Skin effects conductors

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. 

Exciting developments based on electromagnetic induction raced along from that time, giving us the sophisticated products our everyday lives depend on. During most of the period productive uses for eddy current technology were few and few people believed in it as a usefiil tool eddy currents caused power loss in electrical circuits and, due to the skin effect, currents flowed only in the outer surfaces of conductors when the user had paid for all the copper in the cable. The speedometer and the familiar household power meter are examples of everyday uses that we may tend to forget about. The brakes on some models of exercise bicycle are based on the same principle. 

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 a result of the electric field around the conductors the frequency of the system has a very significant bearing on the skin effect. The various curves as established through experiments and, as reproduced in Figures 28.13 (a), (b) and (c) respectively for rectangular, tubular and channel conductors, are thus drawn on the basis. 

If there is more than one current-carrying conductor other than of the same phase, placed adjacent to each other, so that the electric field produced by one can link the other, mutual induction will take place. The magnitude of this will depend upon the amount of current and the spacing between the two. This tends to further distort the selfresistance of the conductor over and above the distortion already caused by the skin effect current distribution... 

However, there may not be an appreciable improvement in the proximity effect between each section, unless the transpositions are increased infinitely, as in the case of a stranded three-phase cable which has continuously twisted conductors and represents an ideal transposition. In addition, there is no change in the skin effect. This arrangement therefore has the purpose primarily of achieving an inductively balanced system and hence a balanced sharing of load and equal phase voltages at the far end. 

Figure 31.11 Skin effect in tubular Isolated conductors in terms of depth of penetration Sp...

Figure 31.17 Curves for skin effect for isolated tubular conductors...

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. 

The capacity of a cable to carry nonlinear loads may be determined as follows. The skin effect factor is calculated first. The skin effect factor depends on the skin depth, which is an indicator of the penetration of the current in a conductor. Skin depth (5) is inversely proportional to the square root of the frequency ... 

Skin effect - The concentration of high frequency alternating currents near the surface of a conductor. 

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... 

Eddy currents will set up their own magnetic fields, opposing the external field. The magnetic field will therefore be attenuated as function of depth (skin effect). The skin depth (depth of penetration) 6 in the case of a uniform, plane electromagnetic wave propagating in a volume conductor with a magnetic permeability p. is ... 

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... 

When a circuit is operating at high frequencies, the skin effect causes the current to be redistributed over the conductor cross-section in such a way as to make most of the current flow where it is encircled by the smallest number of flux lines. This general principle controls the distribution of current, regardless of the shape of the conductor involved. With a flat-strip conductor, the current flows primarily along the edges, where it is surrounded by the smallest amount of flux. 

FIGURE 4.1 Skin effect on an isolated round conductor carrying a moderately high frequency signal. 

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. 

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