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Transmission Lines in Digital Systems for EMC Practitioners by Clayton R. Paul

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Chapter 1

Transmission Lines: Physical Dimensions vs. Electric Dimensions

With the operating frequencies of today's high-speed digital and high-frequency analog systems continuing to increase into the GHz (1GHz = 109 Hz) range, previously-used lumped-circuit analysis methods such as Kirchhoff's laws will no longer be valid and will give incorrect answers. Physical dimensions of the system that are “electrically large” (greater than a tenth of a wavelength) must be analyzed using the transmission-line model. The wavelength, img, of a single-frequency sinusoidal current or voltage wave is defined as img where img is the velocity of propagation of the wave on the system's conductors, and f is the cyclic frequency of the single-frequency sinusoidal wave on the conductor. Velocities of propagation on printed circuit boards (PCBs) lie between 60 and 100% of the speed of light in a vacuum, img. A 1-GHz single-frequency sinusoidal wave on a pair of conductors of total length img will be one wavelength for

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