# Radio link calculation

This section contains some useful formulas for data radio “link budget” calculations. Note that the calculations are based on assumptions of certain circumstances and should only be used as a guideline for radio network design. In reality, many factors can have an impact on the radio link. Planning of a radio network is usually done by first simulating the network in a desk top propogation study using a professional software package. The results are then verified by performing a field survey.

However, the formulas below can be used to calculate if the radio link has an acceptable fade margin or, if not, how much antenna gain that needs to be added or if repeaters have to be used.

**The known factors are often:**

- The distance between two sites
- The (possible) height of the antennas
- The transmit power of the radio
- The receiver sensitivity of the radio
- The antenna gain

The first calculation to be made is the propagation loss. This value tells how much the signal strength is decreased due to the distance between the transmitter and the receiver. For this we use the Egli model. The Egli model is a simplified model that assumes “gently rolling terrain with average hill heights of approximately 50 feet (15 meters)” (Land Mobile Radio Systems, Edward N. Singer, PTR Prentice Hall, 1994, p. 196). Because of this assumption, no terrain elevation data between the transmitter and receiver facilities is needed. Instead, the free-space propagation loss is adjusted for the height of the transmitter and receiver antennas above ground. As with many other propagation models, Egli is based on measured propagation paths and then reduced to mathematical model. In the case of Egli, the model consists of a single equation for the propagation loss.

A = 117 + 40 x log D + 20 x log F – 20 x log (Ht x Hr)

Where

A = Attenuation (dB)

D = distance between the antennas (miles)

F = Frequency (MHz)

Ht = Height of transmitting antenna (feet)

Hr = Height of receiving antenna (feet)

1 mile = 1610 meters = 1.61 kilometres

1 feet = 0.305 meter

Metric system users can use the formula:

A = 117 + 40 x log (D/1.61) + 20 x log F – 20 x log ((Ht / 0.305) x (Hr / 0.305))

Where

D = distance between the antennas (kilometres)

Ht = Height of transmitting antenna (meters)

Hr = Height of receiving antenna (meters)

Example 1

D = 12.5 miles (20 kilometers)

F = 142.000 MHz

Ht = 65 feet (20 meters)

Hr = 16 feet (5 meters)

A = 117 + 40 x log 12.5 + 20 x log 142 – 20 x log(65 x 16)

117 + 43.8764 + 43.0457 – 60.3406 = 143.6 dB

This example shows that a 142 MHz RF signal will be attenuated 143.6 dB over a distance of 12.5 miles (20 kilometres).