On a previous video, we made a warning on the fact that when we had a symbol that was SFX that 1
symbol represented X bits. 2
And so you could have the feeling that the higher the spreading factor, the higher the number of bits 3
contained in the symbol and therefore the higher bitrate. 4
This is not true. 5
Why is it not true? 6
Because we didn't take into account the duration of this symbol. 7
This graph represent the symbol. 8
Duration. 9
According to the spreading factor. 10
And what do we see ? We can see that each time we increase the spreading factor by one. 11
we double the symbol's transmission time. 12
For example, the symbol transmission time at SF12 is equal to twice the symbols transmission time 13
at SF11. 14
So we can clearly see that we start with the fast symbol transmission time at SF7 to a very slow 15
one at SF12. 16
What is the exact value of this duration? 17
The time of a symbol is equal to two power spreading factor divided by the bandwidth. The higher bandwidth 18
the lower the time. 19
And that makes sense. 20
But on the other hand, the higher the spreading factor, the higher the time using a power of two. 21
So as we said, if the spreading factor increases by one then the time increases by two. 22
So how do we link the bitrate to the symbol time? 23
Because at the end there is only one value that matters for the user. 24
It's the bitrate. 25
The bitrate is in this calculation and is always the number of bit transmitted divided by the time to 26
transmit these bits. 27
So it's the number of bit in each symbols divided by the symbol time. 28
So the higher the bandwidth, the higher the bitrate. 29
That was the first point, the higher the spreading factor 30
the higher the number of bit in each symbol. 31
But overall the higher a symbol transmission time using a power of two. 32
So using a higher spreading factor would drastically reduce the bitrate. 33
And this is what we must remember. 34
Let's take an example. 35
We'll take a first case with a transmission at SF7 with a 125 kHz bandwidth, which is 36
a very common case. 37
And then we will also take a second case at SF12 with the same bandwidth. First 38
we're going to verify the bitrate given in all LoRa transceiver technical documentation, and step 39
by step we'll consider a real case by taking into account the LoRa transmission parameters, 40
then the European Regulation and the 868 megahertz band and the LoRaWAN protocol itself at the end. 41
So let's start with the basic calculation. 42
If we take SF7 at 125 kilohertz the bitrate is therefore : SFx bandwidth/2^SF 43
SFx bandwidth/2^SF 44
So seven times 125 kilohertz divided by two power seven. 45
The result is 6 836 kbit per second. 46
In SF12, 47
we have the same formula, except that this time we'll replace the spreading factor by 12 so 12 multiply by 48
125 kilohertz divided by two power 12, which gives 366 bit per second. 49
We see here that using a different spreading factor as a huge influence on the bitrate and as we said, 50
the higher the spreading factor the lower the bitrate. 51
And that's obviously something that you absolutely have to keep in mind when you design a LoRaWAN 52
device.