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 log₁₀( P/P₀) dB 

where

P and P₀ are powers 

For Current and Voltages, it is given by

Lp = 20 log₁₀( X/X₀) dB 

where 

X and X₀ 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 log₁₀ 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  Lp = 10log10( P/P0) dB	Formula S(dBm) = 10 log10 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 = 10log₁₀( 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

ADD

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.