LoRa/LoRaWAN tutorial 5: Decibel, dBm, dBi, dBd

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This is part 5 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 what the decibel is and what the purposes are of the units dBm, dBi and dBd.

A deciBel (dB) is a unit of measurement used to express the ratio of powers, sound pressures or others things on a logarithmic scale.
The deciBel was invented by Bell Labs and named after Alexander Graham Bell.
In this tutorial the deciBel is used to express the ratio of electrical powers (meaning Watts).
A = 10 x log10(Po / Pi) dB
Where Pi is the input power and Po the output power.
Convert deciBel to power ratio:
Po/Pi = 10^(A/10)

The logarithmic scale is used to avoid very big or very small numbers, meaning the ratios. Using decibels is easier to work with.
For example: A power ratio of 1,000,000 (1 million) can be expressed by 60 dB.
A power ratio of 0,000001 can be expressed by -60 dB.
A power ratio of 1,000,000,000,000,000 (1 quadrillion) can be expressed by 150 dB.
A power ratio of 0,000000000000001 can be expressed by -150 dB.
A power ratio of 1,000,000,000,000,000,000,000,000 (1 septillion) can be expressed by 240 dB.
A power ratio of 0,000000000000000000000001 can be expressed by -240 dB.

dB is a ratio it does not represent an absolute value.
If we use a reference input power of 1mW (Pi=1 mW) the unit is expressed as dBm.
A = 10 x log10(Po / 1) dBm
Po/Pi = 10^(A/10)
P = 10^(A/10) mW
Unit dBm represents an absolute value because it uses a fixed reference value 1mW.

Rule of 10s and 3s:
10 dB = x10
-10 dB = ÷10
3 dB = x2
-3 dB = ÷2

Prefixes can be used with SI units.
SI is French for Systeme Internationale which means International System of Units.

Fore example:
-138dBm = 16 aW
-14dBm = 0.04 mW

Other notable deciBel notations are: dBi and dBd (these also represents ratios)
Antenna manufacturers are using these units to measure antenna performance and is useful for comparison purpose.
Manufacturer A has an 868MHz antenna, its gain is 3 dBi
Manufacturer B has an 868MHz antenna, its gain is 2.5 dBi
dBi refers to the antenna gain with respect to an isotropic antenna.
This is an hypothetic point source antenna, that radiates its power uniformly in all directions.

Radiation or antenna pattern reflects the strength of the radio waves from the antenna in different directions.
dBd refers to the antenna gain with respect to a reference dipole antenna.
The radiation pattern of a dipole antenna looks like a donut.

The relationship between dBd and dBi:
dBi = dBd + 2.15

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   • LoRa/LoRaWAN tutorials  

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The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/...

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