Gain with Feedback

Gain with Feedback

AU : May-03, 04, 10, 11, Dec.-04, 05

• Looking at Fig. 9.3.4 we have,

A = X_o / X_i and A_f = X_o / X_s

where          X_o = Output voltage or output current

X_i = Input voltage or input current

X_s = Source voltage or source current

• As it is a negative feedback the relation between X_i and X_s is given as

X_i =  X_s  + (- X_f )

where X_o = Feedback voltage or feedback current

A_f = X_o / X_s =  X_o / X_i +X_f

• Dividing by Xi to numerator and denominator we get,

Important Concept

Looking at equation (9.6.1) we can say that gain without feedback (A) is always greater than gain with feedback [AJ(1 + β A)] and it decreases with increase in P i.e. increase in feedback factor.

• For voltage amplifier, gain with negative feedback is given as

Av_f = A_v / 1 + A_v  β ... (9.6.2)

where          A_v = Open loop gain i.e. gain without feedback

β = Feedback factor

1. Loop Gain

• The difference signal, Xd in Fig. 9.3.4 is multiplied by A in passing through the amplifier, is multiplied by P in transmission through the feedback network, and is multiplied by β in the mixing or difference network. A path of a signal from input terminals through basic amplifier, through the feedback network and back to the input terminals forms a loop. The gain of this loop is the product -A β. This gain is known as loop gain or return ratio.

2. Desensitivity of Gain

• The transfer gain of the amplifier is not constant as it depends on the factors such as operating point, temperature, etc. This lack of stability in amplifiers can be reduced by introducing negative feedback.

We know that, A_f = A / 1 + β A

• Differentiating both sides with respect to A we get,

• Looking at equation (9.6.3) we can say that change in the gain with feedback is less than the change in gain without feedback by factor (1 + β A). The fractional change in amplification with feedback divided by the fractional change without feedback is called the sensitivity of the transfer gain. Hence the sensitivity is (1 + β A). The reciprocal of the sensitivity is called the desensitivity D. It is given as

D = 1 + β A

• The amount of feedback introduced into an amplifier is often expressed in decibels by the definition.

N = dB of feedback = 20 log | A_vf / A_v |

= 20 log | 1 / 1 + Aβ | …

• If negative feedback is under consideration, N will be a negative number.

• Therefore, stability of the amplifier increases with increase in desensitivity.

• If β A >> 1, then

A_f = A / a + β A = A / β A = 1 / β ... (9.6.4)

and the gain is dependent only on the feedback network.

• Since A represents either A_v, G_M, A_I or R_M and A_f represents the corresponding transfer gains with feedback either A_vf, G_Mf, A_If or R_Mf the equation signifies that :

• For voltage series feedback :

A_vf = 1 / β voltage gain is stabilized ... (9.6.5)

• For current series feedback :

A_MF = 1 / β transconductance gain is stabilized ... (9.6.6)

• For voltage shunt feedback :

R_MF = 1 / β transconductance gain is stabilized … (9.6.7)

• For current shunt feedback :

A_If = 1 / β current gain is stabilized … (9.6.8)

Review Questions

1. W/zflf are the effects of negative feedback on gain of an amplifier ?

AU : ECE : May-03, Dec.-OS, Marks 2

2. Derive expressions for the closed loop forward transfer ratio for negative feedback.

AU : ECE : Dec.-04, Marks 6

3. Define loop gain.

4. What is 'return ratio' of a feedback amplifier ?

AU : ECE : May-11, Marks 2

5. Define ’desensitivity’ of transfer gain.

AU : ECE : May-04, Marks 2

6. Define sensitivity and desensitivity of gain in feedback amplifiers.

AU : ECE : May-10, Marks 2