TEM wave propagation

It should be noted that all of the theories and formulas in this chapter are based on transverse electromagnetic (TEM) wave propagation. 

The penetration depth is physically defined as the depth for an electromagnetic wave penetrating into a conductor when the wave hits the conductor surface. The physical concept of the penetration depth is very useful to explain the behavior of a current and a voltage on a conductor and also to derive impedance and admittance formulas of various conductor shapes and geometrical configuration. However, it should be reminded that the concept is based on TEM wave propagation and thus is not applicable to non-TEM propagation. Also, remind that it is just an approximation. 

Suppose the waveguide is composed of an unbounded uniform medium of refractive index i.e. effectively free space . The modal fields are then found from Maxwell s equations to be the fields of transverse electromagnetic, or TEM, waves propagating in the z-direction parallel to the waveguide axis. Thus, the propagation constant )S = n k, the longitudinal components satisfy e = h = 0, and the transverse electric and magnetic fields are related by... 

Figure 9.4. Cross-section of corrugated horn. The grooves in the walls of the horn act like shorted A/4 stubs, and as such appear like open circuits to the waves propagating in the horn. As a result the modes in the horn are very similar to free-space TEM modes which minimizes the discontinuity at the edge of the horn, and hence minimizes the sidelobes.

Formulas in Section 1.7.2 show a satisfactory accuracy in comparison with a number of measured results, and these are good enough from the viewpoint of engineering practice similar to the results in the Electrician Handbook. However, the concept of penetration depth is based on the theory of electrostatics within the TEM mode wave propagation. Thus, the formulas cannot be applied, in principle, to electromagnetic phenomena and non-TEM mode wave propagation. 

However, as massive computation resources are, in general, required, NEA methods can be considered useful tools to set reference cases and study specific problems. Also, a perfect conductor assumption in a finite-difference time-domain (FDTD) method, for example, results in the difficulty in analyzing TEM, TM, and TE transition of wave propagation along a lossy conductor above a lossy earth [8,9,43,44]. 

The first four chapters describe a transient analysis/simulation, which is based on a circuit theory derived by a transverse electro-magnetic (TEM) mode of wave propagation. When a transient involves a non-TEM mode of wave propagation, a circuit theory-based approach cannot provide an accurate solution. Typical examples include arcing horn flashover considering... 

The fundamental modes of all waveguides considered in this text are cut off when F = 0. At cutoff the phase velocity of the mode is equal to that of a z-directed plane wave in an unbounded medium of refractive index n, but the modal fields are not TEM waves except in special cases. In general, a significant fraction of a mode s power can propagate within the core at cutoff, i.e. r]j of Eq. (11-24) is nonzero, and the group velocity differs from the phase velocity. Below cutoff, these modes propagate with loss and are the leaky modes of Chapter 24. 

We next consider a waveguide with a nonuniform refractive-index profile n = n(x, y). The propagation constant now depends on the orientation of the electric field, and the modes are no longer TEM waves. In general the modal fields are not solutions of the scalar wave equation but obey the vector wave... 

Figure 3.3. Waveguides for propagating transverse electromagnetic(TEM), transverse magnetic (TM), and transverse electric (TE) waves. Reprinted with the permission from [5],...

There is a very different story to tell when normal flame propagation gives place to detonation. In this phenomenon the expansion caused by the rise in temperature compresses the adjacent layers and thereby heats them suflSciently to bring them to the point of reaction. Something like a wave of adiabatic compression traverses the tem with a velocity of the order of magnitude of that of sound. The detonation wave differs from a soxmd wave in that a fresh evolution of heat occurs in each volume element, whereby the temperature is maintained and the compression intensified. The speed of travel is about three powers of ten greater than that of normal fiame, and for a given explosive mixture has a characteristic and constant value. 

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