Let the Band Width of an amplifier without feedback is = BW. Band width of an amplifier with negative feed back is . Negative feedback increases Band width.

Proof:- Consider an amplifier with gain ‘A’

Now the frequency response of the amplifier is as shown in the figure. Frequency response curve means gain (dB) Vs frequency (Hz)

the frequency response of an amplifier consists of three regions

- Low frequency region ( -lower cut off frequency).
- Mid frequency region ( between and ).
- High frequency region ( the region -upper cutoff frequency)

Gain in low- frequency region is given as,

-open loop gain,

– frequency,

– lower cut off frequency, where Gain in constant region is .

Gain in High-frequency region is .

In low-frequency region:-

since open loop gain in low-frequency region is and gain with feedback is

From EQN(I) after substituting in the above equation

Now by dividing the whole expression with

, where and

for example lower cut-off frequency implies is decreasing with negative feedback.

In High-frequency region:-

Gain with out feed back in High frequency region is

Now Gain with negative feed back is

Substituting in the above equation

Now by dividing the whole expression with

, where and

for example lower cut-off frequency implies is increasing with negative feedback.

In Mid-frequency region:-

Gain with out feed back is

and the gain with negative feed back is

With out feedback | With feedback |

lower cut-off frequency is | lower cut-off frequency , increases |

upper cut-off frequency is | upper cut-off frequency is |

BW = | increases |

Thus negative feedback decreases lower cut-off frequency and increases upper cut-off frequency.

Over all gain decreases with negative feedback and Band Width increases.