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, 
, of a single-frequency sinusoidal current or voltage wave is defined as 
where 
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, 
. A 1-GHz single-frequency sinusoidal wave on a pair of conductors of total length 
will be one wavelength for
