By Robert Pease
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Assume that the op-amp is ideal; it has inﬁnite bandwidth and can source and sink inﬁnite current. Given this, the transfer function is: H ( s) ϭ vo (s) 1 1 ϭ ϭ Ϫ10 2 L 10 s ϩ 10Ϫ6 s ϩ 1 vi (s) LCs2 ϩ s ϩ 1 R w ww. c om [1-27] Phase (deg); Magnitude (dB) Review of Feedback Systems 21 Bode plot of closed-loop transfer function for gain of ϩ10 amplifier 20 10 0 Ϫ10 Ϫ20 Ϫ30 Ϫ40 Ϫ50 Ϫ100 Ϫ150 104 105 106 Frequency (rad/sec) 107 Figure 1-22: Bode plot of closed-loop transfer function for gain of ϩ10 ampliﬁer.
T. 200 150 Phase (deg); Magnitude (dB) 100 50 0 Ϫ100 Ϫ150 Ϫ200 Ϫ250 Ϫ300 10–2 10–1 100 101 Frequency (rad/sec) (b) Figure 1-14: Unity-feedback system that has a loop transmission magnitude greater than unity where the loop transmission angle is ؊180°. (a) System. T. showing the magnitude is greater than 1 when the angle is more negative than ؊180°. The Routh test shows that this system is BIBO stable since there are no sign changes in the ﬁrst column of the Routh matrix. 92 r/s Therefore, all poles are in the left-half plane and the system is BIBO stable.
Given this, the transfer function is: H ( s) ϭ vo (s) 1 1 ϭ ϭ Ϫ10 2 L 10 s ϩ 10Ϫ6 s ϩ 1 vi (s) LCs2 ϩ s ϩ 1 R w ww. c om [1-27] Phase (deg); Magnitude (dB) Review of Feedback Systems 21 Bode plot of closed-loop transfer function for gain of ϩ10 amplifier 20 10 0 Ϫ10 Ϫ20 Ϫ30 Ϫ40 Ϫ50 Ϫ100 Ϫ150 104 105 106 Frequency (rad/sec) 107 Figure 1-22: Bode plot of closed-loop transfer function for gain of ϩ10 ampliﬁer. ) Figure 1-23: Step response for gain of ϩ10 ampliﬁer. Vi ϩ Ϫ 10 H 10 F Vo 10 Figure 1-24: Ideal op-amp driving a reactive load.