Feedback 1 Figure 8 1 General structure of

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Feedback 1

Feedback 1

Figure 8. 1 General structure of the feedback amplifier. This is a signal-flow diagram,

Figure 8. 1 General structure of the feedback amplifier. This is a signal-flow diagram, and the quantities x represent either voltage or current signals. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 2

Figure E 8. 1 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure E 8. 1 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 3

Figure 8. 2 Illustrating the application of negative feedback to improve the signal-to-noise ratio

Figure 8. 2 Illustrating the application of negative feedback to improve the signal-to-noise ratio in amplifiers. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 4

Figure 8. 3 Illustrating the application of negative feedback to reduce the nonlinear distortion

Figure 8. 3 Illustrating the application of negative feedback to reduce the nonlinear distortion in amplifiers. Curve (a) shows the amplifier transfer characteristic without feedback. Curve (b) shows the characteristic with negative feedback (b = 0. 01) applied. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 5

Figure 8. 4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b)

Figure 8. 4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b) current-mixing current-sampling (shunt–series) topology; (c) voltage-mixing current-sampling (series–series) topology; (d) current-mixing voltage-sampling (shunt–shunt) topology. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 6

Figure 8. 5 A transistor amplifier with shunt–series feedback. (Biasing not shown. ) Microelectronic

Figure 8. 5 A transistor amplifier with shunt–series feedback. (Biasing not shown. ) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 7

Figure 8. 6 An example of the series–series feedback topology. (Biasing not shown. )

Figure 8. 6 An example of the series–series feedback topology. (Biasing not shown. ) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 8

Figure 8. 7 (a) The inverting op-amp configuration redrawn as (b) an example of

Figure 8. 7 (a) The inverting op-amp configuration redrawn as (b) an example of shunt–shunt feedback. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 9

Figure 8. 8 The series–shunt feedback amplifier: (a) ideal structure and (b) equivalent circuit.

Figure 8. 8 The series–shunt feedback amplifier: (a) ideal structure and (b) equivalent circuit. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 10

Figure 8. 9 Measuring the output resistance of the feedback amplifier of Fig. 8.

Figure 8. 9 Measuring the output resistance of the feedback amplifier of Fig. 8. 8(a): Rof : Vt/I. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 11

Figure 8. 10 Derivation of the A circuit and b circuit for the series–shunt

Figure 8. 10 Derivation of the A circuit and b circuit for the series–shunt feedback amplifier. (a) Block diagram of a practical series–shunt feedback amplifier. (b) The circuit in (a) with the feedback network represented by its h parameters. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 12

Figure 8. 10 (Continued) (c) The circuit in (b) with h 21 neglected. Microelectronic

Figure 8. 10 (Continued) (c) The circuit in (b) with h 21 neglected. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 13

Figure 8. 11 Summary of the rules for finding the A circuit and b

Figure 8. 11 Summary of the rules for finding the A circuit and b for the voltage-mixing voltage-sampling case of Fig. 8. 10(a). Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 14

Figure 8. 12 Circuits for Example 8. 1. Microelectronic Circuits - Fifth Edition Sedra/Smith

Figure 8. 12 Circuits for Example 8. 1. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 15

Figure 8. 12 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 12 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 16

Figure E 8. 5 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure E 8. 5 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 17

Figure 8. 13 The series–series feedback amplifier: (a) ideal structure and (b) equivalent circuit.

Figure 8. 13 The series–series feedback amplifier: (a) ideal structure and (b) equivalent circuit. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 18

Figure 8. 14 Measuring the output resistance Rof of the series–series feedback amplifier. Microelectronic

Figure 8. 14 Measuring the output resistance Rof of the series–series feedback amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 19

Figure 8. 15 Derivation of the A circuit and the b circuit for series–series

Figure 8. 15 Derivation of the A circuit and the b circuit for series–series feedback amplifiers. (a) A series–series feedback amplifier. (b) The circuit of (a) with the feedback network represented by its z parameters. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 20

Figure 8. 15 (Continued) (c) A redrawing of the circuit in (b) with z

Figure 8. 15 (Continued) (c) A redrawing of the circuit in (b) with z 21 neglected. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 21

Figure 8. 16 Finding the A circuit and b for the voltage-mixing current-sampling (series–series)

Figure 8. 16 Finding the A circuit and b for the voltage-mixing current-sampling (series–series) case. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 22

Figure 8. 17 Circuits for Example 8. 2. Microelectronic Circuits - Fifth Edition Sedra/Smith

Figure 8. 17 Circuits for Example 8. 2. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 23

Figure 8. 17 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 17 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 24

Figure 8. 17 (Continued). Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 17 (Continued). Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 25

Figure 8. 18 Ideal structure for the shunt–shunt feedback amplifier. Microelectronic Circuits - Fifth

Figure 8. 18 Ideal structure for the shunt–shunt feedback amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 26

Figure 8. 19 Block diagram for a practical shunt–shunt feedback amplifier. Microelectronic Circuits -

Figure 8. 19 Block diagram for a practical shunt–shunt feedback amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 27

Figure 8. 20 Finding the A circuit and b for the current-mixing voltage-sampling (shunt–shunt)

Figure 8. 20 Finding the A circuit and b for the current-mixing voltage-sampling (shunt–shunt) feedback amplifier in Fig. 8. 19. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 28

Figure 8. 21 Circuits for Example 8. 3. Microelectronic Circuits - Fifth Edition Sedra/Smith

Figure 8. 21 Circuits for Example 8. 3. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 29

Figure 8. 21 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 21 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 30

Figure 8. 22 Ideal structure for the shunt–series feedback amplifier. Microelectronic Circuits - Fifth

Figure 8. 22 Ideal structure for the shunt–series feedback amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 31

Figure 8. 23 Block diagram for a practical shunt–series feedback amplifier. Microelectronic Circuits -

Figure 8. 23 Block diagram for a practical shunt–series feedback amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 32

Figure 8. 24 Finding the A circuit and b for the current-mixing current-sampling (shunt–series)

Figure 8. 24 Finding the A circuit and b for the current-mixing current-sampling (shunt–series) feedback amplifier of Fig. 8. 23. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 33

Figure 8. 25 Circuits for Example 8. 4. Microelectronic Circuits - Fifth Edition Sedra/Smith

Figure 8. 25 Circuits for Example 8. 4. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 34

Figure 8. 25 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 25 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 35

Figure 8. 25 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure 8. 25 (Continued) Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 36

Figure E 8. 7 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure E 8. 7 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 37

Figure 8. 26 A conceptual feedback loop is broken at XX¢ and a test

Figure 8. 26 A conceptual feedback loop is broken at XX¢ and a test voltage Vt is applied. The impedance Zt is equal to that previously seen looking to the left of XX¢. The loop gain Ab = –Vr/Vt, where Vr is the returned voltage. As an alternative, Ab can be determined by finding the open-circuit transfer function Toc, as in (c), and the short-circuit transfer function Tsc, as in (d), and combining them as indicated. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 38

Figure 8. 27 The loop gain of the feedback loop in (a) is determined

Figure 8. 27 The loop gain of the feedback loop in (a) is determined in (b) and (c). Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 39

Figure 8. 28 The Nyquist plot of an unstable amplifier. Microelectronic Circuits - Fifth

Figure 8. 28 The Nyquist plot of an unstable amplifier. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 40

Figure 8. 29 Relationship between pole location and transient response. Microelectronic Circuits - Fifth

Figure 8. 29 Relationship between pole location and transient response. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 41

Figure 8. 30 Effect of feedback on (a) the pole location and (b) the

Figure 8. 30 Effect of feedback on (a) the pole location and (b) the frequency response of an amplifier having a single-pole open-loop response. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 42

Figure 8. 31 Root-locus diagram for a feedback amplifier whose open-loop transfer function has

Figure 8. 31 Root-locus diagram for a feedback amplifier whose open-loop transfer function has two real poles. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 43

Figure 8. 32 Definition of w 0 and Q of a pair of complex-conjugate

Figure 8. 32 Definition of w 0 and Q of a pair of complex-conjugate poles. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 44

Figure 8. 33 Normalized gain of a two-pole feedback amplifier for various values of

Figure 8. 33 Normalized gain of a two-pole feedback amplifier for various values of Q. Note that Q is determined by the loop gain according to Eq. (8. 65). Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 45

Figure 8. 34 Circuits and plot for Example 8. 5. Microelectronic Circuits - Fifth

Figure 8. 34 Circuits and plot for Example 8. 5. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 46

Figure 8. 35 Root-locus diagram for an amplifier with three poles. The arrows indicate

Figure 8. 35 Root-locus diagram for an amplifier with three poles. The arrows indicate the pole movement as A 0 b is increased. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 47

Figure E 8. 13 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure E 8. 13 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 48

Figure 8. 36 Bode plot for the loop gain Ab illustrating the definitions of

Figure 8. 36 Bode plot for the loop gain Ab illustrating the definitions of the gain and phase margins. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 49

Figure 8. 37 Stability analysis using Bode plot of |A|. Microelectronic Circuits - Fifth

Figure 8. 37 Stability analysis using Bode plot of |A|. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 50

Figure 8. 38 Frequency compensation for b = 10 -2. The response labeled A¢

Figure 8. 38 Frequency compensation for b = 10 -2. The response labeled A¢ is obtained by introducing an additional pole at f. D. The A² response is obtained by moving the original low-frequency pole to f ¢D. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 51

Figure 8. 39 (a) Two cascaded gain stages of a multistage amplifier. (b) Equivalent

Figure 8. 39 (a) Two cascaded gain stages of a multistage amplifier. (b) Equivalent circuit for the interface between the two stages in (a). (c) Same circuit as in (b) but with a compensating capacitor CC added. Note that the analysis here applies equally well to MOS amplifiers. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 52

Figure 8. 40 (a) A gain stage in a multistage amplifier with a compensating

Figure 8. 40 (a) A gain stage in a multistage amplifier with a compensating capacitor connected in the feedback path and (b) an equivalent circuit. Note that although a BJT is shown, the analysis applies equally well to the MOSFET case. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 53

Figure 8. 41 Circuit of the shunt–series feedback amplifier in Example 8. 4. Microelectronic

Figure 8. 41 Circuit of the shunt–series feedback amplifier in Example 8. 4. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 54

Figure 8. 42 Circuits for simulating (a) the open-circuit voltage transfer function Toc and

Figure 8. 42 Circuits for simulating (a) the open-circuit voltage transfer function Toc and (b) the short-circuit current transfer function Tsc of the feedback amplifier in Fig. 8. 41 for the purpose of computing its loop gain. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 55

Figure 8. 43 Circuit for simulating the loop gain of the feedback amplifier circuit

Figure 8. 43 Circuit for simulating the loop gain of the feedback amplifier circuit in Fig. 8. 41 using the replica-circuit method. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 56

Figure 8. 44 (a) Magnitude and (b) phase of the loop gain Ab of

Figure 8. 44 (a) Magnitude and (b) phase of the loop gain Ab of the feedback amplifier circuit in Fig. 8. 41. Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 57

Figure P 8. 4 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 4 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 58

Figure P 8. 19 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 19 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 59

Figure P 8. 26 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 26 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 60

Figure P 8. 30 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 30 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 61

Figure P 8. 32 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 32 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 62

Figure P 8. 33 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 33 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 63

Figure P 8. 34 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 34 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 64

Figure P 8. 35 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 35 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 65

Figure P 8. 38 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 38 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 66

Figure P 8. 39 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 39 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 67

Figure P 8. 40 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 40 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 68

Figure P 8. 42 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 42 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 69

Figure P 8. 44 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 44 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 70

Figure P 8. 46 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 46 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 71

Figure P 8. 48 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 48 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 72

Figure P 8. 51 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 51 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 73

Figure P 8. 52 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 52 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 74

Figure P 8. 81 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford

Figure P 8. 81 Microelectronic Circuits - Fifth Edition Sedra/Smith Copyright 2004 by Oxford University Press, Inc. 75