Distance Between Towers

Value to Enter:

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.

Significance of This Value:

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.

Background and Technical Perspective:

Free Space Path Loss: The Expanding Spherical Wavefront and the Inverse Square Law

As the distance between transmitter and receiver increases the signal strength decreases. As the electromagnetic signal propagates from transmitter to receiver it spreads out in 3-dimensions. Theoretically this expanding wavefront resembles the surface of a sphere. A sphere with radius=2 has a surface are of 50. A sphere with radius=4 has a surface area of 200. When you double the radius the surface area increases by a factor of 4.This gives rise to the "Inverse Square Law" for signal propagation. When distance from a transmitter doubles, signal strength is reduced by a factor of 4. Signal strength varies inversely as a factor of the square of the relative distance. Additional information on antenna radiation can be found on the Wi-Fi: Just the Facts about Antennas page.

Path Loss Modeling and the Real World

The loss of signal strength resulting from transmission through free, unobstructed space, can be estimated with a high degree of accuracy by applying one of several mathematical formulas called "free space propagation models." Modeling formulas have been created to represent a number of different situations including urban areas, areas with many hills and valleys, and generally flat, open areas. These models take into consideration the various effects of signal reflection, diffraction, and refraction, as well as the reduction in signal power resulting from the expanding spherical wavefront.

The Friis Free Space Equation (in decibel form) is commonly presented as the way to determine signal loss through the air between two points. This model calculates signal strength based on the spherical expansion of the propagating wave front. As the "sphere" gets bigger, the surface increases, and, consequently, the density of the propagating signal energy decreases. The Friis equation is the most widely employed formula for calculating path loss and is often seen written in a form similar to the following:

dBLoss = 96.6 + 20 Log10 (distance in miles) + 20 Log10 (frequency in GHz)

You may see this equation presented with a different "constant of proportionality" (the "96.6" value) when the units (miles, GHz) are different. Of course, for a design involving obstructions, building interiors, or specific noise or interference sources, the Connect802 Suite Spot Predictive Site Survey, employing RF modeling and simulation software, provides a design that incorporates a more complete picture of the wireless network installation location. Unfortunately, the Friis equation only presents part of the story for practical transmission system design. Many factors, beyond simple spherical expansion, come into play to effect the strength of a transmitted signal.

The relationship between theoretical calculations of path loss and the actual path loss experienced in the real-world has been the subject of many research projects and technical papers. A number of mathematical formulas have been developed to estimate link performance based on the type of link being designed (urban versus suburban areas, smooth versus rough terrain, atmospheric conditions, etc There are four widely accepted mathematical models generally used to estimate link attenuation:

• Friis Free Space Path Loss Model: Loss is based solely on the spherical expansion of the RF wavefront. This model does not consider real-world reflection, diffraction, refraction, and absorption and so always produces results that show a path with significantly less attenuation that will actually be found in practice.
• CCIR Model: This model, published by the Comite' Consultatif International des Radio-Communication (the CCIR; now the ITU-R), combines Free Space Path Loss with terrain-induced path loss.
• Hata Model: Based on the CCIR model, the Hata model incorporates empirical measurement curves to represent terrain characteristics for Open, Suburban, Small City, and Large City environments.
• Walfisch-Ikegami Model (WIM): The WIM model is tuned for the 800 - 2000 MHz range, and for distances up to 5 km. It takes refraction into consideration for Non-Line-of-Sight connectivity and works well for antenna towers higher than 30 meters.

The results calculated by the actual model formulas differ dramatically. In fact, the Free Space Path Loss model can allow distances between radios that are 200 times greater than what the CCIR model may suggest (these are the two extremes.) A roughly 1 mile these two models may differ by as much as 50 dB, with as much as 70 dB as antenna towers begin to get more then 5 miles apart.

It's not uncommon to hear the common rule-of-thumb that suggests that a 6 dB increase in link budget results in doubling the transmission distance. This rule is correct only for Free Space Path Loss but is unrealistic in the real-world. In fact, the increase in link budget necessary to double the transmission distance varies with the height of the antennas themselves. A low antenna (under 10-feet above the underlying terrain and obstructions) may require as much as 15 dB to double the transmission distance. An antenna that's higher may only need 10 dB (or less.)

The most significant way to improve the performance of a link is to increase the sensitivity of the receiving radio. The receiver's ability to extract a signal from background noise becomes an ultimately limiting factor to link performance. Consider the fact that adding 3 dB gain to a transmitting antenna doubles the transmit signal strength by a factor of 2. This stronger signal then creates stronger signal reflections and is more significantly diffracted than it would have been had the 3 dB gain not been introduced. Hence, 3 dB gain on the transmitter side doesn't translate (in the real-world) into a 3 dB gain by the time the signal gets to the receiver. On the other hand, making a receiver 3 dB more sensitive specifically lets the receiver acquire a signal that is half as powerful as would have been the case if the 3 dB improvement had not been introduced. A 3 dB improvement in receiver sensitivity translates directly (in the real-world) into a 3 dB improvement at the receiver.

The Connect802 Antenna System Designer assumes a modified Hata model and adjusts performance assumptions based on the differences between antenna gain and improved receiver sensitivity. Calculations based on the Hata model formulas suggest that a 10% increase in receiver sensitivity results in a 75% increase in transmission distance.