Antenna length for 868 and 433 MHz

[bluejedi]

@bluejedi

@rudiniemeijer

The wavelength for the 868 MHz band is thus 299.792.458 / 868.000.000 = 34,54 cm. Half of this is 17,27 cm and a quarter is 8,63 cm.

To be more exact:

868 MHz band LoRaWAN frequencies range from 867.1 MHz to 868.5 MHz (FSK not included) or 867.1 MHz to 868.8 MHz (FSK included) with corresponding middle frequencies 867.8 Mhz and 867.95 MHz respectively.
The optimal LoRaWAN antenna length for 868 MHz band should thus be calculated with (velocity factor not included):

299,792,458 / 867,800,000 = 0.345462 m (FSK channel not included), or
299,792,458 / 867,950,000 = 0.345402 m (FSK channel included)

In practice this will make too little difference (with using 868.0 MHz for the calculation) to be significant.

Correction:
I had forgotten the 869.525 MHz frequency used for the RX2 downlink:

868 MHz band LoRaWAN frequencies range from 867.100 MHz to 869.525 MHz with middle frequency 868.3125 MHz. The optimal LoRaWAN antenna length would thus be (velocity factor not included):

299,792,458 / 868,312,500 = 0.3452587 m for full wave length (1λ) antenna
0,1726294 m for half wave length (½λ) antenna
0,0863147 m for quarter wave length (¼λ) antenna

In practice this still makes too little difference (with using 868.0 MHz for the calculation) to be significant.