Bhag Singh Guru

Electromagnetic Field Theory Fundamentals: Waveguides and cavity resonators

Introduction In our discussion of transmission lines, we pointed out that the resistance of a conductor increases with an increase in the signal frequency, leading to an increase in power loss along the line. This power loss becomes intolerable at microwave frequencies (in the GHz range) and makes the transmission line almost impractical. At such high frequencies hollow conductors, known as waveguides, are employed to guide electrical signals efficiently. Figure 10.1 shows a typical waveguide assembly. In the study of transmission lines with at least two conductors, we found that the propagating wave has field components in the transverse direction and is referred to as the transverse electromagnetic (TEM) wave. However, as a waveguide consists of only one hollow conductor, we do not expect it to support the TEM wave. In this chapter, we show that a waveguide can support the other two types of waves, the transverse magnetic (TM) and the transverse electric (TE) waves. These waves can exist inside a hollow conductor under certain conditions. TM and TE waves can also propagate in a region bounded by a parallel-plate transmission line, in which case the two conducting plates are said to form a parallel-plate waveguide . The propagation of an electromagnetic wave inside a waveguide is quite different than the propagation of a TEM wave. When a wave is introduced at one end of the waveguide, it is reflected from the wall of the waveguide whenever it strikes it.

Electromagnetic Field Theory Fundamentals: Electromagnetic field theory

Introduction What is a field? Is it a scalar field or a vector field? What is the nature of a field? Is it a continuous or a rotational field? How is the magnetic field produced by a current-carrying coil? How does a capacitor store energy? How does a piece of wire (antenna) radiate or receive signals? How do electromagnetic fields propagate in space? What really happens when electromagnetic energy travels from one end of a hollow pipe (waveguide) to the other? The primary purpose of this text is to answer some of these questions pertaining to electromagnetic fields. In this chapter we intend to show that the study of electromagnetic field theory is vital to understanding many phenomena that take place in electrical engineering. To do so we make use of some of the concepts and equations of other areas of electrical engineering. We aim to shed light on the origin of these concepts and equations using electromagnetic field theory. Before we proceed any further, however, we mention that the development of science depends upon some quantities that cannot be defined precisely. We refer to these as fundamental quantities; they are mass (m) , length (l) , time (t) , charge (q) , and temperature ( T ). For example, what is time? When did time begin? Likewise, what is temperature? What is hot or cold? We do have some intuitive feelings about these quantities but lack precise definitions. To measure and express each of these quantities, we need to define a system of units.

Electromagnetic Field Theory Fundamentals: Plane wave propagation

Introduction We have stated a this in Chapter 7 and we state it again: Maxwells equations contain all the information necessary to characterize the electromagnetic fields at any point in a medium. For the electromagnetic (EM) fields to exist they must satisfy the four Maxwell equations at the source where they are generated, at any point in a medium through which they propagate, and at the load where they are received or absorbed. In this chapter, we concentrate mainly on the propagation of EM fields in a source-free medium. As the fields must satisfy the four coupled Maxwell equations involving four unknown variables, we first obtain an equation in terms of one unknown variable. Similar equations can then be obtained for the other variables. We refer to these equations as the general wave equations. We will show in Chapter 11 that the fields generated by time-varying sources propagate as spherical waves. However, in a small region far away from the radiating source, the spherical wave may be approximated as a plane wave, that is, one in which all the field quantities are in a plane normal to the direction of its propagation (the transverse plane). Consequently, a plane wave does not have any field component in its direction of propagation (the longitudinal direction). We first seek the solution of a plane wave in an unbounded dielectric medium and show that the wave travels with the speed of light in free space.