Transmission line behavior represents a true departure from lumped circuit theory. This is most poignant when we consider the input impedance of a quarter-wavelength shorted transmission line. Circuit theory cannot account for the fact that the input impedance is actually infinite, or an open, rather than a short. But circuit theory can be used as a foundation to understand these effects. This comes about when we expand our circuit theory to account for the distributed nature of the circuit elements.

In circuit theory we implicitly assume that all signals travel throughout the circuit infinitely fast. In reality, signals cannot travel faster than the speed of light. Thus there is always a delay from one point in a circuit to another point. In fact circuit theory is strictly valid in the limit of a truly lumped circuit, or a circuit with zero physical dimension.

Thus distributed effects become important when circuits become electrically large. In time-harmonic problems, we can relate the speed of light to the wavelength, hence the distributed effects become important when physical circuit dimensions approach the wavelength of electromagnetic propagation in the medium ?. For example, a circuit with dimensions of 3 cm in free space is electrically large when the operating frequency approaches f = c/(.1 ?) or about 10 GHz. We have arbitrarily used ?/10 to denote this boundary, whereas in reality the cutoff is application dependent. If the waveforms are non-sinusoidal, then the high-frequency spectral content of the waveform...