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الموضوع: ما هو تفسير ظاهرة Skin effect ؟؟

  1. #1
    Junior Engineer الصورة الرمزية عادل منذر
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    ما هو تفسير ظاهرة Skin effect ؟؟

    بسم الله الرحمن الرحيم
    السلام عليكم ورحمة الله وبركاته

    The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near to the surface of the conductor is greater than that at its core. That is, the electric current tends to flow at the "skin" of the conductor.

    The skin effect causes the effective resistance of the conductor to increase with the frequency of the current.

    Here is the question,
    what is the explan of this phenomenon, and why in round conductors the current concentrate near to the surface???




    And what is the real difference between the isolated conductors and non-isolated with respect to the effect of skin effect??

  2. #2
    عضو فى رابطة مهندسى الكهرباء العرب الصورة الرمزية بندراوي
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    السلام عليكم ورحمة الله وبركاته
    شكراً لك اخي الكريم

  3. #3
    Consultant SCADA & AMI الصورة الرمزية موسى سعيد أبو خطوه
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    شكراً لك مهندس / أبو إمام
    على هذا الموضوع المهم

  4. #4
    Junior Engineer الصورة الرمزية عادل منذر
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    بسم الله الرحمن الرحيم
    السلام عليكم ورحمة الله وبركاته

    Note:
    The skin effect is caused by the self-inductance of the conductor, which causes an increase in the inductive reactance at high frequencies, thus forcing the carriers, i.e., electrons, toward the surface of the conductor. At high frequencies, the circumference is the preferred criterion for predicting resistance than is the cross-sectional area. The depth of penetration of current can be very small compared to the diameter.

    IF there any one can answer my question above (written in red) plz to do that?

  5. #5
    V.I.P Member الصورة الرمزية ahmedhafez
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    الف شكر لك اخي الكريم
    سبحان الله وبحمده سبحان الله العظيم

  6. #6
    ahmed fathy mohammed
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    بسم الله الرحمن الرحيم
    فى البداية أود أن أهنأ جميع السادة المشتركين بحلول شهر رمضان المبارك كل عام و أنتم بخير

    بالنسبة لظاهرة ال skin effect هى ظاهرة مرور التيار الكهربى على الطبقات الخارجية لسطح الموصل و ذلك فى الترددات الكبيرة

  7. #7
    Consultant SCADA & AMI الصورة الرمزية موسى سعيد أبو خطوه
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    السلام عليكم ورحمة الله وبركاتــــــــــــــه

    Your continued donations keep Wikipedia running! Skin effect
    From Wikipedia, the free encyclopedia
    Jump to: navigation, search
    The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. That is, the electric current tends to flow at the "skin" of the conductor.

    *******s
    [hide]
    1 Introduction
    2 Effect on impedance of round wires
    3 Mitigation
    4 Examples
    5 See also
    6 External links
    7 References



    [edit] Introduction
    The skin effect causes the effective resistance of the conductor to increase with the frequency of the current. The effect was first described in a paper by Horace Lamb in 1883 for the case of spherical conductors, and was generalized to conductors of any shape by Oliver Heaviside in 1885. The skin effect has practical consequences in the design of radio-frequency and microwave circuits and to some extent in AC electrical power transmission and distribution systems. Also, it is of considerable importance when designing discharge tube circuits.

    Main article: skin depth
    The current density J in an infinitely thick plane conductor decreases exponentially with depth δ from the surface, as follows:


    where d is a constant called the skin depth. This is defined as the depth below the surface of the conductor at which the current density decays to 1/e (about 0.37) of the current density at the surface (JS). It can be calculated as follows:


    where

    ρ = resistivity of conductor
    ω = angular frequency of current = 2π × frequency
    μ = absolute magnetic permeability of conductor , where μ0 is the permeability of free space (4π×10−7 N/A2) and μr is the relative permeabilty of the conductor.
    The resistance of a flat slab (much thicker than d) to alternating current is exactly equal to the resistance of a plate of thickness d to direct current. For long, thin conductors such as wires, the resistance is approximately that of a hollow tube with wall thickness d carrying direct current. For example, for a round wire, the AC resistance is approximately:


    where

    L = length of conductor
    D = diameter of conductor
    The final approximation above is accurate if D >> d.

    A convenient formula (attributed to F.E. Terman) for the diameter DW of a wire of circular cross-section whose resistance will increase by 10% at frequency f is:



    [edit] Effect on impedance of round wires
    For round wires with radius R on the order of or smaller than d, the assumption of exponential decrease of J with depth δ is no longer valid. In this case, J must be found by solving


    If we transform variables from r to j − 1 / 2r, this equation has the form of a zeroth-order Bessel equation. Using the boundary condition J(R) = JS and considering that J must be finite at r = 0 for a solid wire, the solution to this equation is


    where J0(x) is the zeroth order Bessel function of the first kind, and Ber(x) and Bei(x) are Kelvin functions.

    The total current in the wire may be found by integrating J(r) from 0 to R. It may more easily be found by relating it to the derivative of the electric field at the surface of the wire via its magnetic field. Ampere's Law at the wire surface gives an azimuthal magnetic field


    Maxwell's Equations in cylindrical coordinates gives


    where the electric field E points in the direction of the current. Equating these two functions at r = R gives


    where the prime on the J0 in the numerator indicates a first derivative, and we have used J(r) = σE(r). The impedance in the wire is given by


    where R' and L' are the resistance and reactance per unit length of the wire. Plugging in for E(R) and I gives
    where the fundamental resistance R0 and unitless scaled "radius" are given by

    and
    [edit] Mitigation
    A type of cable called litz wire (from the German Litzendraht, braided wire) is used to mitigate the skin effect for frequencies of a few kilohertz to about one megahertz. It consists of a number of insulated wire strands woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total current to be distributed equally among them. Litz wire is often used in the windings of high-frequency transformers, to increase their efficiency.

    Large power transformers will be wound with conductors of similar construction to Litz wire, but of larger cross-section.

    High-voltage, high-current overhead power transmission lines often use aluminum cable with a steel reinforcing core, where the higher resistivity of the steel core is largely immaterial.

    In other applications, solid conductors are replaced by tubes, which have the same resistance at high frequencies but of course are lighter.

    Solid or tubular conductors may also be silver-plated providing a better conductor (the best possible conductor excepting only superconductors) than copper on the 'skin' of the conductor. Silver-plating is most effective at VHF and microwave frequencies, because the very thin skin depth (conduction layer) at those frequencies means that the silver plating can economically be applied at thicknesses greater than the skin depth.

    [edit] Examples
    In copper, the skin depth at various frequencies is shown below.
    frequency d
    60 Hz 8.57 mm
    10 kHz 0.66 mm
    100 kHz 0.21 mm
    1 MHz 66 µm
    10 MHz 21 µm

    In Engineering Electromagnetics, Hayt points out that in a power station a bus bar for alternating current at 60 Hz with a radius larger than 1/3rd of an inch (8 mm) is a waste of copper, and in practice bus bars for heavy AC current are rarely more than 1/2 inch (12 mm) thick except for mechanical reasons. A possible solution to this problem consists of using cables with multiple insulated conductors. A thin film of silver deposited on glass is an excellent conductor at microwave frequencies.

    [edit] See also
    Proximity effect
    Surface wave
    "The Skin Effect Myth" for Tesla coils
    skin depth

    [edit] External links
    Skin Effect in HiFi Cables
    Skin Effect Relevance in Speaker Cables

    [edit] References
    William Hart Hayt, Engineering Electromagnetics Seventh Edition,(2006), McGraw Hill, New York ISBN 0-07-310463-9
    Paul J. Nahin, Oliver Heaviside: Sage in Solitude, (1988), IEEE Press, New York, ISBN 0-87942-238-6
    Terman, F.E. Radio Engineers' Handbook, McGraw-Hill 1943 -- for the Terman formula mentioned above
    S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, John Wiley & Sons, Inc., New York (1965).
    Retrieved from "http://en.wikipedia.org/wiki/Skin_effect"
    Category: Electronics


    Disclaimers

  8. #8
    Consultant SCADA & AMI الصورة الرمزية موسى سعيد أبو خطوه
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    شكراً لك اخي الكريـــــــــــــــــم
    مهندس / أبو إمام على طرح هذا
    الموضوع .


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    http://www.sayedsaad.com/montada/showthread.php?t=2843

  9. #9
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    رد: ما هو تفسير ظاهرة Skin effect ؟؟

    م/ أبو إمام
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  10. #10
    Junior Engineer الصورة الرمزية khaled ahmed
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