If the two-wire line and the half-wave frames are developed into a waveguide that is closed at both ends (as shown in view (B) of figure 1-16), the distribution of H lines will be as shown in figure 1-17. If the waveguide is extended to 1 1/2l, these H lines form complete loops at half-wave intervals with each group reversed in direction. Again, no H lines can form outside the waveguide as long as it is completely enclosed.
Figure 1-17. - Magnetic field pattern in a waveguide.
Figure 1-18 shows a cross-sectional view of the magnetic field pattern illustrated in figure 1-17. Note in view (A) that the field is strongest at the edges of the waveguide where the current is highest. The minimum field strength occurs at the zero-current points. View (B) shows the field pattern as it appearsl/4 from the end view of the waveguide. As with the previously discussed E fields, the H fields shown in figures 1-17 and 1-18 represent a condition that exists at only one instant in time. During the peak of the next half cycle of the input current, all field directions are reversed and the field will continue to change with changes in the input.
Figure 1-18. - Magnetic field in a waveguide three half-wavelengths long.
BOUNDARY CONDITIONS IN A WAVEGUIDE. - The travel of energy down a waveguide is similar, but not identical, to the travel of electromagnetic waves in free space. The difference is that the energy in a waveguide is confined to the physical limits of the guide. Two conditions, known as BOUNDARY CONDITIONS, must be satisfied for energy to travel through a waveguide.
The first boundary condition (illustrated in figure 1-19, view (A)) can be stated as follows:
For an electric field to exist at the surface of a conductor it must be perpendicular to the conductor.
Figure 1-19A. - E field boundary condition. MEETS BOUNDARY CONDITIONS
The opposite of this boundary condition, shown in view (B), is also true. An electric field CANNOT exist parallel to a perfect conductor.
Figure 1-19B. - E field boundary condition. DOES NOT MEET BOUNDARY CONDITIONS
The second boundary condition, which is illustrated in figure 1-20, can be stated as follows:
For a varying magnetic field to exist, it must form closed loops in parallel with the conductors and be perpendicular to the electric field.
Figure 1-20. - H field boundary condition.
Since an E field causes a current flow that in turn produces an H field, both fields always exist at the same time in a waveguide. If a system satisfies one of these boundary conditions, it must also satisfy the other since neither field can exist alone. You should briefly review the principles of electromagnetic propagation in free space (NEETS, Module 10, Introduction to Wave Propagation, Transmission Lines, and Antennas). This review will help you understand how a waveguide satisfies the two boundary conditions necessary for energy propagation in a waveguide.
WAVEFRONTS WITHIN A WAVEGUIDE. - Electromagnetic energy transmitted into space consists of electric and magnetic fields that are at right angles (90 degrees) to each other and at right angles to the direction of propagation. A simple analogy to establish this relationship is by use of the right-hand rule for electromagnetic energy, based on the POYNTING VECTOR. It indicates that a screw (right-hand thread) with its axis perpendicular to the electric and magnetic fields will advance in the direction of propagation if the E field is rotated to the right (toward the H field). This rule is illustrated in figure 1-21.
Figure 1-21. - The Poynting vector.
The combined electric and magnetic fields form a wavefront that can be represented by alternate negative and positive peaks at half-wavelength intervals, as illustrated in figure 1-22. Angle is the direction of travel of the wave with respect to some reference axis.
Figure 1-22. - Wavefronts in space.
If a second wavefront, differing only in the direction of travel, is present at the same time, a resultant of the two is formed. The resultant is illustrated in figure 1-23, and a close inspection reveals important characteristics of combined wavefronts. Both wavefronts add at all points on the reference axis and cancel at half-wavelength intervals from the reference axis. Therefore, alternate additions and cancellations of the two wavefronts occur at progressive half-wavelength increments from the reference axis. In figure 1-23, the lines labeled A, C, F, and H are addition points, and those labeled B, D, E, and G are cancellation points.
Figure 1-23. - Combined wavefronts.
If two conductive plates are placed along cancellation lines D and E or cancellation lines B and G, the first boundary condition for waveguides will be satisfied; that is, the E fields will be zero at the surface of the conductive plates. The second boundary condition is, therefore, automatically satisfied. Since these plates serve the same purpose as the "b" dimension walls of a waveguide, the "a" dimension walls can be added without affecting the magnetic or electric fields.