Difference between dB, dBM and dBi || Solved Examples on dB, dBm, and dBi-
Decibel is the unit of
sound intensity. It is the ratio of two physical quantities and then the
logarithm of the ratio is taken. It is also used in electricity to measure
current, voltage, and power. It can also be defined as the difference between
two power levels. But most commonly it is used to measure the relative loudness
of sounds. One decibel is equal to 1/10 bel. Decibel is a dimensionless
quantity as it is the logarithmic ratio.
The formula is given by
L_{p} = 10 log_{10}( P/P_{0}) dB
where
P and P_{0} are powers
For Current and Voltages, it is given by
Lp = 20 log_{10}( X/X_{0}) dB
where
X and X_{0} are either both voltages or both are currents
Decibel
Milliwatts(dBm) is
used to express decibels in terms of milliwatts. It helps to predict the actual
power output. It is used to measure the signal strength of wires and cables. It
is equivalent to 0.001 watts. It is a dimensionless quantity like decibels.
The formula is given
by
S_{dBM} =
10 log_{10} P
where
P is Power
Decibel Relative to
Isotropic Gain(dBi) is
used to measure the forward gain of an antenna. The forward gain of the antenna is
defined as the ratio of the signal transmitted in a single maximum direction.
dBi also reflects the antenna’s maximum efficiency. It highlights a comparison
between a real antenna and an isotropic antenna (hypothetical).
The formula to
calculate the power gain of the antenna is
G(dBi) = 10 log(G)
where G(dBi) is the
gain of an isotropic antenna and G is the comparison between a real antenna and
an isotropic antenna (hypothetical)
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:
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
Difference between dB, dBm, and dBi
dB |
dBm |
dBi |
dB stands for Decibels. |
dBm stands for Decibel Milliwatts. |
dBi stands for Decibel Relative to
Isotropic Gain. |
It is the measure of loudness. |
It is a unit used to express
decibels in milliwatts and is often used to measure the strength of the
signal in wires and cables. |
It draws a comparison between a
real antenna and a hypothetical isotropic antenna. |
dB gives the ratio. |
dBm gives absolute power. |
dBi is used to measure the
strength of the hypothetical antenna. |
Formula L_{p} =
10log10( P/P_{0}) dB |
Formula S(dBm) = 10 log_{10 }P |
Formula G(dBi) = 10 log(G) |
dB is used to measure sound
intensity |
It is used to measure small values
and is used in wires. |
dBi is used to measure the
performance of the antenna |
Solved Examples on dB, dBm, and dBi
Solution:
Example 1: The ratio of two intensities of sounds is given as 3. Find the difference between the two sound levels.
Let the intensity of
two sound levels be a and b.
b/a = 3
As we all know decibel
is used to measure the difference between sound levels. Let the two sound
levels be named x and y
y – x = 10log_{10}(
b/a)
=> y – x = 10
log(3)
=>y – x =
10×(0.477)
=>y – x = 4.77 dB
Example 2: Convert 4mW
to dBm
Solution:
The power(P) given is
4mW
S(dBM) = 10 log
P
= 10 log (4)
= 6.02 dBm
Example 3: Find the
gain of an isotropic antenna provided the comparison gain is given by 5Watt
Solution:
G = 5W (given)
Using the formula
G(dBi) = 10 log(G)
=>G(dBi) = 10
log(5)
=>G(dBi) = 6.98 dBi
Example 4: Convert 10mW to dBm
Solution:
The power(P) given is
10mW
S(dBM) = 10 log
P
= 10 log (10)
= 10 dBm
FAQs on dB, dBm, and dBi
Question 1: Does decibel measures the amplitude or the frequency of the sound?
Answer:
Decibel is used to measure the sound
intensity. Frequency is used to measure the number of sound waves in one second
and is measured in hertz. Decibel is used to measure the amplitude of the
sound.
Question 2: What does
the higher dBi mean?
Answer:
Higher dBi means more forward gain of
the antenna. More forward gain means that the strength of the signal is more
but the direction will be narrow. The signal will not spread in a broader
direction.
Question 3: Define
dBm. What value is suitable in dBm for cables and wires?
Answer:
dBm stands for Decibel Milliwatts. It is
often used to measure the strength of the signal in wires and cables. For values
greater than -70dBm, the signal is excellent. For values -100 dBm or -110 dBm
the signal strength is considered poor.
Question 4: Write one use of dB, dBi, and dBm
Answer:
The uses are as
follows:
1. dB is used to measure
the loudness of the sound.
2. dBi is used to measure
the forward gain of the antenna.
3. dBm is used to measure
signal strength in cables and wires.
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