may be calculated by... 

The naturai zero phase sequence inductive reactance of the grounded neutral may be considered to be too small compared to this and ignored for ease of calculations. Thus the resistance Rq of the grounded neutral circuit may be considered as its impedance, i.e. 

A complete solution for calculating the inductive coupling between a high-voltage line and metal conductors (e.g., pipelines) is possible with the help of series expansion [10,11] and computers. The following section provides advice on these calculations. 

The number of turns for both windings is determined by calculating the minimum inductance and the number of turns for the lowest current output. This is done using Equations 3.32 and 3.29. The other winding will have the identical number of turns. 

Real world values do not allow a capacitor of this large a value. The largest value capacitor that will pass the ac leakage current test is 0.05 pF. This is 50 percent of the calculated capacitor value, so the inductor must be increased 200 percent in order to maintain the same corner frequency. The inductance then becomes 900 pH and the resultant damping factor is 2.5 which is acceptable. The resulting schematic is shown in Figure 3-77. 

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