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Coupling through Substrate for Millimeter Wave Frequencies
Published in Thomas Noulis, Noise Coupling in System-on-Chip, 2018
Vasileios A. Gerakis, Alkis A. Hatzopoulos
The reduction in the quality of the inductors by utilizing shields has been noted previously [24]. Placing a shield underneath the inductor may dramatically decrease the inductance and increase the resistance of the inductor. This is due to the close distance between the layers of the shield and the inductor, which is approximately 4.2 μm for the cases studied in this chapter. At this close distance, the proximity effect occurs, which alters the paths in which current flows inside the inductor and causes greater resistance and reduced inductance values, leading to the reduction of the quality factor of the inductor. The proximity effect is increased by decreasing the distance between the metals. To test this, the 1-piece shield was placed at the fifth and the seventh metal layer, instead of the second one, expecting to increase the proximity effect, due to the smaller distance between the inductor and the shield, and lead to higher resistance and lower inductance values for the inductor. After simulating these two cases, the anticipated result was observed and led to the reduction of the maximum quality factor value for the two cases, from 18.2 for the inductor with the shield at the second metal layer to 15.4 at the second metal layer, and 12.6 at the seventh layer.
Transient-Voltage Response of Coils and Windings
Published in Leonard L. Grigsby, Electric Power Transformer Engineering, 2017
Proximity effect is the increase in losses in one conductor due to currents in other conductors produced by a redistribution of the current in the conductor of interest by the currents in the other conductors. A method of finding the proximity effect losses in the transformer winding consists of finding a mathematical expression for the impedance in terms of the flux cutting the conductors of an open-winding section due to an external magnetic field. Since windings in large power transformers are mainly built using rectangular conductors, the problem reduces to the study of eddy current losses in a packet of laminations. Lammeraner and Stafl (1966) provide an expression for the flux as a function of frequency in a packet of laminations. It is given in the following equation: Φ=2alμ1+jH0tanh(1+j)ba
Transformer–System Interactions and Modeling
Published in S.V. Kulkarni, S.A. Khaparde, Transformer Engineering, 2017
Frequency-dependent winding conductor properties: Frequency-dependent skin and proximity effects in windings can be handled in a similar way. The effects have been discussed in Section 12.7.5. At frequencies beyond a few kHz, these effects become dominant and the flux concentrates at the conductor surface (the skin effect) and its distribution gets skewed as well (the proximity effect). Effectively, this represents a diamagnetic effect (see Section 12.2.7), in which the flux is repelled from the volume of winding conductors making the relative permeability less than 1 (the conductor material, being either Cu or Al, is nonmagnetic having relative permeability of 1 in the absence of the high frequency effects). The losses due to the skin and the proximity effects can be considered by using the complex permeability based approach. The diamagnetic effect makes the real part of the complex permeability less than 1, whereas its imaginary part represents the losses. The effective complex permeability tensor of a winding conductor can be found by subjecting it to a magnetic field in all three directions [45, 46]. The diamagnetic effects do not contribute significantly at lower frequencies. As the frequency increases to a value at which the core effect becomes negligible (typically for f > 106 Hz), the winding inductance approaches its air core value and the diamagnetic effects become significant. However, if there exists a short-circuited winding during an investigative test such that there is negligible flux in the core, the diamagnetic effects influence the winding inductance even at lower frequencies [47].
Modelling of ferroalloy production processes in the SAF and converter
Published in Mineral Processing and Extractive Metallurgy, 2020
Haijuan Wang, Zhanbing Yang, Hurman Eric
Many of 2D models mentioned here assume the axial symmetry so the calculations can be projected to the 2D radial cross section of the electrode which will simplify the calculation. However, the axisymmetric models only captured the skin effect, yet the proximity effects between electrodes is also important (Herland et al. 2018). As studied by Lupi (2017), there are two effects in an AC furnace, which are the skin effect and the proximity effect. The skin effect causes the currents to accumulate near the surface of conductors while the proximity effect induces currents in the surrounding conductors. The induced eddy currents can have a high intensity and effectively modify the current distribution. Axisymmetric models will capture the skin effect, given that the AC formulation is used, but they will not capture proximity effects between electrodes. In this case, 3D single-electrode models have been investigated numerically.
Optimal design of spiral coil electromagnetic acoustic transducers considering lift-off sensitivity operating on non-ferromagnetic media
Published in Nondestructive Testing and Evaluation, 2018
Wenze Shi, Yunxin Wu, Hai Gong, Tao Zhang, Liangchen Tan, Lei Han, Jiangang Yang, Wei Li
The equivalent impedance of the coil is not only dependent on the electrical conductivity and magnetic permeability of the coil conductor, lift-off and frequency [16,28] but also depends on the electrical conductivity and magnetic permeability of the sample and the backplate near the coil, as well as the plate-to-coil distance. As shown in Figure 11, due to the eddy current effect existing in the backplate and specimen, the current densities and will shift to the coil conductor borders that are near to the plate and specimen, respectively. Because of the proximity effect existing in the conductors, the current densities and will move away from the adjacent borders of the conductors.