Real Schematics (Part 2)

Transmission Lines Part 1 of this article series on the world of real schematics ended with a look at wiring. Picking up where that left off, this article looks at real schematics from a transmission line perspective. George shows how transmission line characteristics can be represented by breaking them into schematic elements. Our excursion into the world of real schematics ended last month (December, Circuit Cellar 341) with wiring. We saw that as long as an AC source connects to a load by conductors shorter than one eighth of the source’s signal wavelength λ, the schematic diagram Figure 1a with lumped component values is a fair rendering of the circuit. The source wavelength λ in meters is approximately c/f where c is the speed of light in meters/second and f is the signal’s frequency in Hertz. The speed of light is slightly less than 300 × 106 meters/second—or 299.792458 × 106 m/s to be precise. In engineering and many sciences 300 × 106 m/s is considered a good approximation. FIGURE 1 - The derivation of a transmission line All around us you can see power cords, coaxial TV and computer cables, twin leads, telephone wires and many other wired interfaces. Once their length comes close to one-eighth of the shortest wavelength they carry, they begin to take on transmission line characteristics. A schematic rendering of such a circuit is shown by Figure 1b. Keep in mind, though, that λ/8 is an empirical value at which the transmission line aspects could begin to be observed. It’s not a precise wavelength at which the circuit characteristics suddenly change. You can describe a transmission line as consisting of an infinite number of infinitesimal resistors, inductors and capacitors spread along its entire length as depicted by Figure 1b. Letter G stands for conductance, which is the reciprocal of resistance or 1/R. The unit of conductance is Siemens expressed by symbols S, Ω-1, ℧&nbs