# Technical techniques: A primer for transmission lines

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One of the most fascinating types of transmission lines is the waveguide. Radio waves — if confined within a hollow tube of conducting material and if the dimensions of the tube are appropriate for the frequency of operation — will travel the length of the tube with little loss. Such a tube is a waveguide. It comes in three physical forms: rectangular, elliptical and circular.

### Rigid waveguide

Rectangular is the most common waveguide form in the radar industry. Elliptical is used for terrestrial microwave. Circular was most popular for the long-haul, high density, point-to-point microwave service such as AT&T. Radio energy travels within this confined area by reflecting off the sidewalls of the guide. The reflections occur so that the electric and magnetic fields of the waves set up a definite pattern within the guide. These patterns are called modes.

In addition, every mode has a cutoff frequency. This is the lowest frequency that will propagate down the waveguide. The lowest frequency that can travel through the waveguide is called the dominant mode. A dominant mode is the frequency that has a wavelength equal to twice the width of the guide. This mode has the simplest field pattern and is not as susceptible to impedance mismatches and reflections as the more complex modes. Usually, a rectangular guide has a width greater than half a wavelength but no more than one wavelength, and the height is half this width.

A rectangular waveguide can be thought of as a special case of a two-wire transmission line supported by quarterwave shorted stubs as shown in Figure 1. The voltage is a maximum at the center point corresponding to the imaginary two wires and a voltage minimum at the shorted ends.

Figure 2 shows the transverse electrical TE 10 mode. It’s characterized by the fact that the electric vector (E vector) is always perpendicular to the direction of propagation. Note that the electric “E” field exists within the waveguide and is maximum in the center and zero at the ends. From this we can see that the “E” field is the voltage field.

Energy is inserted or removed by a simple probe spaced a quarter-wavelength from a shorted end of waveguide and at the center of the guide as shown in Figure 3. The probe is considered a quarterwave antenna with ground plane because the entire waveguide is made of conductive material, usually oxygen-free high conductivity copper. Remember, to make an antenna broadband, increase its diameter or add capacity. Most coax-to-waveguide adaptors have the quarterwave antenna captured in a polystyrene tube that not only fixes the probe, but also adds a sufficient amount of capacity making it a broadband antenna.

A contributing factor of efficient wave propagation within a hollow waveguide is not having any abrupt change in the physical dimensions. In other words, dents or foreign material within the waveguide disturb the E and H field causing reflections that result in a standing wave pattern. Any system using a waveguide is most vulnerable to damage here. A sign often seen on radar installations is “Warning-Waveguide-Do not chip or dent.” This warning is valid whether the waveguide is circular, rectangular or elliptical.

An exception to this rule is when probes are installed for tuning purposes. A machine screw installed in the center of the guide will either add capacity or inductance, depending on its placement within the VSWR pattern. Once the “E” field is disturbed, it remains disturbed all along the line until it reaches another point of opposite disturbance where it can be canceled. Tuning screws are frequency dependent and will have different effects depending on where they’re placed, not only along the line but how deeply they penetrate. Small dents appropriately placed on a rigid waveguide can add opposite reactive components that cancel those within the waveguide. The experienced person can tune a waveguide by carefully applying pressure at precise points along a waveguide while observing the return loss. Waveguide components such as the E and H bends often have a decal near distortions stating “dent tuned,” meaning, don’t call us because of apparent damage.

Adding several tuning screws close together ensures tuning ability for either kind of reactance. Tunable elliptical waveguide connectors have tuning screws where the transition is from elliptical to rectangular. These tuning screws take care of the connecter discontinuities and do little for transmission line discontinuities many wavelengths away.

By observing the H field of Figure 2, we see that this field has a definite pattern. If the interior of the waveguide had walls spaced identical to the field pattern, a cavity could be made out of this guide. Indeed that is what is done. Walls placed within the guide (as shown in Figure 4) add inductance, and a tuning screw adds capacity that will tune this area to a specific (waveguide) frequency. Energy travels from one compartment to the other (aperture coupling), but only at a frequency that is resonant to the E 3 H field.

This method of tuning a waveguide is usually used for “front ends” of a microwave transceiver. Its bandwidth is a function of how many “rooms” and how large the door is between rooms.

As in coax transmission lines, waveguide transmission line cavities described above have low “Q” values, (less than 50), meaning it’s a broadband device. High Q values cannot be obtained with waveguide dimensions and are constructed as large cylinders connected to the waveguide. High Q values are required for reference oscillators or AFC cavities.

### Elliptical waveguide

Elliptical waveguide is an efficient modification of rigid or rectangular waveguide. Its physical shape tends to follow the “E” field shown in Figure 5. The advantage of the elliptical waveguide is manufacturing convenience. It’s composed of a strip of copper that is corrugated, folded over, welded and jacketed. It’s available in continuous lengths up to shipping limits of around 3,000 feet. The only joints are the connectors on each end. Elliptical waveguides can be bent in either the E or H plane without hardship or damage. Rigid, on the other hand, was limited to 20-foot lengths requiring choke and cover flanges at each 20-foot distance. Prefabricated 90° bends were needed (two more flanges) to change directions.

All hollow waveguides need air under pressure (3psi-5psi) to prevent moisture migration to the inside. Any leak allows air to escape and prevents moisture from getting in. For high-power installations, 15psi of pressure or more raises the voltage level that the waveguide will handle without internal arc-over.

### Circular waveguide

A circular waveguide is perfectly symmetrical and, as with a rigid guide, the inside must be free of imperfections such as dents and foreign material. A circular guide can handle circular, horizontal or vertical polarizations. The only difference is the way energy is fed and removed from the guide. It is preferred for long runs because it has less attenuation than either a rigid or an elliptical waveguide. It also has a cut-off frequency limit the same as rectangular or elliptical. One of the great advantages is where dual polarization is required for a given path, such as one polarization for analog and the other digital, two regular waveguide runs are eliminated. Or, in the case of AT&T, one frequency is horizontal and the adjacent channel is vertical. This cross-field approach yields about 30dB of isolation between polarizations. Where both ends of the waveguide have circular-to-rectangular transitions, it is considered a “closed system.” An open system is one in which there is only rectangular transition at the feed point, the antenna having no transition. The horn or the cornucopia-style of antenna that AT&T used is an example of an open system.

A circular waveguide operated below the cutoff frequency is used in the older signal generators for attenuation. The Measurements Corp. signal generator used the circular waveguide below the cutoff frequency by incorporating a small loop as the injector, and another loop for pickup that was transported along the waveguide in a linear fashion. The linear distance was calibrated in decibels of attenuation. Attenuation of several orders of magnitude can be obtained using this method.

Buller is a special projects engineer for Tacoma Power, Tacoma, WA. For many years, he served as an electronics design engineer for the Washington State Patrol. He is a member of IEEE, NARTE, APCO and ARRL, and he is a Fellow of the Radio Club of America. His email address is [email protected].

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