Conductor resistance skin effect

Resistive losses within the current-carrying conductors, i.e. within the electrical circuit itself, caused by the leakage flux (Figure 2.6), as a result of the deep conductor skin effect. This effect increases conductor resistance and hence the losses. For more details refer to Section 28.7. 

In a d.c. system the current distribution through the cross-section of a current-canying conductor is uniform as it consists of only the resistance. In an a.c. system the inductive effect caused by the induced-electric field causes skin and proximity effects. These effects play a complex role in determining the current distribution through the cross-section of a conductor. In an a.c. system, the inductance of a conductor varies with the depth of the conductor due to the skin effect. This inductance is further affected by the presence of another current-carrying conductor in the vicinity (the proximity effect). Thus, the impedance and the current distribution (density) through the cross-section of the conductor vaiy. Both these factors on an a.c. system tend to increase the effective... 

The phenomenon uneven distribution of current within the same conductor due to the inductive effect is known as the skin effect and results in an increased effective resistance of the conductor. The ratio of a.c. to d.c. resistance, R JR. is the measure of the skin effect and is known as the skin effect ratio . Figure 28.13(a) illustrates the skin elTect for various types and sizes of aluminium in flat sections. For easy reference, the skin effects in isolated round (solid or hollow) and channel conductors (in box form) are also shown in Figures 28.13(b) and (c) respectively. 

Since the skin effect results in an increase in the effective resistance of the busbar system it directly influences the heating and the voltage drop of the conductor and indirectly reduces its current-carrying capacity. If is the resistance as a result of this effect then the heat generated... 

As frequency increases, the current is forced out of the center of the conductor toward its periphery, a phenomenon known as the skin effect . A measure of the depth of penetration of the current into the conductor is the skin depth, defined as 8 = V(p/ir/p,), where / is the frequency and x is the conductor permeability (1.26 X 10 6 H/m for nonmagnetic conductors). For copper, the skin depth is 2 p,m at 1 GHz. When the skin depth is less than the conductor thickness, the line resistance becomes greater than the dc resistance. 

Current flowing in a cable produces PR losses. When the load current contains harmonic content, additional losses are introduced. To compound the problem, the effective resistance of the cable increases with frequency because of the phenomenon known as skin effect. Skin effect is due to unequal flux linkage across the cross section of the conductor which causes AC currents to flow only on the outer periphery of the conductor. This has the effect of increasing the resistance of the conductor for AC currents. The higher the frequency of the current, the greater the tendency of the current to crowd at the outer periphery of the conductor and the greater the effective resistance for that frequency. 

Qualitatively different low-frequency, shielding,and skin effect losses were found depending upon the value of the classical skin depth for the transverse resistivity of the composite, in comparison with the twist length and conductor radius. This general set of solutions agrees with losses calculated for particular field situations... 

At high frequencies, the surface of the insulator may have a different resistivity from the bulk of the material owing to impurities absorbed on the surface, external contamination, or water moisture hence, electric current is conducted chiefly near the surface of the conductor (i.e., skin effect). The depth, S, at which the current density falls to 1/e of its value at the surface is called the skin depth. The skin depth and the surface resistance are dependent upon the AC frequency. The surface resistivity, R, expressed in 2, is the DC sheet resistivity of a conductor having a thickness of one skin depth ... 

The effective resistance offered by a given conductor to radio frequencies is considerably higher than the ohmic resistance measured with direct current. This is because of an action known as the skin effect, which... 

At dc, current in a conductor flows with uniform density over the cross-section of the conductor. At high frequencies, the current is displaced to the conductor surface. The effective cross-section of the conductor decreases and the conductor resistance increases because of the skin effect. 

The loaded Q is determined by the plate load impedance and output circuit capacitance. Unloaded Q is determined by the cavity volume and the RF resistivity of the conductors resulting from the skin effect. For best cavity efficiency, the following conditions are desirable ... 

For a lossy transmission fine due to parasitic resistance of on-chip interconnects, an exponential attenuating transfer function can be applied to the signal transfer at any point on the transmission line. The rate of the attenuation is proportional to the unit resistance of the interconnect. When operating frequency increases beyond a certain level, the on-chip transmission media exhibits the skin effect in which the time-varying currents concentrate near the skin of the conductor. Therefore, the unit resistance of the transmission media increases dramatically. 

Structural steel, compared with copper, is a poor conductor at any frequency. At DC, steel has a resistivity 10 times that of copper. As frequency rises, the skin effect is more pronounced because of the magnetic effects involved. A no. 6 copper wire can have less RF impedance than a 12-in steel I beam. Furthermore, because of their bolted, piecemeal construction, steel racks and building members should not be depended upon alone for circuit returns. 

Effective resistance The increased resistance of a conductor to an alternating current resulting from the skin effect, relative to the direct-current resistance of the conductor. Higher fi equencies tend to travel only on the outer skin of the conductor, whereas dc flows uniformly through the entire area. 

The field does not penetrate the conductor uniformly and therefore the largest current flow is at the periphery of the plasma. This is the so-called skin effect and coupled with a suitable gas-flow geometry it produces an annular or doughnut-shaped plasma. Electrically, the coil and plasma form a transformer with the plasma acting as a one-turn coil of finite resistance. 

Magnet coil losses represent the summation of resistive losses in each volume element of the coil. Each volume element dissipates electrical energy at a rate determined by the product of the volume resistivity of the conducting material and the square of current density, i.e., as pj . We will assume that either the current varies sufficiently slowly in time or that the conductors are sufficiently well subdivided that skin effects may be ignored. (This assumption is, however, not without its economic consequences.) The total energy dissipated by the coil is then simply the integral of pj over the volume of the magnet ... 

Therefore, when using round wires, if we choose the diameter as twice the skin depth, no point inside the conductor will be more than one skin depth away from the surface. So no part of the conductor is unutilized. In that case, we can consider this wire as having an ac resistance equal to its dc resistance — there is no need to continue to account for high-frequency effects so long as the wire thickness is chosen in this manner. 

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