As mentioned previously, voltages and currents are no longer spatially constant on the geometric scale of interest to RF circuit design engineers. As a consequence, Kirchoff’s voltage and circuit laws cannot be applied over the macroscopic line dimension. However, this problem can be circumvented when the transmission line is broken down into smaller (in the limit infinitesimally small) segments. Those segments are still large enough to contain all relevant electric characteristics such as loss, as well as inductive and capacitive line effects. The main advantage of this reduction to a microscopic representation is the fact that a distributed parameter description can now be introduced whose analysis follows Kirchoff’s laws on a microscopic scale. Besides providing an intuitive picture, the approach also lends itself to a two-part network analysis. To develop an electric model, let us consider once again a two-wire transmission line. As indicates, the transmission line is aligned along the z-axis and segmented into elements of length $\Delta$z.

If we focus our attention on a single section residing between z and z + $\Delta$z we notice that each conductor (1 and 2) is described as a series connection of resistor and inductor ($R_1$, L1, and R2, L2). In addition, the charge separation created by conductors 1 and 2 gives rise to a capacitive effect denoted by C. Recognizing that all dielectrics suffer losses, we need to include a conductance G. Again attention is drawn to the fact that all circuit parameter R, L, C and G are given in values per unit length. Similar to the two-wire transmission line, the coaxial cable in figure 2.11 can also be recognized as a two conductor configuration with the same lumped parameter representation.

A generic form of an electric equivalent circuit is developed as shown in figure 2-12, where the resistances and inductances of the two conductors are usually combined into single elements. This representation is not suitable for all transmission line applications. For instance, when dealing with transient wave propagation and signal integrity issues of inductive and capacitive crosstalks, it generally makes more sense to retain the parameter representation shown in figure2.11. However, for our treatment of transmission lines we will exclusively use the model shown in fig.2.12

To summarize the advantages of the electric circuit representation, we

• Provides a clear intuitive physical picture
• Lends itself to a standardized two-port network representation
• Permits the analysis with Kirchhoff’s voltage and current laws
• Provides building blocks that allow the expansion from microscopic to macroscopic forms

There are also two significant disadvantages worth nothing:

• It is basically a one-dimensional analysis that does not take into account field fringing in the plane orthogonal to the direction of propagation and therefore cannot predict interference with other component of the circuit.
• Material-related nonlinearities due to hysteresis effects are neglected.

Despite these disadvantages, the equivalent circuit representation is a powerful mathematical model for describing the characteristics transmission line behavior. With this model in place, we can now embark on developing generalized transmission line equations.