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Plane Waves David Sutrisno Dodi Fikri Enggou Prastyo Galih Ilham

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5.1 General Wave Equation We’ll consider that medium is free of any charge : Material media that are linear, isotropic, homogeneous and time invariant.

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Maxwell’s equation in the point form Gauss’s law : Gauss’s law for magnetic fields: Faraday’s law : Ampere’s circuital law: Constitutive relations:

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This is the Helmholtz wave equation for E

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Time harmonic wave equation Persamaan Helmholtz untuk time- harmonic fields, time derivative menjadi, sehingga :

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Persamaan gelombang Helmholtz umumnya ditulis dalam bentuk : ….(a) Dimana gamma adalah konstanta propagasi yang didefinisikan sebagai berikut : Gamma is equal to a real part (the attenuation, alpha, in nepers per meter) and an imaginary part (the phase constant, or beta, in radians per meter). …… (b)

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Persamaan (a) adalah persamaan Helmholtz untuk time- harmonic medan listrik. Untuk time-harmonic medan magnet persamaannya :

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Intrinsic impedance n (eta) Merupakan perbandingan antara dan Inserting the expression for gamma from (b), we find

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Examples 5.1 Given material with, and and an a wave with f = 1.00 GHz, we want to find

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Propagating Field Relation Example 5.2 Consider the case where And we want to find H.

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5.2 PROPAGATION IN LOSSLESS, CHARGE FREE MEDIA

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5.3 PROPAGATION IN DIELECTRICS

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Permitivitas kompleks

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Loss Tangent

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Low loss dielectrics

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Tabel parameter bahan dielektrik Copper10 Seawater47212 Glass100.01

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Contoh soal In a media with properties s = 0.00964 S/m, e r = 1.0, m r = 100., and f = 100. MHz, a 1.0 mA/m amplitude magnetic field travels in the +x direction with its field vector in the z direction. Find the instantaneous form of the related electric field intensity.

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Propagation In Conductors S.402 | Tuesday, 4 April 2011

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Propagation In Conductors Since for good conductor, the interior bracketed term can be written: And the expressions for α and β are then shown to be equal:

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The intrinsic impedance is approximated by: Since. We can rearrange this equation by considering Leading to

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Can also be written: A consequence ol the large σ is the decrease in the propagation velocity and wavelength. We have: And since

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Current in Conductors The resistor for such a slab is The amplitude decreases as The corresponding current density by Ohm’s law is

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To calculate the current through a surface extending from 0 to infinity in the z direction and of width w in the y direction. We integrate, then we have: We can use this expression and the one for current to find the R for length L of slab of width, that extwnds from z=0 to infinity. We have

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Or Where Changing the limits on our integration for the current:

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Then easy to show that the skin effect resintance can be written: Skin effect for cylindrical (wire or pipe)

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P5.20: Calculate the skin depth at 1.00 GHz for (a) copper, (b) silver, (c) gold, and (d) nickel.

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