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LoRaWAN®

    Overview

    The Things Fundamentals

  • What are LoRa and LoRaWAN?
  • LoRaWAN Architecture
  • Regional Parameters
  • LoRaWAN Relay
  • Message Types
  • Security
  • Device Classes
  • End Device Activation
  • Spreading Factors
  • Adaptive Data Rate
  • Limitations
  • Additional Information

  • Frequency Plans by Country
  • Frequency Plans
  • Duty Cycle
  • Glossary
  • Modulation & Data Rate
  • Addressing & Activation
  • Academic Research
  • Antenna Connectors
  • Antenna Types
  • dB, dBm, dBi and dBd
  • EIRP and ERP
  • Forward Error Correction and Code Rate
  • LoRa Physical Layer Packet Format
  • LoRaWAN® Concentrators
  • LoRaWAN® Transceivers
  • NetID and DevAddr Prefix Assignments
  • Preparing for The Things Certified Fundamentals
  • Regional Limitations of RF Use in LoRaWAN
  • RSSI and SNR
  • The Things Certified Security

dB, dBm, dBi and dBd

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

Questions: #

  1. Convert 5 dBi to dBd.

XdBd = XdBi - 2.15 = 5 - 2.15 = 2.85 dBd

  1. Convert 2 dBd to dBi.

XdBi = XdBd + 2.15 = 2 + 2.15 = 4.15 dBi

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