LoRa/LoRaWAN tutorial 15: Data Rate, Chip Rate, Symbol Rate, Chip Duration and Symbol Duration 

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This is part 15 of the LoRa/LoRaWAN tutorial.
In this video series different topics will be explained which will help you to understand LoRa/LoRaWAN.
It is recommended to watch each video sequentially as I may refer to certain LoRa/LoRaWAN topics explained earlier.
In this video I will explain how data rate, chip rate, symbol rate, chirp duration and symbol duration are calculated.
The unit of bandwidth (BW) is Hertz (Hz) which is the number of vibrations or wave cycles per second.
This bandwidth is interchangeably with chip rate:
BW = Rc = chip rate (chips/s) [1]
For example: BW=125 kHz
BW = Rc = 125000 chips/s
The Symbol Rate (Rs) is calculated as follow:
Rs (symbols/sec) = BW / 2^SF = Rc / 2^SF [1]
Bandwidth (BW) in Hz
Spreading Factor (SF): 7-12
For example: BW=125 kHz, SF=7
Rs = 125000 / 2^7 = 977 symbols/sec
The chip rate is always higher than the symbol rate: Rc is greater than Rs
To calculate the data rate (DR) or bit rate (Rb):
Rb (bits/sec) = SF x (BW / 2^SF) x (4(4+CR))
Bandwidth (BW) in Hz
Spreading Factor (SF): 7-12
Code Rate (CR): 1-4
For example: SF=7, CR=1
BW=125 kHz, Rb = 7 x (125000 / 2^7) x (4 / (4 + 1)) = 5.5 kbits/s
BW=250 kHz, Rb = 7 x (250000 / 2^7) x (4 / (4 + 1)) = 10.9 kbits/s
BW=500 kHz, Rb = 7 x (500000 / 2^7) x (4 / (4 + 1)) = 21.9 kbits/s
If you increase the bandwidth, the bit rate or data rate is increased.
For example: BW=125 kHz, CR=1
SF=7, Rb = 7 x (125000/2^7 ) x (4/(4+1)) = 5.5 kbits/s
SF=8, Rb = 8 x (125000/2^8 ) x (4/(4+1)) = 3.13 kbits/s
SF=9, Rb = 9 x (125000/2^9 ) x (4/(4+1)) = 1.76 kbits/s
SF=10, Rb = 10 x (125000/2^10) x (4/(4+1)) = 0.98 kbits/s
SF=11, Rb = 11 x (125000/2^11) x (4/(4+1)) = 0.54 kbits/s
SF=12, Rb = 12 x (125000/2^12) x (4/(4+1)) = 0.29 kbits/s
If you increase the Spreading Factor, the bit rate or data rate is decreased.
Because Rc = BW [1], the chip duration is calculated as follow:
Tc (sec) = 1 / BW
Bandwidth (BW) in Hz
For example: BW=125 kHz
Tc = 1 / 125000 = 8 µs
The symbol duration or sweep time is calculated as follow:
Ts(sec) = 2^SF / BW [1]
Bandwidth (BW) in Hz
Spreading Factor (SF): 7-12
For example: SF7
BW=125 kHz, Ts = 2^7 / 125000 = 1.024 ms
BW=250 kHz, Ts = 2^7 / 250000 = 512 µs
BW=500 kHz, Ts = 2^7 / 500000 = 256 µs
If the BW increases, the Symbol duration decreases.
For example: BW=125 kHz
SF=7, Ts = 2^7 / 125000 = 1.024 ms
SF=9, Ts = 2^9 / 125000 = 4.096 ms
SF=12, Ts = 2^12 / 125000 = 32.768 ms
If the SF increases, the Symbol duration increases.
An overview of symbol durations with respect to different Spreading Factors.
If the SF increases by one the symbol duration doubles.
If you increase the SF by 1:
The symbol duration or sweep time doubles compared to the previous SF.
It reduces the bit rate approximately by half compared to the previous SF.
The Time on Air (ToA) (=message transmission time) increases which means the distance increases.
To give you an idea what the Time on Air is for a 10 byte payload and BW=125kHz:
SF7, transmission time = 41 ms
SF12, transmission time = 991 ms
LoRa devices uses a higher spreading factor when the signal is weak or there is lot of interference.
Using a higher spreading factor means a longer Time on Air (ToA).
If an end device is further away from a gateway the signal get weaker and therefore needs a higher spreading factor.
Check out all my other LoRa/LoRaWAN tutorial videos:
• LoRa/LoRaWAN tutorials
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The presentation used in this video tutorial can be found at:
www.mobilefish.com/developer/...
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