It can be seen from the table above that penetration of a 1-inch obstruction requires more signal cycles at higher frequencies. At higher frequencies the electromagnetic wave is required to interact with an obstruction many more times than at lower frequencies. Consequently, if an 800 MHz signal experienced a 94 dB loss while traversing a particular transmission path the 45 GHz signal would experience a 130 dB loss.

For outdoor RF, enter the distance between the bases of the antenna towers or mounting points and check the button to indicate whether you're calculating based on Miles, Feet, or Kilometers. The calculator is able to run the Free Space Path Loss equation down to a distance between towers of 1/4" (.04166 feet) with any smaller value being ignored. Plus, for distances greater than 50-feet the calculator will attempt to calculate earth curvature and will process Antenna Height if none is provided.

In order to determine the Free Space Path Loss, as well as a number of other calculated values that depend on the distance from the transmitter to the receiver the distance between towers must be entered. Alternatively, if the Antenna Height for both Radio #1 and Radio #2 are entered the Connect802 Wireless Network Path Link Budget and Antenna Calculator will determine the maximum separation distance for the two towers relative to earth curvature and Fresnel zone clearance.

NOTE: The calculator allows input of "Distance Between Towers" as small as 1/4" (.04166 feet), an unrealistically small value. When the antennas for which calculations are being performed are too close together the Near Field radiation from one will re-radiate from the other and the actual, measured signal strength will vary significantly from the simple Free Space Path Loss value.

Visual line-of-sight extends to the earth's horizon. To calculate the distance to the horizon the assumption is made that the earth's surface is a perfect sphere at which point simple geometry allows calculation. An antenna is some particular height above the ground (the tower height value.) From this height a line is constructed to meet the circle on the horizon and extend to the top of the other tower (a line tangent to the circle that intersects the tops of the two towers). This distance is referred to as the Visual Line-of-Sight (VLOS). Careful study of the geometry reveals that the VLOS distance is very slightly longer than the distance along the ground between two points. The ground distance follows the circumference of the earth and is a measurement of the distance between the bases of the two towers. VLOS is the distance from the top of one tower to the top of the other tower. The towers are perpendicular to the surface of the earth and, hence, tilt "away" from each other slightly (because they are both parallel to radii of the circle). By the Pythagorean Theorem for right triangles it should be evident that the difference between the VLOS and the ground distance is essentially equal to the short leg of the "tilt" triangle (the horizontal, upper-most leg depicted in the diagram to the right.) The distance between the bases of the two towers (along the surface of the earth) can be seen to be slightly shorter than the VLOS distance from tower top to tower top.

It is well known that the earth bulges slightly at the equator and is slightly elongated at the poles. The planet is not a geometric sphere but, rather, an ellipsoid. Consequently, a great circle path, covering some predetermined number of degrees of arc, will be longer in some directions than in others. A distance measured on a great circle is called a geodetic line. The United States Department of Defense has adopted a reference system that is considered the best fit for the whole earth. This reference system is called the World Geodetic System, and the most recent base measurements were made a standard in 1984, giving rise to the WGS84 standard.

The WGS1984 ellipsoid uses an equatorial radius of 3963.19 miles and a polar radius of 3940.90 miles. The Antenna Designer uses the average of these two values (3952 miles) as the value for the radius of the earth. This is slightly smaller than the average (based on inhabited land mass) used for GPS navigation (3963 miles) but the difference is, at worst, a more conservative value for the calculation of antenna system design.

Radio signals, like all electromagnetic radiation (such as light), diffract (bend) when they pass from a medium of one density into a medium of a different density. This is how a lens bends light rays (light moves from the low-density air into the higher-density glass of the lens.) This is why a person trying to spear a fish under the surface of the water must adjust their aim (because the fish isn't where it appears to be!)

The earth's atmosphere becomes less dense with altitude. The greatest change in density (per foot of increased height) takes place close to the ground. Consider a radio wave propagating from a vertical antenna. It moves perpendicular to the antenna. Consequently (because the earth "curves away from under the ray") the signal will begin to encounter less dense portions of the atmosphere. This change in density tends to curve the ray back towards the earth. As a result, a signal can, to a small degree, "follow" the curve of the earth around and reach a point that is actually beyond the visible horizon. This distance, which is slightly greater than the VLOS, is called the Radio Line-of-Sight (RLOS). A constant of proportionality of 4/3 is used to relate VLOS to RLOS in standard atmospheric conditions. Standard temperature is 59 degrees Fahrenheit (15 degrees Celsius). Standard barometric pressure is 29.92 inches (1013.25 mb) of barometric pressure. Deviations in temperature and pressure that are consistent with those experienced close to the ground will not effect the practical results of calculations for wireless communication networks. Atmospheric conditions do change dramatically as altitude increases, so interpretation of results for heights greater than 2000 feet should be cautious.

The term "Radio Line-of-Sight" is sometimes used to refer to the radius of the Fresnel Zone. The origin of this usage is unclear and using the term in this way seems to be inappropriate.

If a building, tree line, rolling hillside, or other obstruction is present between the installation location for Radio #1 or Radio #2, you may enter the distance to the obstruction and its height to incorporate the obstruction into the Antenna System Designer calculations. Note that the obstruction for Radio #1 must be be between Radio #1 and the horizon, with the same requirement applying to Radio #2. The "horizon" is based on the half-way point when Distance Between Locations is specified. When one installation height, or both heights are specified, the "horizon" is calculated based on the Refractive Index selected.

An antenna must be high enough to get above the tallest obstruction between it and the horizon by a factor equal to at least 60% of the first Fresnel Zone radius. The Antenna System Designer calculates all these values. The diagram below depicts the various values used, and calculated, that relate to the distance to the horizon (LOS Distance #1 and LOS Distance #2 in the diagram.) The height of the towers (or other installation locations) determines the respective LOS distance to the horizon. The Refractive Index adjusts the value used as the LOS distance to represent a visual distance, a radio frequency distance, or other distances based on the ratios that all cause a signal to reach further around the sphere of the earth than the flat, geometric calculations would conclude. The values entered into the Antenna System Designer and results returned are represented graphically below.

Here's another aspect to consider. The required height of a tower consists of the height necessary to 'get over the horizon'. This is height 'b' shown above. The tower must be high enough to provide a visual line-of-sight to the horizon. However, the tower must also be high enough to provide 60% Fresnel Zone clearance at the horizon. Height 'd' represents the Fresnel Zone clearance height, with the tower's overall height being b+d. The 'true' height attributable to line-of-sight requirements is actually an extension of the radius of the circle (the 'LOS Height #2' shown in the diagram.) Because the tower 'tilts away' (by a distance equal to 'c') there is a slight error in this part of the calculation as well. As before, this discrepancy is small enough to be ignore for practical calculations. If you're taking the final exam in a math class, however, this type of 'hand waving' won't get you a passing grade!

Enter either the total antenna cable loss (for each radio) or the dB loss per foot (or meter) and the length of the cable length. A default value of 3dB is provided for each radio. If you're calculating for Wi-Fi access points with integrated antennas the total cable loss values should be changed to zero for both radios.

Cable loss reduces the signal energy between the radio base station and the antenna. A low loss antenna cable (LMR 400) has a loss of 0.23 dB per foot at 2.4 GHz and 0.35 dB per foot at 5.8 GHz. Standard loss cable is often closer to 1 dB per foot. For cable runs less than roughly 10 feet the default value of 3 dB will often suffice for general calculation estimates. When running cable 100 feet up an antenna tower the manufacture's attenuation specifications must be obtained for the cable being used.

Electrical resistance is in a cable is the result of opposition to the movement of electrons. The power output of a cable can be derived from Ohm's and Watt's laws when the voltage is not alternating (DC current.) When a signal is alternating (at, for example, 2.4 GHz) the moving electrons tend to push away from the core of the conducting cable and move towards the outside of the cable. This is called the skin effect. In essence, it's as though the cable had less cross-sectional area than the area that is actually present. Skin effect causes the current to occupy a smaller cross-sectional area. Consequently, the relative resistance to current flow is greater for alternating current than for direct current. There are, as might be imagined, a wide variety of manufacturer's options as to cable types, conductor materials, and construction methods to optimize the signal carrying capabilities for a particular frequency, or range of frequencies, and for a particular use.

Enter the transmitter power that will be used for the radio. The value is the power output of the transmitting radio (which is the input power supplied to the antenna distribution system), and not the aggregate output power after considering antenna gain (often called the EIRP, "Effective Isotropic Radiated Power".) A typical Wi-Fi client device (notebook computer, hand-held inventory scanner, PDA, or tablet PC) often has an input power of 30mW. Some high-power mesh routers boast power specifications of 23 dBm (200 mW). For many years a typical 802.11 access point operated at 100 mW (20 dBm).

When the two radios are specified with different input power levels, the calculator uses the smaller value for calculations. The single most arbitrarily limiting factor in a wireless network link is the power level of the weakest transmitter. The lowest power level defines performance for both sides of the link. The power level is used by the calculator as part of the link suitability assessment. Power level and antenna gain are attenuated by cable loss, rain fade, link fade, and free space path loss.

Radio transmit power is typically configurable within the operating limits of the equipment. There are FCC mandated maximum limits regarding the effective output power when the actual transmit power is focused by some dB gain in the transmission antenna. These are limits on what is referred to as Effective Isotropic Radiated Power (EIRP).

When the calculator makes an assessment regarding the suitability of your collective input values it weighs the power and gain in your system against the aggregate losses (Free Space Path Loss, cable attenuation, rain fade, and link fade.) If the power and gain is able to provide a received signal strength that is at, or above, your specified receiver sensitivity value the link is considered suitable. For perspective, considering that "dBm" is a logarithmic value, an RF signal measured at -56 dBm is 256 times stronger than a signal measured at -80 dBm

Enter the dBi gain value for the both antennas. Even a standard antenna has some gain, that's just the nature of the underlying physics. Many 802.11 access points come with an antenna roughly 3- to 5-inches long as standard equipment. This type of antenna has a gain of 2.15 dB, which is the default value for the calculator.

The antenna gain is used by the calculator as part of the link suitability assessment. Power level and antenna gain are attenuated by cable loss, rain fade, link fade, and free space path loss.

A theoretical point source that radiates an electromagnetic field does so in a perfect sphere, with energy propagating outwards equally in all directions. This theoretical antenna is called an isotropic radiator. The simplest real-world antenna is a length of wire, called a dipole radiator. Signal energy from a dipole radiates outward to the sides (perpendicular to the length of the antenna) but not out the ends. This is analogous to the way light shines out of a fluorescent light tube. The transmission volume has a torus shape (doughnut shape) around the radiating element. Instead of radiating out in a spherical shape the energy is "flattened" into a torus. Relative to a sphere, the torus has less volume for the same radius. The density of energy in the torus is greater than that of the sphere (in the direction perpendicular to the antenna.) This is a basic antenna gain factor that is the natural result of the way a dipole radiator creates the electromagnetic field.

Gain measured relative to a theoretical isotropic radiator is assigned the measurement unit "dBi" (decibels relative to isotropic.) Unless specified otherwise, if you see a gain expressed simply as "dB" it probably implies "dBi". The inherent gain of a dipole antenna is 2.15 dBi. The dipole, by the nature of the toroidal field volume, introduces this gain. An alternative unit of measurement is to specify gain in terms of "dBd" (decibels relative to a standard dipole). Although less common, dBd is sometimes given in antenna specifications. An antenna with 0 dBd gain has a gain of 2.15 dBi.

Surveyors often use K=6/3 and this results in what is commonly called the "Visual Line-of-Sight"

For elevations greater than 5000 over Mean Sea Level use the Low Density, K=2/3 value (i.e.: Denver, Colorado)

Use K=Infinity for "flat earth" calculations. These are slant-range designs where one antenna essentially looks "up" at the other, whether it's up to the top of a very tall building or from an earth station to a satellite.

Use K=1 to solve distance-to-the-horizon calculations as if the earth were a perfect, geometric sphere, with no refraction effects considered.

When performing computations or analyzing data related to spatial relationships it's necessary to understand the differences in measurements for distances on the earth's surface. Data obtained from, or applied to, the real earth (surrounded by a real atmosphere) typically differs from that which would be obtained based on the assumption of a spherical earth and derived using Euclidean or planar metrics. The geometric calculations that could be performed are based on distances being assumed to be a length of an arc of a great circle on a sphere. This geometric result is called a geodetic line, and it is the distance between two points (an antenna and the horizon, for example) that would be experienced by a person walking along a road between the two points. On the other hand, the changes in atmospheric density caused by altitude (density decreases as altitude increases), temperature (hot air is less dense than colder air), and water vapor (moist air is less dense than dry air.. a fact that may seem 'backwards' but it's true.)

When an wave moves from a region of lesser density into an area of greater density it bends towards the denser medium in accordance with several well established principles of physics. The pencil in the glass of water (below) appears to bend as it enters the water because the water is denser than air. The degree to which a propagating wave bends is represented by the refractive index for the medium through which the wave is passing. The refractive index is often represented by the capital letter "K".

The term "earth bulge" and "earth height" are often used interchangeable. It's generally considered that the term "earth bulge" refers not to the actual height of the ground (relative to the center of the earth) but, rather, to the apparent height that creates an obstruction for an electromagnetic wave. This apparent height is calculated based on the refractive index of the atmosphere. It's only when K=1 that the apparent height of the earth bulge is equal to the actual height of the earth at a particular distance.

Refer to the Refractive Index discussion (above) to understand how the curvature of the earth appears greater than the physical, geometric spherical representation that might be used to calculate line-of-sight to the horizon based on a tangent line from a point at some height above the surface.

Enter the dB loss per mile, or per kilometer, associated with Rain Fade for the entire end-to-end link. This value can be derived from the standard tables shown (and explained) below or from actual field measurements. If you're unsure, and if you live in an area where rainfall can be heavy and prolonged, use 0.8 dB/mile (0.5 dB/km) as a 'worst-case' value for Wi-Fi, WiMAX or other system operating below 10 GHz. Between 57 GHz and 64 GHz you should enter a value of 12 dB/km to account for oxygen absorption.

For frequency management and general planning purposes it may be sufficient to make simple (and optimistic) assumptions based on Free Space Path Loss (which accounts for spatial spreading losses.) Additional detail can be incorporated into a design model to improve the accuracy of the predictions. The International Telephony Union (ITU) has a number of recommendations described in the ITU Radio Regulations (ITU-R P.620-5, ITU-R P.837-4, ITU-R P.1546-1, and revisions in ITU-R P.620-5). Weather monitoring stations around the world report rainfall rates which are used to determine both average rain amounts as well as local gradients in rainfall (where, for example, a low-lying area receives more or less rainfall than a higher-elevation location a few miles away.)

The degree to which signals are degraded in the atmosphere is dependent on two factors:

As the transmitted signal energy passes through water droplets it is both absorbed and scattered to varying degrees. Absorption is the aspect where part (or all) of the energy is converted to heat as it penetrates the water droplet. Scattering is the disruption of the direction of travel of the RF signal as it passes through the non-uniform shape, and differing density of the water droplet. Scattering may cause refraction of the wave (bending due to the difference in density between the air and the water) or diffraction (bending of the signal around the edges of an object that is smaller than 1 wavelength.) Some perspective is:

Select the option that most accurately describes the terrain underneath the proposed radio link. The options are:

The Terrain Roughness selection describes the smoothness of the "top" of the span between the antennas. Some of this smooth (or irregular) "top" will penetrate the first 40% of the Fresnel Zone and, consequently, the degree to which it is smooth or rough will effect the degree to which the signal is reflected, diffracted, and attenuated. Remember that the height of the tallest obstruction will, ultimately, have to be added (by you, the designer; not by the calculator) to the antenna heights calculated by the Connect802 Antenna System Designer.

An RF wave, propagating across a relatively smooth portion of the earth's surface (large lake, expansive meadow, etc.) will not "strike" the surface of the earth. By this it is meant that the curving surface always curves "away" or "down" while the wave continues to propagate in a direction that is essentially tangential to the sphere. This (when considered by itself) is the reason that the RF wavefront encounters less-dense atmosphere as it expands (the RF signal is moving tangentially to the sphere) which makes it refract downwards towards the earth resulting in the 4/3 factor for radio Line-of-Sight. (See discussion above under Tower Height).

When the earth's surface is not smooth, however, the RF signal will be absorbed, reflected, and diffracted to varying degrees by the terrain features that create "roughness". Very sophisticated RF modeling formulae exist that take into consideration specific terrain obstruction features. These formulae assess incident angles of RF rays as they refract and reflect from surfaces as well as using Gaussian distribution models of scattering losses. The Connect802 Antenna System Designer takes a more pragmatic approach to terrain roughness modeling. In "free space" (smooth surface) the assumption is made that an additional 2 dB of gain will be required to overcome the natural irregularities of the earth's surface. In suburban areas (where most buildings are the same height) a 3 dB gain is required, and in urban areas where there is dramatic height difference between buildings a 5 dB gain is added. Since exact sets of incident angle data are not typically available in most practical, field situations these values are appropriate. It's felt that this is a sufficiently reasonable approximation of what would otherwise be a calculation based on potentially unavailable input data.

Enter any additional fade margin you would like to apply to the calculation. A very widely used, "typical" link fade margin is 10 dB and this value becomes the default if no other value is entered. You may want to use a fade margin of 12 dB to be conservative and a fade margin of 6 dB to be aggressive. You could also considering Increasing your fade margin by and additional 3 dB in a highly reflective environment and by another 3 dB to 6 dB in an electrically noisy environment. Hence, a automotive repair shop, with many power tools and arc welding rigs might require a Link Fade Margin margin as high as 21 dB (12+3+6)

The Link Fade Margin is applied to link budget calculations as a way to compensate for normal and ordinary deviations in link characteristics. It comprises both "Fade Margin" (caused by multipath reflections) as well as other factors that may effectively attenuate the transmitted signal. There are a number of factors that may cause the theoretical calculations for a link to vary from the measured signal characteristics. The Link Fade Margin allows the designer to input additional loss that will be incorporated into calculated results.

Enter the length of the longest linear dimension of the antenna itself. For a dipole or yagi it's simply the length of the antenna. For a parabolic dish the dimension is the diameter of the dish. For any other shape, use the longest single dimension (which could be a diagonal across a rectangular element as in a grid sectional parabolic antenna.)

Near Field Radiation and the Near Field / Far Field Boundary distances are dependent on the value you enter for the Maximum Linear Dimension. These linear dimension value and the resulting calculated results do not change the dB gain/loss, antenna tower height, or suitability of the calculations. Therefore, if the dimension is left at its default "1 foot" value, or adjusted to your best estimation of size, it will not change the link-budget calculation. Knowing the Near Field/Far Field boundary will, however, give you insight into the installation location specifics for an antenna. For example:

Metal objects in the Near Field region will significantly distort the antenna's transmit and receive characteristics. Metal objects that might accidentally end up in the Near Field or within 1/2 wavelength of the antenna include aluminum wall studs or plumbing pipe concealed behind drywall, ceiling supports in retail or warehouse buildings where the ceiling is exposed and an antenna is mounted on the support gridwork, and antenna towers where improper mounting places a side-mounted antenna too close to the tower. Keep metal objects a minimum of 1/2 wavelength away from any antenna and avoid metal objects in the Near Field as much as is practical.

The electric current impressed on the radiating element of an antenna alternates in strength at the frequency of the transmitter (2.4 GHz, 5.8Hz, etc.) During the first 1/4 of each wavelength the current is increasing, creating an expanding magnetic field around the conductor. During the next 1/4 cycle the current is decreasing to zero, and the magnetic field collapses. A portion of the energy stored in the magnetic field is returned to the radiating element. This is called the induction energy. It is the energy stored in the magnetic field during one 1/4 cycle, and returned to the antenna in the next. Induction energy exists only in very close proximity to the radiating element. This region is called the Near Field. Induction energy is greatest within 1/2 wavelength of the radiating element.

The expanding and collapsing magnetic field sets in motion an electromagnetic field that continues to expand away from the antenna. This is called the radiating energy and this is what travels through space between the transmitter and receiver. It's the radiating energy that we normally think about when considering a wireless network design. Radiating energy exists in the region called the Far Field. The Far Field is also referred to as the Fraunhofer Region after Joseph Fraunhofer who is best known for his work in the early 1800's with spectral absorption lines, the dark lines in a solar spectrum that help scientists determine the chemical makeup of stars.

Because the radiating characteristics of an antenna are closely related to the interaction of the collapsing Near Field and the radiating element it can be useful to know the distance to the boundary between the Near Field and the Far Field. A metal object in the Near Field will absorb some of the induction energy created by the antenna. Since there is no transmitter circuitry attached to this metal object there is no place for the induced energy to go. The energy is re-radiated from the metal object just as if the object were another antenna. When these interactions are carefully calculated the elements of a Yagi antenna can be designed so as to create a directional beam. When the interactions are the result of unintended metal objects in the environment they can cause unexpected antenna behaviors.

A detailed discussion of the Near Field and Far Field must take place in a context that is well outside the scope of the present overview. Keep unintended metal objects out of the Near Field as much as is practical and definitely avoid metal objects within 1/2 wavelength of the radiating element.

Do not depend solely on the results calculated by the Connect802 Antenna System Designer in any case were loss of life, property damage, or other liability is at risk relative to the proposed point-to-point wireless link being designed. Results may be subject to arithmetic rounding errors. This calculator is designed to provide results with a level of precision that is sufficient for use in typical outdoor, point-to-point wireless network design. Calculated values represent the arbitrary arithmetic results of standard path loss, Fresnel zone, earth curvature, and link budget formulas. Measurements made in the field may vary from those calculated here since manufacturing tolerances and measurement accuracy introduce variability. Attenuation in cable connectors may vary substantially from theoretical values if oxidation is present. While every effort has been made to assure the accuracy of the calculations, Connect802 makes no guarantee of the accuracy or suitability of this information. Contact Connect802 with any questions or concerns. "We've Got You Covered!"