**Gain of the Amplifier**

- The ratio of the output quantity to the input quantity of the amplifier is called as Gain of the Amplifier.

**Gain of Multi Stage
Amplifier**

- Let us consider three amplifiers having respective gain of G1, G2 and G3. The total gain of the amplifier is

G = G1 × G2 × G3

- The gain of the multistage amplifier G is less than produce of G1 × G2 × G3 due to loading of next stages.

**Decibel Gain**

- The gain of the amplifier is very large therefore it is represented by common logarithm ( base 10 ). The unit of gain is bel or db.

**Power gain **

- The ratio of output power to the input power in log to the base 10 is called as power gain of the amplifier.

Power Gain = Log_{10} ( P_{OUT} / P_{IN
}) bel

** ****1 bel
= 10 db**

= 10 Log_{10} ( P_{OUT} / P_{IN }) db

**Voltage Gain**

- The ratio of the output voltage to the input voltage in log of base 10 is called as voltage gain of the amplifier.

Let P_{OUT} = V_{OUT}^{2} / R

P_{IN} = V_{IN}^{2} / R

- Voltage gain = 10 Log
_{10}( P_{OUT}/ P_{IN }) db

= 10 Log_{10} [ V_{OUT}^{2}
/ R ] / [ V_{IN}^{2} / R ] db

= 20 Log_{10} ( V_{OUT}
/ V_{IN} ) db

**Current Gain**

- The ratio of the output current to the input current in log of base 10 is called as voltage gain of the amplifier.

Let P_{OUT} = I_{OUT}^{2}R

P_{IN} = I_{IN}^{2}R

- Current Gain = 10 Log
_{10}( P_{OUT}/ P_{IN }) db

= 10 Log_{10} [ I_{OUT}^{2}R ] / [ I_{IN}^{2}R
] db

= 20 Log_{10 }( I_{OUT} / I_{IN} )

Finally

Power Gain |
Log |
10 Log |

Current Gain |
Log |
20 Log |

Voltage Gain |
Log |
20 Log |

**Bandwidth **

- It is range of frequencies over which the voltage gain is equal to or greater than 70.7% of the maximum gain.
- The f1 and f2 is range of frequencies over which the gain is equal / greater than 70.7% of the maximum gain.

Where f1 = Lower cut off frequency

f2 =
Higher cut off frequency

- Bandwidth = f2 – f1
- It is important that the signal frequencies lie between f1 and f2 for distortion less amplification.

**Bandwidth in terms of
db**

- Let us consider that the maximum gain of the amplifier is 100.
- Fall in voltage gain from 100 to 70.7%

= 20 Log_{10} ( 100 ) – 20 Log_{10} (
70.7 ) db

= 20 Log_{10} ( 100 / 70.7 ) db

= 20 Log_{10} ( 1.414 ) db

= 3db

*The bandwidth of the amplifier is defined as the range of
frequency over which the voltage gain fall by 3 db from the maximum gain.*

- The frequency f1 or f2 is called as half power frequency or 3 db frequency.

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