Voltage Gain & Bandwidth

 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 = Log₁₀ ( P_OUT / P_IN ) bel

                  1 bel = 10 db

                          = 10 Log₁₀ ( 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_OUT² / R

                P_IN = V_IN² / R

• Voltage gain = 10 Log₁₀ ( P_OUT / P_IN ) db

                            = 10 Log₁₀ [ V_OUT² / R ] / [ V_IN² / R ] db

                            =  20 Log₁₀ ( 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_OUT²R

                P_IN = I_IN²R

• Current Gain = 10 Log₁₀ ( P_OUT / P_IN ) db

                              = 10 Log₁₀ [ I_OUT²R ] / [ I_IN²R ] db

                             = 20 Log₁₀ ( I_OUT / I_IN )

Finally

Power Gain	Log10 ( POUT / PIN ) bel	10 Log10 ( POUT / PIN ) db
Current Gain	Log10 ( IOUT / IIN ) bel	20 Log10 ( IOUT / IIN ) db
Voltage Gain	Log10 ( VOUT / VIN ) bel	20 Log10 ( VOUT / VIN ) db

 

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 Log₁₀ ( 100 ) – 20 Log₁₀ ( 70.7 ) db

         = 20 Log₁₀ ( 100 / 70.7 ) db 

         = 20 Log₁₀ ( 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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