# 4.11: Summary


Design is an iterative process and initial RF design is based on frequency-independent characteristics. For a transmission line, quantities such as the characteristic impedance, effective permittivity, phase and group velocities, and the RLGC parameters are taken as fixed. The RLGC parameters are the basis of the simplest lumped-element circuit model of a transmission line. Each of the components of this model will vary with frequency. The resistance per unit length, $$R$$, increases with frequency as charges concentrate on the surface of conductors and charges bunch (i.e., become less spread out). Both of these effects are due to the finite time it takes to transmit the EM signal that rearranges charges to support an alternating wave.

An EM signal on a transmission line is described by Maxwell’s equations and there can be many possible solutions depending on the boundary conditions. With transmission lines and other microwave structures such as resonators these are called modes. All transmission lines have at least two solutions, the forward- and backward-traveling waves. While strictly these are also modes, this classification is avoided by microwave engineers. Microwave engineers identify modes as different solutions to Maxwell’s equations that, for transmission lines, are different orientations of the fields largely in the transverse direction to propagation. Each mode will, in general, have forward- and backward-traveling components. A two-conductor transmission line is designed to have dimensions that are small enough that there is only one mode, or else special precautions are taken to avoid a second mode being established. Sometimes multimoding is desirable. If these multimoded structures are used there are strict design criteria that enable the special functionality that is made available to be exploited. Multimoding sets the upper bound on the frequency of operation of most transmission line structures.

The most popular microwave transmission lines—microstrip, stripline and CPW—can all support multiple modes, but most are cut off by keeping transverse dimensions small with respect to a wavelength. When it is possible for a second (or higher-order) mode to exist, whether that mode is generated depends on the coupling mechanism between modes. This coupling mechanism is a discontinuity, which of course is common if circuit structures are to be incorporated. Stripline and CPW can support a second mode at quite low frequencies. With stripline the dominant second mode is the parallel-plate waveguide mode supported by the two ground planes of stripline.

A microwave designer must always be aware of frequency dependence and multimoding and choose dimensions to avoid their occurrence except when the use is intentional and controlled.

This page titled 4.11: Summary is shared under a not declared license and was authored, remixed, and/or curated by Michael Steer.