1. Decibel Gain
Power Gain The power gain G of an amplifier is the ratio of output power to the input power If the output power is 15W and input power is 0.5W then The output power is 30 times greater then the input power

2. Decibel Gain
The power gain of an audio amplifier is measured in the units of ‘BEL’ in the honor of Graham Bell the inventor of Telephones.
1 Bel= 10 deciBel
As a unit the Bel was actually devised as a convenient way to represent power loss in he telephone system wiring rather then gain in amplifiers. It is defined in logarithmic scale since human ear is sensitive to sound energy only in logarithmic scale.
The decibel power gain (G) is defined in terms of the normal gain (G) dB

3. Decibel Gain Decibels:
If the circuit has a power gain of 100, its decibels power gain is dB

4. Decibel Gain 10 dB for each factor of 10:
If the power gain is 10; then the decibel power gain is
If the power gain is 100; then the decibel power gain is
If the power gain is 1000; then the decibel power gain is

5. Decibel Gains G G/ 1 10 100 1000 10000 0dB 10dB 20dB 30dB 40dB
Similar results applies to power gain of less than 1. When the power gain is 0.1; the decibel gain is -10dB

6. Decibel Gain
3 dB for each factor of 2: If the power gain is 2, then the decibel power gain is G=4, the decibel power gain is G=8, the decibel power gain is When the normal power gain doubles, the decibel power gain increases by approximately 3dB

7. Decibel Gains Negative Decibels:
If power gain is less than 1 there is a power loss (attenuation), and the decibel power gain is negative. For instance, if the output power is 1.5W and the input power is 3W, then
And the decibel power gain is
When the power gain is 0.25,
When the power gain is 0.125,

8. Decibel Gain

9. Ordinary Gain Multiply The figure shows two stage s in an amplifier
Ordinary Gain Multiply The figure shows two stage s in an amplifier. The first stage has an input power of P1, an output power of P2, and a power gain The second stage has an input power of p2,an output power of P3, and a power gain of The total power gain of the two stages is

10. For example, a first stage power gain is 100 and the second stage power gain is 200, the total power gain is

11. Decibel Gain Decibel Gains Add:
Since the total gain of two cascaded stages is
We can take the logarithm of both sides to get
Multiplying both sides by 10 gives
Which can be written as

13. Relation of power and voltage gains
The rms voltage across the amplifier input terminal equals V1 and the rms voltage across the amplifier output terminals equals V2. therefore, the input power to the amplifier is
And the output power is
The power gain from input to out equals

14. Decibel voltage gain (A/) is For example if A is 40, then
Voltage measurements are more common than power measurements. Therefore it is not surprising that decibels are also used to specify voltage gain.
Decibel voltage gain (A/) is
For example if A is 40, then A 1
0.5
0.25
0.125
0dB
-6dB
-12dB
-18dB A 1 2 4 8
0dB
6dB
12dB
18dB

15. Factors of 2 and 10: When A=2 When A=4 When A=8
When the voltage gain doubles the decibel gain increases by 6dB.
If the voltage gain decreases by a factor of 2, hen the decibel gain decreases by 6dB.
Also when the voltage gain increases by a factor of 10 , the decibel gain increases by 20 dB.

16. A 1 10
100
1000
0dB
20dB
40dB
60dB

17. Half power point:
The frequency at which the output power is half of the input power is called the half power point. This is also called the cutoff frequency
At the cut off frequency
A=0.707 As
For R1 =R2