In this chapter briefly discuss some units that are used to measure the performance of transceivers (gateways and end devices) and antennas
dB (decibel) #
The decibel can be used to express the ratio of two physical quantities such as power, sound intensity, sound pressure, voltage, and current on a logarithmic scale. In LoRaWAN we use decibel to express the ratio between two power levels usually given in watt (W) or milliwatt (mW).
The power ratio, N can be expressed in decibel using the formula,
N = 10 log10 (Pout/Pin) dB
where Pout is the output power and Pin is the input power.
Note:When we are dealing with the power levels we use 10log units.
For example, if an amplifier turns a 1 W signal into a 1000 W signal, its power ratio can be expressed as:
N = 10 log10 (Pout/Pin) = 10 log10 (1000/1) = 30 dB
Decibel doesn’t provide an absolute value. By looking at the decibel value you can’t say the input and output power of a device or cable etc, but you can say whether it offers a gain or a loss.
A power ratio greater than 0 dB is treated as a gain. For example, if an amplifier turns a 2 W signal into a 10 W signal, the power ratio is:
N = 10 log10 (Pout/Pin) = 10 log10 (10/2) = 10 log10 (5) = 6.9 dB (gain)
A power ratio less than 0 dB is treated as a loss (negative gain or attenuation). For example, if 10 W of power is fed into a cable but only 8 W is measured at the output, the power ratio is:
N = 10 log10 (Pout/Pin) = 10 log10 (8/10) = 10 log10(0.8) = -0.9 dB (loss)
The power ratio of 0 dB means there is no gain or loss.
dBm (decibel per milliwatt) #
If you use the reference input power (Pin) of 1 mW the power ratio, N can be expressed in dBm:
N = 10 log10(Pout / 1) dBm
By using the above formula, Pout can be expressed in mW which is an absolute value.
Pout/Pin = 10(N/ 10)
Pout = 10(N/ 10) mW
For example, if a LoRaWAN gateway has an output power of 22 dBm, how much power does it generate in W?
Pout = 10(N / 10) = 10(22 / 10) = 10(2.2) = 158.48 mW = 0.158 W
Rule of 10s and 3s #
By using only 10s and 3s, one can easily convert a dBm value to its corresponding absolute power value without using the logarithmic scale.
- 10 dB = x10 (makes output power 10 times as the input power, for example, input=10 W and output=100 W)
- -10 dB = ÷10 (makes output power 1/10 times as the input power, for example, input=100 W and output=10 W)
- 3 dB = x2 (doubles the power, for example, input=5 W and output=10 W)
- -3 dB = ÷2 (halves the power, for example, input=10 W and output=5 W)
For example, if you want to convert 1 dBm its corresponding absolute power value, 1 can be written as, 10 -3 -3 -3.
Then apply the rule:
1 dB = 10 dB -3 dB -3 dB -3 dB = x10 ÷2 ÷2 ÷2 = 1.25
Remember Pin is always 1 mW and ’m' in dBm stands for milliwatt. So we multiply the above answer by 1 mW.
1 dBm = 1 mW x 1.25 = 1.25 mW
When you write any dBm value using 10s and 3s remember,
- If possible avoid using 3s
- Never use more than five 3s
Let’s take another example:
For example, if a LoRaWAN gateway has an output power of 17 dBm, how much power does it generate in mW?
17 can be written as, 10 +10 -3
Then apply the rule:
17 dB = 10 dB +10 dB -3 dB = x10 x10 ÷2 = 50
17 dBm = 1 mW x 50 = 50 mW
Antenna gains #
The units dBi and dBd are used to express antenna gains.
dBi (decibel relative to isotropic) #
The gain of an antenna can be measured relative to an isotropic antenna and is expressed in dBi. An isotropic antenna is a hypothetical antenna that radiates power uniformly in all directions. The gain of an isotropic antenna is 0 dB which means it has no gain or loss.
dBd (decibel relative to dipole) #
The gain of an antenna can be measured relative to a reference dipole antenna and is expressed in dBd. A reference dipole antenna offers a fixed 2.15 dB of gain over an isotropic antenna.
The following equation represents the relationship between dBi and dBd:
dBi = dBd + 2.15 dB
- Convert 5 dBi to dBd.
XdBd = XdBi - 2.15 = 5 - 2.15 = 2.85 dBd
- Convert 2 dBd to dBi.
XdBi = XdBd + 2.15 = 2 + 2.15 = 4.15 dBi