6.2 Wireline channels  (Page 3/3)

By using the second of the transmission line equation [link] , we can solve for the current's complex amplitude. Consideringthe spatial region $x> 0$ , for example, we find that $$\frac{d V(x)}{d x}=-(\gamma V(x))=-(\stackrel{\sim }{R}+i\times 2\pi f\stackrel{\sim }{L})I(x)$$ which means that the ratio of voltage and current complex amplitudes does not depend on distance.

A related transmission line is the optic fiber. Here, the electromagnetic field is light, and it propagates down acylinder of glass. In this situation, we don't have two conductors—in fact we have none—and the energy ispropagating in what corresponds to the dielectric material of the coaxial cable. Optic fiber communication has exactly thesame properties as other transmission lines: Signal strength decays exponentially according to the fiber's space constant andpropagates at some speed less than light would in free space. From the encompassing view of Maxwell's equations, the onlydifference is the electromagnetic signal's frequency. Because no electric conductors are present and the fiber is protected byan opaque “insulator,” optic fiber transmission is interference-free.

To summarize, we use transmission lines for high-frequency wireline signal communication. In wireline communication, wehave a direct, physical connection—a circuit—between transmitter and receiver. When we select the transmission linecharacteristics and the transmission frequency so that we operate in the high-frequency regime, signals are not filteredas they propagate along the transmission line: The characteristic impedance is real-valued—the transmissionline's equivalent impedance is a resistor—and all the signal's components at various frequencies propagate at the samespeed. Transmitted signal amplitude does decay exponentially along the transmission line. Note that in the high-frequencyregime the space constant is approximately zero, which means the attenuation is quite small.