Waveguides

Author: J.B. Hoag

An electromagnetic wave, traveling outward from a transmitter on the earth's surface, is guided by a double layer of conducting materials, i.e., the ground and the ionosphere, to curve and pass beyond the bulge of the earth. Let us imagine that we shall build a small scale model of this double conducting layer, out of sheets of tin, galvanized iron, brass, or copper. We must use a tiny dipole antenna and a very short wavelength. For simplicity, we shall not curve the metal plates into spherical form but shall leave them flat. It might profit us to keep the waves from spreading sideways, by using a second set of plates at right angles to the first. This would give us a long rectangular metal box which would confine the waves and, by reflecting them back and forth, as in Fig. 38 N, force them to travel down the length of the box. The waves would be guided; this is a waveguide. A cylindrical or an elliptical metal pipe may also be used.

Fig. 38 N. Two shapes of conducting surfaces which will guide electromagnetic waves

It is necessary to understand that the same guide can operate with several types or modes of vibration of the three-dimensional electric and magnetic field patterns. Fig. 38 O shows various methods of feeding energy into a rectangular waveguide, together with the resultant field patterns of the E₁₁ and the H₀₁ waves inside the guide.

Fig. 38 O. Methods of launching electromagnetic waves into a rectangular waveguide, together with the E11 and H01 field patterns. (See references to Barrow at end of chapter)

The electric fields are shown by solid lines, the magnetic fields by dotted lines or by small dots and circles. These are the patterns at a given instant; actually, the waves are in rapid motion down the guide at velocities somewhat less than that of light.

Fig. 38 P. Various feeding methods and the resultant field patterns for a cylindrical waveguide. Electric lines of force, solid; magnetic lines, black dots when toward observer, small circles when away. (See references to Southworth at end of chapter)

In Fig. 38 P, the structures for launching waves down a cylindrical waveguide are shown, together with the corresponding field patterns, in the respective cases.

The same electrode structures shown in Figs. 38 O and 38 P can be used for the reception of their corresponding waves, the oscillator being replaced by a crystal or diode detector.

Fig. 38 Q. A receiver for the H1 type of waves in a cylindrical guide. (Southworth; Bell System Tech. Jr. April, 1936)

Figure 38 Q shows a detector mounted in a resonant cavity of a cylindrical guide for the reception of H₁ waves. In order that the reception shall be strong, the electrode used must not only be of the same type as that used at the transmitter, but it must also be oriented in the same direction. Different types of waves may thus be transmitted down the same tube and sorted from each other at the receiving end.

It is only possible to transfer energy down a waveguide when the wavelength is sufficiently short. As shorter and shorter wavelengths are applied to the end of a guide, a critical value or cutoff wavelength is found. All waves shorter than this will pass down the tube, all longer waves will not; the system acts like a high-pass filter. Table 38 A gives the equations for the cutoff frequencies. It will be observed that the wavelength must be approximately equal to or less than the opening of the pipe before energy will pass down the guide.

Table 38 A - CUTOFF WAVELENGTH
Cylindrical Waveguides	Rectangular Waveguides
λ= E0* 1.31 d√(με) E1 0.82 d√(με) H0 0.82 d√(με) H1 1.71 d√(με)	λ= When a = b E11 2ab/√(a2 + b2) 1.41 a E12 2ab/√(4a2 + b2) 0.9 a H01* 2b 2.0 a H11 2ab/√(a2 + b2) 1.41 a
d = diameter of pipe	a, b =inside height and width of rectangle μ = ε = 1
με = permeability and dielectric constant of material inside the guide. For air μ = ε = 1 λ = wavelength in free space. Inside the guide, the waves are shorter, due to their lower velocity.
* Frequently used modes of vibration.

When sufficiently short waves are used that the guide is reasonably small and not too costly, waveguides prove to be unusually satisfactory as paths for electromagnetic energy because their losses can be made smaller (by proper operation) than with other forms of conducting systems. The loss of energy in a waveguide depends on the mode of vibration and on the frequency. A typical attenuation curve is shown in Fig. 38 R.

Fig. 38 R. Loss in a square waveguide, H 01 waves

Also, the loss depends on the metal used in the construction of the guide. In the case of an E_o wave, the minimum attenuation in decibels per mile, is as follows: copper, 1.9; aluminum, 2.5; lead, 6.5; iron, 45. The value of 1.9 just cited may be compared with that of 8.3 for a two-and-one-half inch diameter copper coaxial line, and of 25 for a No. 6-gauge open line.

The same guide may be used for the simultaneous and independent transmission of several waves. At the receiving end, short waves can be separated from longer ones by using a constriction in the waveguide, or a diaphragm with a hole in it. Only waves shorter than that permitted by the cutoff values of Table 38 A will pass beyond the constriction or hole. Also, filtering action may be accomplished so as to pass one mode of vibration and restrict another. For example, if a series of radial wires are mounted in a plane at right angles to the axis of a cylindrical tube, the E_o waves will be reflected whereas the H_o waves will pass through and continue on down the tube. If a series of parallel wires are mounted transversely across the tube, H₁ waves will pass through at one position of the wires but will be cut off when the wires have been rotated 90 degrees. An examination of Fig. 38 P will show that this filtering action occurs when the electric vector of the electromagnetic wave is parallel to the conducting wires of the filter.

If the end of a waveguide is left open, radiation will take place into the space beyond the mouth of the guide. The end of the guide may be flared in a simple manner, as in Fig. 38 S, or in more complicated fashions, such as the exponential horn, in order to obtain either broadcast or highly directional radiation of microwave energy.

Fig. 38 S. An electromagnetic horn and its field patterns for various flare angles Φ. (See reference to Barrow at end of chapter)