**Effect of Negative Feedback on Bandwidth:**

The effect of negative feedback on bandwidth is given below as

From Eq. (19.8) voltage gain with feedback is given as

and from the above result it may be concluded that the voltage gain may be made to depend entirely on the feedback network. However, it is now important to consider the fact that even if Î² is constant, the voltage gain A_{v} is not, since it depends on frequency. This means that at certain low or high frequencies Î²A_{v}Â will not be much larger than unity, and, therefore, Eq. (19.26) will not be valid.

When negative feedback is applied in an amplifier, cutoff frequencies are also affectedâ€”lower cutoff frequency is lowered by a factor of (1 + Î²A) while upper cutoff frequency is raised by the same factor (1 + Î²A). This is explained below.

**(i) Lower Cutoff Frequency f _{1}:** The voltage gain at a frequency f in low frequency range of R-C coupled amplifier is given as

where f_{1} is lower cutoff frequency and j j = âˆš-1.

When negative feedback is applied

Substituting the value of A_{vl}Â from Eq. (19.27) in Eq. (19.29) we have

By dividing numerator and denominator by 1 + Î² A_{vm},Â this equation may be rewritten as

where

From above equations we see that the midband amplification with feedback A_{vmf}Â equals the midband amplification without feedback divided by 1 + Î²A_{vm}.Â Also the lower cutoff frequency with feedback fâ€²_{1 }equals the lower cutoff frequency without feedback f_{1} divided by the same factor (1 + Î²A_{vm}) i.e., lower cutoff frequency is reduced when negative feedback is applied.

**(ii) Upper Cutoff Frequency:** The voltage gain at frequency f in the high frequency range of R-C coupled amplifier is given as

When negative feedback is applied

Substituting the value of A_{vh} from Eq. (19.32) in Eq. (19.33), we have

By dividing the numerator and denominator by 1 + Î²A_{vm},Â the above equation may be rewritten as

where

Thus we see that upper cutoff frequency with feedback equals the corresponding cutoff frequency without feedback f_{2} multiplied by the factor (1 + Î²A_{vm})Â i.e., upper cutoff frequency is raised when negative feedback is applied in an amplifier.

The effect of negative feedback on frequency response curve is shown in Fig. 19.16.

**Bandwidth:**

The effect of negative feedback on bandwidth is given as

Since fâ€²_{2}Â > f_{2}Â and fâ€²_{1}Â < f_{1} hence the negative feedback on bandwidth is increased.

Assuming fâ€²_{2}Â >> fâ€²_{1}Â and f_{2}Â >> f_{1}Â bandwidth may be rewritten

as

times bandwidth without feedback.

Thus we see that bandwidth of an amplifier with negative feedback is increased by the same factor by which voltage gain is reduced and gain bandwidth product remains the same. However, since the amplifier with feedback has lower gain, the net operation is to trade bandwidth for gain.