Developing the Waveguide from Parallel Lines
You may better understand the transition from ordinary transmission line concepts to waveguide theories by considering the development of a waveguide from a two-wire transmission line. Figure 1-5 shows a section of two-wire transmission line supported on two insulators. At the junction with the line, the insulators must present a very high impedance to ground for proper operation of the line. A low impedance insulator would obviously short-circuit the line to ground, and this is what happens at very high frequencies. Ordinary insulators display the characteristics of the dielectric of a capacitor formed by the wire and ground. As the frequency increases, the overall impedance decreases. A better high-frequency insulator is a quarter-wave section of transmission line shorted at one end. Such an insulator is shown in figure 1-6. The impedance of a shorted quarter-wave section is very high at the open-end junction with the two-wire transmission line. This type of insulator is known as a METALLIC INSULATOR and may be placed anywhere along a two-wire line. Note that quarter-wave sections are insulators at only one frequency. This severely limits the bandwidth, efficiency, and application of this type of two-wire line.
Figure 1-5. - Two-wire transmission line using ordinary insulators.
Figure 1-6. - Quarter-wave section of transmission line shorted at one end.
Figure 1-7 shows several metallic insulators on each side of a two-wire transmission line. As more insulators are added, each section makes contact with the next, and a rectangular waveguide is formed. The lines become part of the walls of the waveguide, as illustrated in figure 1-8. The energy is then conducted within the hollow waveguide instead of along the two-wire transmission line.
Figure 1-7. - Metallic insulators on each side of a two-wire line.
Figure 1-8. - Forming a waveguide by adding quarter-wave sections.
The comparison of the way electromagnetic fields work on a transmission line and in a waveguide is not exact. During the change from a two-wire line to a waveguide, the electromagnetic field configurations also undergo many changes. These will be discussed later in this chapter. As a result of these changes, the waveguide does not actually operate like a two-wire line that is completely shunted by quarter-wave sections. If it did, the use of a waveguide would be limited to a single-frequency wavelength that was four times the length of the quarter-wave sections. In fact, waves of this length cannot pass efficiently through waveguides. Only a small range of frequencies of somewhat shorter wavelength (higher frequency) can pass efficiently.
As shown in figure 1-9, 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.
Figure 1-9. - Labeling waveguide dimensions.
NOTE: This method of labeling waveguides is not standard in all texts. Different methods may be used in other texts on microwave principles, but this method is in accordance with Navy Military Standards (MIL-STDS).
The ability of a waveguide of a given dimension to transport more than one frequency may be better understood by analyzing the actions illustrated in figure 1-10. A waveguide may be considered as having upper and lower quarter-wave sections and a central section which is a solid conductor called a BUS BAR. In view (A), distance mn is equal to distance pq, and both are equal to one quarter-wavelength (l/4).
Figure 1-10A. - Frequency effects on a waveguide. NORMAL OPERATING FREQUENCY
NOTE: Throughout NEETS, 1/4l and l/4 are both used to represent one quarter-wavelength and are used interchangeably. Also, l/2 and 3/2l will be used to represent one half-wavelength and 1 1/2 wavelengths, respectively.
Distance np is the width of the bus bar. If the overall dimensions of the waveguide are held constant, the required length of the quarter-wave sections DECREASES as the frequency increases. As illustrated in view (B), this causes the width of the bus bar to INCREASE. In theory the waveguide could function at an infinite number of frequencies higher than the designed frequency; as the length of each quarter-wave section approaches zero, the bus bar continues to widen to fill the available space. However, in practice, an upper frequency limit is caused by modes of operation, which will be discussed later.
Figure 1-10B. - Frequency effects on a waveguide. INCREASING FREQUENCY
Figure 1-10C. - Frequency effects on a waveguide. DECREASING FREQUENCY
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. In practical applications, the wide dimension of a waveguide is usually 0.7 wavelength at the operating frequency. This allows the waveguide to handle a small range of frequencies both above and below the operating frequency. 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.
Q.9 At very high frequencies, what characteristics are displayed by ordinary