Energy Propagation in Waveguides

Since energy is transferred through waveguides by electromagnetic fields, you need a basic understanding of field theory. Both magnetic (H FIELD) and electric field (E FIELD) are present in waveguides, and the interaction of these fields causes energy to travel through the waveguide. This action is best understood by first looking at the properties of the two individual fields.

E FIELD. - An electric field exists when a difference of potential causes a stress in the dielectric between two points. The simplest electric field is one that forms between the plates of a capacitor when one plate is made positive compared to the other, as shown in view (A) of figure 1-11. The stress created in the dielectric is an electric field.

Electric fields are represented by arrows that point from the positive toward the negative potential. The number of arrows shows the relative strength of the field. In view (A), for example, evenly spaced arrows indicate the field is evenly distributed. For ease of explanation, the electric field is abbreviated E field, and the lines of stress are called E lines.

Figure 1-11A. - Simple electric fields. CAPACITOR

Figure 1-11B - Simple electric fields. TWO-WIRE TRANSMISSION LINE

The two-wire transmission line, illustrated in figure 1-11, view (B), has an instantaneous standing wave of voltage applied to it by the generator. The line is short-circuited at one-wavelength, at the positive and negative voltage peaks, but the arrows, representing each field, point in opposite directions. The voltage across the line varies sinusoidally. Therefore, the density of the E-lines varies sinusoidally.

The development of the E field in a waveguide can be illustrated by a two-wire transmission line separated by several, double quarter-wave sections, called half-wave frames, as illustrated in figure 1-12. As shown, the voltage across the two-wire line varies in a sine-wave pattern and the density of the E field also varies in a sine-wave pattern. The half-wave frames located at high-voltage points (1) and (3) have a strong E field. The frames at the zero-voltage points (2) have no E fields present. Frame (4) has a weak E field and is located at a point between maximum and minimum voltage. This illustration is a buildup to the three-dimensional aspect of the full E field in a waveguide.

Figure 1-12. - E fields on a two-wire line with half-wave frames.

Figure 1-13, view (A), shows the E-field pattern created by a voltage sine wave applied to a one-wavelength section of waveguide shorted at one end. The electric fields are represented by the arrows shown in views (B) and (C). In the top view of view (A), the tip of each arrow is represented by a dot and the tail of each arrow is represented by an X. The E field varies in density at the same sine-wave rate as the applied voltage. This illustration represents the instant that the applied voltage wave is at its peak. At other times, the voltage and the E field in the waveguide vary continuously from zero to the peak value. Voltage and E-field polarity reverse with every reversal of the input. Note that the end view shown in view (B) shows the E field is maximum at the center and minimum near the walls of the waveguide. View (C) shows the arrangement of electromagnetic fields within a three-dimensional waveguide.

Figure 1-13. - E field of a voltage standing wave across a 1-wavelength section of a waveguide.

H FIELD. - The magnetic field in a waveguide is made up of magnetic lines of force that are caused by current flow through the conductive material of the waveguide. Magnetic lines of force, called H lines, are continuous closed loops, as shown in figure 1-14. All of the H lines associated with current are collectively called a magnetic field or H field. The strength of the H field, indicated by the number of H lines in a given area, varies directly with the amount of current.

Figure 1-14. - Magnetic field on a single wire.

Although H lines encircle a single, straight wire, they behave differently when the wire is formed into a coil, as shown in figure 1-15. In a coil the individual H lines tend to form around each turn of wire. Since the H lines take opposite directions between adjacent turns, the field between the turns is cancelled. Inside and outside the coil, where the direction of each H field is the same, the fields join and form continuous H lines around the entire coil.

Figure 1-15. - Magnetic field on a coil.

A similar action takes place in a waveguide. In figure 1-16, view (A), a two-wire line with quarter-wave sections is shown. Currents flow in the main line and in the quarter-wave sections. The current direction produces the individual H lines around each conductor as shown. When a large number of sections exist, the fields cancel between the sections, but the directions are the same both inside and outside the waveguide. At half-wave intervals on the main line, current will flow in opposite directions. This produces H-line loops having opposite directions. In view (A), current at the left end is opposite to the current at the right end. The individual loops on the main line are opposite in direction. All around the framework they join so that the long loop shown in view (B) is formed. Outside the waveguide the individual loops cannot join to form a continuous loop. Thus, no magnetic field exists outside a waveguide.

Figure 1-16A. - Magnetic fields on a two-wire line with half-wave frames.

Figure 1-16B. - Magnetic fields on a two-wire line with half-wave frames.