#### Basics of Waveguides

Figure 1: rectangular waveguide

Figure 1: rectangular waveguide

Figure 1: rectangular waveguide

Waveguides have several advantages over two-wire and coaxial transmission lines. For example, the large surface area of waveguides greatly reduces copper (I²R) losses. Two-wire transmission lines have large copper losses because they have a relatively small surface area. The surface area of the outer conductor of a coaxial cable is large, but the surface area of the inner conductor is relatively small. At microwave frequencies, the current-carrying area of the inner conductor is restricted to a very small layer at the surface of the conductor by an action called skin effect. Skin effect tends to increase the effective resistance of the conductor.

Although energy transfer in coaxial cable is caused by electromagnetic field motion, the magnitude of the field is limited by the size of the current-carrying area of the inner conductor. The small size of the center conductor is even further reduced by skin effect and energy transmission by coaxial cable becomes less efficient than by waveguides.

Waveguides are the most efficient way to transfer electromagnetic energy. Waveguides are essentially coaxial lines without center conductors. They are constructed from conductive material and may be rectangular, circular, or elliptical in shape.

Figure 2: forming a waveguide by adding quarter-wave sections

Figure 2: forming a waveguide by adding quarter-wave sections

Figure 2: forming a waveguide by adding quarter-wave sections

A waveguide is forming by adding quarter-wave sections shorted at one end on each side of a two-wire line. The lines become part of the walls of the waveguide, as illustrated in the following figure. The energy is then conducted within the hollow waveguide instead of along the two-wire transmission line.

If the frequency of a signal is decreased so much that two quarter-wavelengths are longer than the wide dimension of a waveguide, energy will no longer pass through the waveguide. This is the lower frequency limit, or cut-off frequency, of a given waveguide.

The widest dimension of a waveguide is called the „a” dimension and determines the range of operating frequencies.
The narrowest dimension determines the power-handling capability of the waveguide and is called the „b” dimension.

The cut-off wavelength of a rectangular waveguide can be calculated by:

 λcut-off = 2 · a λcut-off = cut-off wavelength [m] a = the widest dimension of the waveguides cross section. [m]
##### Energy Propagation in Waveguides

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. The rate at which the waves travel into the waveguide is constant at approximately 300,000,000 meters per second.

The E field is maximum at the center and minimum near the walls of the waveguide. The density of the E field varies in a sine-wave pattern.

Figure 3: E- field in a waveguide (end view shown, Snapshot, H10- Mode)

Figure 3: E- field in a waveguide (end view shown, Snapshot, H10- Mode)

Figure 3: E- field in a waveguide (end view shown, Snapshot, H10- Mode)

Bild 4: Wanderwelle im Hohlleiter

Figure 4: Traveling wave in a wave guide

Figure 4: Traveling wave in a wave guide

Figure 5: H- field in a waveguide (top view shown, snapshot)

Figure 5: H- field in a waveguide (top view shown, snapshot)

Figure 5: H- field in a waveguide (top view shown, snapshot)

The development of the E field in a waveguide happens by double quarter-wave sections, called half-wave frames.

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.

The losses into a waveguide depends of the frequency. The required dimension of the waveguide decreases as the frequency increases.

The wide, or „a”, dimension determines the frequency range of the waveguide, and the narrow, or „b”, dimension determines power-handling capability. The physical size of the waveguides depends of the traveling frequency. (The waveguides becomes too great for use at frequencies less than 1000 megahertz.)

The „b” dimension is governed by the breakdown potential of the dielectric, which is usually air. Dimensions ranging from 0.2 to 0.5 wavelength are common for the „b” sides of a waveguide. To improve the power-handling capability it is inside the hollow leader an air pressure is produced which one doesn't let any humidity penetrate into the waveguide.

External link to: Technical information for Waveguides

Publisher: Christian Wolff
Text is available under the GNU Free Documentation License, and the