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