The specialized branch of mathematics known as topology studies obscure relationships between seemingly unrelated items. For example, a topologist might point out that a coffee cup and a doughnut are topologically equivalent, both being solid objects with a single hole.
Topological equivalence between two objects means that if the first object were made from an infinitely stretchy, rubber-like substance, you could stretch or mold the first object into the shape of the other object without tearing any new holes or closing off any existing holes.
You can extend the concept of equivalence relations to the field of digital communications. By changing the impedance, stretching the distance, or adjusting the bandwidth, you can often mold one problem into a form that looks a lot like another problem.
Look, for example, at the relationship between the telegraph and the telephone (Figure 1). Both use copper-based transmission media but at varying distances and speeds. Telegraph systems operate with simple circuitry at distances of hundreds of miles and at an average bandwidth of perhaps 10 or 20 baud. If you want your telegraph to go faster, the required circuitry gets more complex (Reference 1).
The telephone uses the same type of wiring, but, unlike the telegraph, it uses the wiring at a greatly reduced distance and correspondingly higher bandwidth.
Plain-old-telephone-service connections operate with simple circuitry at maximum distances of 1 mile and maximum bandwidths of 3 kHz. If you want your telephone line to operate at digital-subscriber-line speeds, the required circuitry gets more complex—just like in the telegraph problem. The type of wire, the distance, and the sophistication of your circuitry determine the achievable speed of applications such as the telegraph and the telephone. The shorter the wire, the greater it's natural bandwidth. The more sophisticated the circuitry, the closer you can push toward full use of the ultimate bandwidth of your channel. The physical principles controlling the behavior of the wires are the same in both telephone and telegraph applications; they just operate at different points on the speed-distance curve. You can usually scale up the speed of any copper-based communications system by scaling down its length.
The speed-distance scaling principle applies equally well to wiring used in LAN applications. In the early 1980s, several companies noticed that, although telephone service was required to operate at distances as great as 1 mile, in-building data wiring needed to go only about 100 m. The available bandwidth of unshielded-twisted-pair-type telephone wiring at that short distance is enormous, as demonstrated by the ever-popular 10-Mbps Ethernet 10BaseT, 100-Mbps Fast Ethernet 100BaseTX, and 1000-Mbps Gigabit Ethernet 1000BaseT. Shrinking the wire distances from a telephonecentric 1-mile requirement to a datacentric 100m gets you easily from telephone speeds to 10 Mbps. To get to 100 Mbps, you use better cabling (Category 5). To get to 1000 Mbps, you use four pairs of Category-5 cabling and advanced adaptive-equalization techniques.
Going further, you can apply the speed-distance-scaling principle to pc-board traces. They are transmission lines too, just like in the telegraph, telephone, and LAN applications. Being shorter, they of course work at higher speeds. For applications that reach about 1 GHz at 12-in. distances, simple CMOS totem-pole switching circuitry works fine. Applications faster than 1 GHz or longer than 12 in. require advanced circuitry along with a solid understanding of trace impedance, terminations, crosstalk, high-frequency losses, and, sometimes, multilevel signaling and adaptive equalization.
Transmission-line theory will next become important on chip. Today's chip-layout software takes into account the RC propagation delays of major bus structures and clock lines. In tomorrow's designs, at even higher speeds, the full RLC nature of the on-chip transmission channels will emerge. Ringing, terminations, and adaptively equalized multilevel signaling will all eventually appear on chip, just as they do on board. It's inevitable. If you want to know what will happen on chip tomorrow, look at pc-board design today; the problems are equivalent.
 Israel, Paul, Edison: A Life of Invention, John Wiley & Sons, 1998.