Microwave path design:The basics
Part 1 – This four-part primer on propagation-related basics, for those learning about microwave communications, begins with "line-of-sight" determinations and the evaluation of path clearances with regard to refractive effects.
Microwave communications path design poses many challenges. In addition to static gain and loss considerations, terrain and propagation dynamics can play a large role in determining whether a proposed path will have the required signal levels, clearances and reliability.
This four-part series will only scratch the surface with regard to these considerations, and it is not intended to cover all aspects of path design or any one in great depth. The primary focus of the series is to serve as a primer on some of the propagation-related basics for those who may be new to the microwave communications field.
Given this disclaimer, the following tasks are some of the fundamental components of microwave path design: * determining whether a proposed path is "line-of-sight." * evaluating path clearances with regard to refractive effects. * evaluating path clearances with regard to Fresnel zones. * considering path reflections. * deriving a power budget and the fade margin. * path reliability.
Part 1 of this series deals with the first two components; the others will be discussed in Parts 2, 3 and 4.
Determining line-of-sight Although there are situations where microwave paths are designed to work without line-of-sight conditions, they would not be considered the "norm" for industrial microwave systems and therefore will not be dealt with here. In most situations, if a prospective path is not line-of-sight, then an alternate route is considered.
Determining whether a path is line-of-sight can be partially accomplished with the aid of a topographical map. This type of map will show the various elevations along the length of the path between proposed endpoints. Plotting these elevations at intervals will produce a path profile showing terrain relative to the antenna elevations, as shown in Figure 1 below left. This graphical representation aids in determining not only whether a line-of-site condition exists between endpoints but also in measuring clearances between the main beam (center) of the path and the surrounding terrain.
Topographical information for many areas throughout the world is now available on CD-ROM. Various software applications have been developed to design microwave paths based on this information. Since this option can be a bit "pricey," many opt to use inexpensive topographical maps, which may be used with the same success.
When evaluating a proposed path, the path profile should be developed first. This will identify path obstructions from terrain features. A field survey should follow, which offers the necessary visual confirmation that the height of foliage or of man-made objects (which are not indicated on a topographical map) will not be located in or too near the proposed path.
If visual confirmation is difficult because of the distance between path endpoints, a mirror can be used to reflect the sun's light from one path endpoint back toward the other. If the mirror's flash of reflected sunlight is seen back at the opposite endpoint, the path is line-of-sight. This is referred to as "flashing" a path. Alternate methods might include the use of high-intensity search or strobe lights.
Evaluating path clearances-refraction When the dielectric constant of the atmosphere changes with height-above-ground, the refractive index will also change. This refractive variation in turn causes the propagating wavefront to effectively "bend." If a condition exists where the dielectric constant of the atmosphere is constant with height-above-ground, no refraction will occur and the wavefront will travel in a straight line. This is not the "norm," however. Because of dielectric variations typically present, a wavefront usually will be refracted so that it will follow a path somewhere between a straight line and the true curvature of the earth (referred to as R). A wavefront propagating through the environment will be slowed by, and be effectively bent toward, an atmosphere that is more dense, such as one with a high water-vapor content (dense clouds or fog). That is why, rather than traveling in a straight line, the wavefront is normally bent earthward-which serves to extend its horizon.
Because atmospheric conditions are dynamic, the bending effect of the propagating wavefront will vary. To provide a simple model describing the path traveled by a wavefront for a particular refractive condition, engineers have developed a factor, K, where is considered the "equivalent" earth radius. This equivalent radius describes the bending of the wavefront relative to the true earth radius, as shown in Figure 2 on page 28.
The refractive index can change drastically with time. This means the microwave beam between path endpoints will "bow" to a greater or lesser extent. In fact, it may "bow" in an upward or a downward direction, depending on the value of K at the time. It is therefore important to evaluate clearances from path obstructions over a wide range of K in order to determine whether adequate path clearances are maintained under various degrees of refraction. Often, three values of K are used in the calculations. Two of the three values describe the limits or boundaries of refraction that might occur (although with anomalous conditions, values exist outside these limits), while the third describes what is considered "normal" or expected. The value of K = infinity, also known as "super-standard" atmosphere, is one extreme where the wavefront follows the true curvature of the earth. The other extreme value of K typically used is 2/3 and is termed "substandard" atmosphere. It is also a condition commonly referred to as "earth bulge." The median value of K=4/3 is used to evaluate the path under "normal" atmospheric conditions in temperate climates.
There are two methods of graphically displaying the various equivalent earth radii with respect to the terrain between path endpoints: the "flat earth" method and the "curved earth" method. Figure 3 above is an example of a "flat earth" path profile. It is called "flat earth" because the horizontal axis (or baseline) has been kept flat and represents the earth's curvature as a flat line. The various equivalent earth radii represented by the different values of K are shown by bending the path beam line between antennas. The three lines shown in Figure 3 correspond to the refractive conditions where K = infinity, K=4/3 and K=2/3.
Elevations of terrain features between path endpoints are plotted using the flat baseline as a reference. The profile allows one to see if there is sufficient path clearance over the terrain for each value of K.
The curved earth approach, as shown in Figure 4 on the left, leaves the beam line between antennas straight and instead bows the horizontal baseline to correspond to one particular value of K. Elevation of all terrain features must be added to that of the bowed baseline reference. The straight beam line between antennas must now be checked for sufficient clearance from all terrain features for that value of K.
With the curved earth profile, the one limit of K=infinity would be shown with the baseline flat. Here (as with the flat-earth approach) is the one "extreme" condition where the wavefront (shown as a straight line) follows the true curvature of the earth (also shown as a straight line). As the value of K gets smaller and reaches the other limit of K=2/3, the equivalent earth radius bulges upward more in the center, hence the term "earth bulge." As these profiles show, paths with values of K=4/3 and K=2/3 have less path clearance with respect to terrain features than when K=infinity.
The following equation can be used to calculate how much the horizontal axis (or baseline) of a "curved earth" profile will bow upward at any point along the path for a particular value of K:
H = (d1*d2)/(1.5*K)
where h is the vertical variation in height (ft.). d1 is the distance (mi.) from one end of the path to the point being considered. D2 is the distance (mi.) from the point considered to the other end of the path.
With the "flat earth" profile, h is subtracted from the direct ray (K=infinity) reference line (for positive values of K) at various distances along the path in order to develop a graphical representation of the amount of wavefront bowing that will occur for the value of K under investigation.
With the "flat earth" profile, the wavefront, rather than the baseline, is shown "bowed," and the amount of bowing changes as the value of K changes. The distance between the bowed wavefront and the terrain features can be measured graphically to determine path clearances for each value of K.
Whichever profiling method is used ("curved earth" or "flat earth"), it can be seen graphically that smaller values of K result in greater bulging or "bowing." This in turn results in less path clearance with regard to terrain features.
Because the microwave path has radial dimension, the clearances considered are not only those above and below the center of the path, but also to either side.
Initially, these graphical methods allow path clearances to be measured as distances, in feet. Once this information has been obtained, it is however, typically converted to a more meaningful design measurement, called the Fresnel zone.
The next article in this series will discuss path clearances with regard to Fresnel zones.
References Laine, R.U., Determining Antenna Heights for Coastal Areas, Lenkurt Electric, Monograph 197.
"Microwave Systems, Microwave Path-Testing," Bell Systems Practices, AT&T Standard, September 1962.
"Microwave Transmission Engineering (Part One and Two)," GTE-Lenkurt Demodulator, July/August, 1972.
White, R.F., Engineering Considerations for Microwave Communications Systems, 4th Ed., GTE-Lenkurt, San Carlos, CA, 1983.