CHAPTER 3. FILTER CIRCUITS59Figure 3.13: Transfer function and phase shift for the above circuit.3.7.2Ampliﬁer with Negative FeedbackFeedback is a widely used technique to improve the characteristics of an imperfect ampliﬁer.A generalized ampliﬁer with negative voltage feedback is shown in ﬁgure 3.15.The overall transfer function (closed-loop gain) can be written asH(s)=v3v1.(3.79)Realizing thatv2 = v1− v4;v2 =v3A(s)andv4 = Fv3.(3.80)we may writeH(s)=A1+ AF.(3.81)If|AF|1⇒ H(s)=1/F. The transfer function is now independent of the ampliﬁergain. F is the transfer function of a stable resistive network which means that H will alsobe stable.