# Horizontal Sector Antenna Calculator for Wifi Signal Coverage

### Sector Antenna Basics

A sector antenna is designed to deliver its signal in a pattern of radiated power that is optimised to reach its target area. In this way no signal energy wasted in areas where it is not needed. This leads to increased efficiency and reduced interference with other signals. All antennas are characterised by their horizontal and vertical beam patterns. The diagram above shows a typical sector pattern where you can see the signal distribution in the horizontal and vertical planes. In this example the antenna provides a specified gain of 14 dBi in a horizontal sector of 120 degrees. It also has a vertical sector providing 14 dBi gain in a zone of 15 degrees in the vertical plane.

### The Benefits of Using a Sector Antenna

Lets use the illustration of sail boats racing out in the bay. In the picture assume that the boats are racing at a maximum distance (X) Km from the shore. Also assume that the sailing course is length (Y). This is measured perpendicular to the line of length (X) from the proposed shore antenna to the end of the sailing zone. We are considering the use of a sector antenna to reach the sailing zone to ensure that the wifi signal energy available is radiated only where it is needed and none is wasted. That is we intend to established a sectored wifi beam that covers the sailing zone.

### Antenna beam footprints and Antenna Gain

But this is only one part of what we need to do to. We now need to look at some antenna specification sheets to see what gain they achieve and what their horizontal and vertical beam footprint looks like. So we start with these horizontal and vertical beam footprint diagrams below.

The diagrams show the relative signal strength of a typical sector antenna. What these diagrams show is how the relative signal changes with angular position. Lets take the horizontal pattern. We see the reference point marked as 0 on the right on the centre line. It is here we can expect a maximum signal level from the antenna. If we then measure the signal level at different points of the compass moving round in a circle we can plot points at different power levels thus creating the red line representing the antenna footprint. On the centre line at a point marked as (-3) is a circle which intersects the red line above and below the centre line.

#### The half power point used for Gain measurement

In the diagram the (-3) point intersects the red line at compass points 60 degrees either side of the centre line ensuring that the half power point indicated by the (-3) meaning minus 3 dB ensures that in this sector all points can expect to receive half the maximum power achieved at the reference point (0). By convention the antenna gain is measured at these end points.

### The Formula for Calculating the Sector Antenna Horizontal Beam Width

The formula for calculating the required sector coverage by our antenna is calculated using the formula below. Note the **Arctan** function is the inverse of the **Tan** function. This function is mathematically expressed as **Tan ^(-1)** and is often seen on calculators keyboards with this symbol.

#### HBW (Horizontal Beam Width) = 2 x Arctan(Y/2X)

For your convenience we have created a sectored antenna beam angle calculator. So using the calculator lets plug the numbers from our sailing example. Please note you can use any distance units you like in the calculator as long as you use the same units for entering distances.

**Assume: X = 5000 meters, Y = 6000 meters then the calculator says we need a 62 degree horizontal sector antenna**