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New PDF release: 11.Components, Packaging, and Manufacturing Technology

By John G. Webster (Editor)

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Qualitative discussion of solution in this general form is quite difficult. There are two simplifiations that can be used: (1) low loss approximation, which assumes r Ӷ Ͷᐉ and g Ӷ Ͷc, and (2) low loss conductor on a perfect dielectric, which assumes r Ӷ Ͷᐉ and g ϵ 0. In order to describe the role of conductor losses in signal transmission, we shall use the second approximation as well as the complex algebra relations given in Reference 4 in order to obtain the attenuation coefficient α∼ = r 2Z0 the ‘‘unit time delay’’ τ˜ = β ∼ 1 r =τ 1+ ω 2 2ω 2 and the characteristic impedance 1 r Zc ∼ = Z0 1 + 2 2ω 2 −j r 2ω where Z0 ϭ ͙ᐉ/c is the characteristic impedance and ␶ ϭ ͙ᐉc is the unit time delay of lossless line.

247. , 1990. 2. D. E. , Measurement based large-signal diode modeling system for circuit and device design, IEEE Trans. Microw. , 41: 2211–2217, 1993. 3. S. Ramo, J. R. Whinnery, and T. , p. 817. New York: Wiley, 194. 4. C. S. Chang, Electrical design of signal lines for multilayer printed circuit boards. IBM J. Res. , 32 (5): 647–657, 1988. 5. com/ tmo/hpeeof. 6. T. , Darmstadt, January 1994. 7. , Pittsburgh, 1995. 8. W. J. R. Hoefer and P. So, The Electromagnetic Wave Simulator, New York: Wiley, 1991.

The time-average power dissipated in the actual conductor in the steady ac state is Pc = 1 2 j∗ S j ρ dS where S is the conductor cross section, j is the current density, and j* is the conjugate current density. The calculation of power involves solution of quasi-static field equations. The power dissipated in the model is PM = 1 2 I rac 2 where I is the magnitude of the total current flowing through the conductor and rac is the equivalent ac resistance. The power equivalency (PM ϭ Pc) yields the ac resistance j∗ rac = S j ρ dS I2 which accounts for the skin effect well known in electromagnetism.

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11.Components, Packaging, and Manufacturing Technology by John G. Webster (Editor)


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