The decibel is a logarithmic unit used to express the ratio of two power levels or amplitudes. It is commonly used to measure sound levels or power in electronic systems. A decibel represents one tenth of a bel, with 0 dB representing a ratio of 1. Power gain in decibels is calculated as 10 times the log of the ratio between output and input power. A doubling of power equals a 3 dB gain. Total system gain is the sum of individual stage gains. Attenuation is expressed as a negative decibel value. Voltage and current gains can also be expressed in decibels by taking the log of the ratio of output to input levels.

1. THE DECIBEL-dB
THE DECIBEL IS A LOGARITHMIC UNIT OF MEASUREMENT THAT EXPRESSES THE
MAGNITUDE OF POWER OR AMPLITUDE RELATIVE TO A SPECIFIED REFERENCE
LEVEL AND IS COMMONLY USED IN THE MEASUREMENT OF SOUND OR POWER
WHEN INVESTIGATING ELECTRONIC SYSTEMS.
A DECIBEL IS ONE TENTH OF A BEL, A SELDOM-USED UNIT.

2. DECIBEL-POWER GAIN
THE POWER GAIN (Ap) OF AN AMPLIFIER IS THE LOGARITHMIC RATIO
BETWEEN INPUT POWER(Pi) AND OUTPUT POWER (Po)
Ap=10 log
𝑷𝒐
𝑷𝒊
𝒅𝑩

3. Decibel – Power Gain
 Ap=
𝑷𝒐
𝑷𝒊
=
𝟐𝟎𝟎
𝟏𝟎𝟎
= 𝟐
 Ap= 10 log 𝐥𝐨𝐠𝟏𝟎
𝟐𝟎𝟎
𝟏𝟎𝟎
=3dB
 A 3dB GAIN IS A DOUBLING OF POWER

4. Power gain
gain Gain(dB)
1 0
10 10
100 20
1000 30
10000 40
100000 50

5. MULIT-STAGE POWER GAIN
SYSTEM GAIN(Ap) IS THE SUM OF THE INDIVIDUAL STAGE GAINS
Ap= Ap1+ Ap2 =10+100= 110dB

6. DECIBLE(Db)
A1=10^4 : A2=10^5 = A1X A2 => 10^9
It can be easily written as:
10log10( 10^4) 10log10 10^5
=40dB =50dB
40+50=90dB

7. DECIBEL-ATTENUATION
IT IS ALSO POSSIBLE TO EXPRESS A REDUCTION OF POWER IN DECIBELS- THIS
IS KNOWN AS ATTENUATION AND THE RESULT TAKES A NEGATIVE SIGN
INDICATING A REDUCTION.
Ap =10𝐥𝐨𝐠𝟏𝟎
𝟎.𝟎𝟎𝟏
𝟎.𝟏𝟎
= −𝟐𝟎𝒅𝑩
A REDUCTION OF ONE HUNDRED TIMES IS EXPRESSED AS -20dB

8. DECIBEL-AMPLITUDE GAIN
IT IS ALSO COMMON TO EXPRESS THE RATIO OF VOLTAGE OR CURRENT IN DECIBELS
Ap =20log10
𝑉𝑜
𝑉𝑖
𝑑𝐵
THE OUTPUT RESISTANCE (Ro) MUST BE EQUAL TO THE INPUT RESISTANCE (Ri),
i.e.., the condition for maximum power transfer

9. DECIBEL – AMPLITUDE GAIN
𝑽𝒐
𝑽𝒊
=
𝟐𝟎𝟎
𝟐𝟎
= 𝟏𝟎
Av =20𝐥𝐨𝐠𝟏𝟎
𝟐𝟎𝟎
𝟐𝟎
= 𝟐𝟎𝒅𝑩
A VOLTAGE GAIN OF TEN TIMES IS EQUAL TO +20dB

10. VOLTAGE GAIN
VOLTAGE GAIN GAIN(dB)
0.01 -40
0.1 -20
0.5 -6
1 0
2 6
10 20
100 40

11. Db Ratios
dBm is an abbreviation for the power ratio in decibels (dB) of the measured power referenced
to one milliwatt (mW). It is used in radio, microwave and fibre optic networks as a convenient
measure of absolute.
dBW is referenced to one watt (1000 mW)and is an absolute unit,used when measuring
absolute power.
In audio is typically referenced relative to a 600 ohm impedance , while in ratio frequency
work dBm is typically referenced relative to a 50 ohm impedance
RELATION:
PdBw =>P dBm
x=> (x+30)dBm

12. Decibel scale: