## Free Space Path Loss Diagrams

Free Space Path Loss (or FSPL) represents the amount of energy that a given radio wave loses as it travels through the air away from its source. Understanding FSPL will help us understand how far a Wi-Fi signal can go. It is also widely used by Wi-Fi survey tools to predict Wi-Fi signal propagation.

*d*in km and

*f*in GHz):

This loss is relative to 2 main components:

**Frequency****Distance**

### FREQUENCY

**frequency**. Here, we are talking about the frequency of the radio wave. As you can see in the formula above, the higher the frequency is, the higher the loss will be. In Wi-Fi, this means that a 2.4GHz signal is less prone to loss than a 5GHz signal. We commonly say that 2.4GHz travels further away than 5GHz.

**receive aperture**and will be able to better “hear” the incoming signal.

The FSPL formula in Wi-Fi defines that, in the first meter:

- A 2.4GHz signal is loosing about
**40dB**- Calculation for channel 1: 20log(0.001) + 20log(2.412) + 92.45 = 40.09dB
- Calculation for channel 11: 20log(0.001) + 20log(2.462) + 92.45 = 40.28dB
- Calculation for channel 13: 20log(0.001) + 20log(2.472) + 92.45 = 40.31dB

- A 5GHz signal is loosing about
**47dB**- Calculation for channel 36: 20log(0.001) + 20log(5.180) + 92.45 = 46.74dB
- Calculation for channel 52: 20log(0.001) + 20log(5.260) + 92.45 = 46.87dB
- Calculation for channel 100: 20log(0.001) + 20log(5.500) + 92.45 = 47.26dB
- Calculation for channel 149: 20log(0.001) + 20log(5.745) + 92.45 = 47.64dB
- Calculation for channel 165: 20log(0.001) + 20log(5.825) + 92.45 = 47.76dB

- A 6GHz signal is loosing about
**48.5dB**- Calculation for channel 1: 20log(0.001) + 20log(5.955) + 92.45 = 47.94dB
- Calculation for channel 49: 20log(0.001) + 20log(6.195) + 92.45 = 48.29dB
- Calculation for channel 97: 20log(0.001) + 20log(6.435) + 92.45 = 48.62dB
- Calculation for channel 109: 20log(0.001) + 20log(6.495) + 92.45 = 48.70dB
- Calculation for channel 129: 20log(0.001) + 20log(6.595) + 92.45 = 48.83dB
- Calculation for channel 181: 20log(0.001) + 20log(6.855) + 92.45 = 49.17dB
- Calculation for channel 201: 20log(0.001) + 20log(6.955) + 92.45 = 49.30dB
- Calculation for channel 253: 20log(0.001) + 20log(7.115) + 92.45 = 49.49dB

### DISTANCE

Here, we are talking about the distance travelled by the Wi-Fi wave away from the source. Common sense tells us that it would make sense if the signal was to lose power as it travels away from its source.

The FSPL formula tells us exactly by how much following the **inverse square law**.

The inverse square law tells us that as the distance from the source doubles, the energy is spread out over 4 times the area. This results in the signal loosing 4 times it’s original amplitude. In other words, the Wi-Fi signal is loosing 6dB every time the distance from the source is doubled (This is represented in red in the diagram above).

So, if we know the power of our signal leaving the access point, we can calculate how far this signal will go. This is assuming there is no source of attenuation between the transmitter and the receiver.

### INTRODUCING A WALL

### RESSOURCES ON FSPL

- Wikipedia article on Free Space Path Loss: https://en.wikipedia.org/wiki/Free-space_path_loss
- Effect of Transmit power changes on AP by Nigel Bowden: http://wifinigel.blogspot.ca/2014/11/effect-of-transmit-power-changes-on-ap.html
- Wi-Fi Free Space Loss Calculator by Nigel Bowden: http://wifinigel.blogspot.ca/2014/05/wifi-free-space-loss-calculator.html
- FSPL diagram by Devin Akin: http://divdyn.com/so-called-ghost-frames-not-exist/