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ANALOG SIGNAL PROCESSING
1
Basic introduction
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 2
Figure 1.1 Two alternative representations of a signal source: (a) the Thévenin form, and (b) the Norton form.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 3
Figure 1.2 An arbitrary voltage signal vs(t).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 4
Figure 1.3 Sine-wave voltage signal of amplitude Va and frequency f = 1/T Hz. The angular frequency v = 2pf rad/s.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 5
Figure 1.4 A symmetrical square-wave signal of amplitude V.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 6
Figure 1.5 The frequency spectrum (also known as the line spectrum) of the periodic square wave of Fig. 1.4.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 7
Figure 1.6 The frequency spectrum of an arbitrary waveform such as that in Fig. 1.2.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 8
Figure 1.7 Sampling the continuous-time analog signal in (a) results in the discrete-time signal in (b).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 9
Figure 1.8 Variation of a particular binary digital signal with time.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 10
Figure 1.9 Block-diagram representation of the analog-to-digital converter (ADC).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 11
Figure 1.10 (a) Circuit symbol for amplifier. (b) An amplifier with a common terminal (ground) between the input and output ports.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 12
Figure 1.11 (a) A voltage amplifier fed with a signal vI(t) and connected to a load resistance RL. (b) Transfer characteristic of a linear voltage amplifier with voltage gain Av.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 13
Figure 1.12 An amplifier that requires two dc supplies (shown as batteries) for operation.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 14
Figure 1.13 An amplifier transfer characteristic that is linear except for output saturation.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 15
Figure 1.14 (a) An amplifier transfer characteristic that shows considerable nonlinearity. (b) To obtain linear operation the amplifier is biased as shown, and the signal amplitude is kept small. Observe that this amplifier is operated from a single power supply, VDD.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 16
Figure 1.15 A sketch of the transfer characteristic of the amplifier of Example 1.2. Note that this amplifier is inverting (i.e., with a gain that is negative).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 17
Figure 1.16 Symbol convention employed throughout the book.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 18
Figure 1.17 (a) Circuit model for the voltage amplifier. (b) The voltage amplifier with input signal source and load.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 19
Figure 1.18 Three-stage amplifier for Example 1.3.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 20
Figure 1.19 (a) Small-signal circuit model for a bipolar junction transistor (BJT). (b) The BJT connected as an amplifier with the emitter as a common terminal between input and output (called a common-emitter amplifier). (c) An alternative small-signal circuit model for the BJT.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 21
Figure E1.20
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 22
Figure 1.20 Measuring the frequency response of a linear amplifier. At the test frequency v, the amplifier gain is characterized by its magnitude (Vo/Vi) and phase f.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 23
Figure 1.21 Typical magnitude response of an amplifier. |T(v)| is the magnitude of the amplifier transfer function—that is, the ratio of the output Vo(v) to the input Vi(v).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 24
Figure 1.22 Two examples of STC networks: (a) a low-pass network and (b) a high-pass network.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 25
Figure 1.23 (a) Magnitude and (b) phase response of STC networks of the low-pass type.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 26
Figure 1.24 (a) Magnitude and (b) phase response of STC networks of the high-pass type.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 27
Figure 1.25 Circuit for Example 1.5.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 28
Figure 1.26 Frequency response for (a) a capacitively coupled amplifier, (b) a direct-coupled amplifier, and (c) a tuned or bandpass amplifier.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 29
Figure 1.27 Use of a capacitor to couple amplifier stages.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 30
Figure E1.23
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 31
Figure 1.28 A logic inverter operating from a dc supply VDD.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 32
Figure 1.29 Voltage transfer characteristic of an inverter. The VTC is approximated by three straightline segments. Note the four parameters of the VTC (VOH, VOL, VIL, and VIH) and their use in determining the noise margins (NMH and NML).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 33
Figure 1.30 The VTC of an ideal inverter.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 34
Figure 1.31 (a) The simplest implementation of a logic inverter using a voltage-controlled switch; (b) equivalent circuit when vI is low; and (c) equivalent circuit when vI is high. Note that the switch is assumed to close when vI is high.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 35
Figure 1.32 A more elaborate implementation of the logic inverter utilizing two complementary switches. This is the basis of the CMOS inverter studied in Section 4.10.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 36
Figure 1.33 Another inverter implementation utilizing a double-throw switch to steer the constant current IEE to RC1 (when vI is high) or RC2 (when vI is low). This is the basis of the emitter-coupled logic (ECL) studied in Chapters 7 and 11.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 37
Figure 1.34 Example 1.6: (a) The inverter circuit after the switch opens (i.e., for t 0). (b) Waveforms of vI and vO. Observe that the switch is assumed to operate instantaneously. vO rises exponentially, starting at VOL and heading toward VOH .
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 38
Figure 1.35 Definitions of propagation delays and transition times of the logic inverter.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 39
Figure P1.6
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 40
Figure P1.10
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 41
Figure P1.14
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 42
Figure P1.15
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 43
Figure P1.16
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 44
Figure P1.17
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 45
Figure P1.18
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 46
Figure P1.37
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 47
Figure P1.58
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 48
Figure P1.63
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 49
Figure P1.65
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 50
Figure P1.67
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 51
Figure P1.68
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 52
Figure P1.72
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 53
Figure P1.77
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 54
Figure P1.79
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Copyright 2004 by Oxford University Press, Inc.
Operational Amplifiers
55
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 56
Figure 2.1 Circuit symbol for the op amp.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 57
Figure 2.2 The op amp shown connected to dc power supplies.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 58
Figure 2.3 Equivalent circuit of the ideal op amp.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 59
Figure 2.4 Representation of the signal sources v1 and v2 in terms of their differential and common-mode components.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 60
Figure E2.3
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 61
Figure 2.5 The inverting closed-loop configuration.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 62
Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps.
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Figure 2.7 Analysis of the inverting configuration taking into account the finite open-loop gain of the op amp.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 64
Figure 2.8 Circuit for Example 2.2. The circled numbers indicate the sequence of the steps in the analysis.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 65
Figure 2.9 A current amplifier based on the circuit of Fig. 2.8. The amplifier delivers its output current to R4. It has a current gain of (1 + R2/R3), a zero input resistance, and an infinite output resistance. The load (R4), however, must be floating (i.e., neither of its two terminals can be connected to ground).
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 66
Figure E2.5
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 67
Figure E2.6
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 68
Figure 2.10 A weighted summer.
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Figure 2.11 A weighted summer capable of implementing summing coefficients of both signs.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 70
Figure 2.12 The noninverting configuration.
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Figure 2.13 Analysis of the noninverting circuit. The sequence of the steps in the analysis is indicated by the circled numbers.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 72
Figure 2.14 (a) The unity-gain buffer or follower amplifier. (b) Its equivalent circuit model.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 73
Figure E2.9
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Figure E2.13
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 75
Figure 2.15 Representing the input signals to a differential amplifier in terms of their differential and common-mode components.
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Figure 2.16 A difference amplifier.
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Figure 2.17 Application of superposition to the analysis of the circuit of Fig. 2.16.
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Figure 2.18 Analysis of the difference amplifier to determine its common-mode gain Acm ; vO / vIcm.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 79
Figure 2.19 Finding the input resistance of the difference amplifier for the case R3 = R1 and R4 = R2.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 80
Figure 2.20 A popular circuit for an instrumentation amplifier: (a) Initial approach to the circuit; (b) The circuit in (a) with the connection between node X and ground removed and the two resistors R1 and R1 lumped together. This simple wiring change dramatically improves performance; (c) Analysis of the circuit in‘ (b) assuming ideal op amps.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 81
Figure 2.21 To make the gain of the circuit in Fig. 2.20(b) variable, 2R1 is implemented as the series combination of a fixed resistor R1f and a variable resistor R1v. Resistor R1f ensures that the maximum available gain is limited.
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Figure 2.22 Open-loop gain of a typical general-purpose internally compensated op amp.
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Figure 2.23 Frequency response of an amplifier with a nominal gain of +10 V/V.
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Figure 2.24 Frequency response of an amplifier with a nominal gain of –10 V/V.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 85
Figure 2.25 (a) A noninverting amplifier with a nominal gain of 10 V/V designed using an op amp that saturates at ±13-V output voltage and has ±20-mA output current limits. (b) When the input sine wave has a peak of 1.5 V, the output is
clipped off at ±13 V.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 86
Figure 2.26 (a) Unity-gain follower. (b) Input step waveform. (c) Linearly rising output waveform obtained when the amplifier is slew-rate limited. (d) Exponentially rising output waveform obtained when V is sufficiently small so that the initial slope (vtV) is smaller than or equal to SR.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 87
Figure 2.27 Effect of slew-rate limiting on output sinusoidal waveforms.
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Figure 2.28 Circuit model for an op amp with input offset voltage VOS.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 89
Figure E2.23 Transfer characteristic of an op amp with VOS = 5 mV.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 90
Figure 2.29 Evaluating the output dc offset voltage due to VOS in a closed-loop amplifier.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 91
Figure 2.30 The output dc offset voltage of an op amp can be trimmed to zero by connecting a potentiometer to the two offset-nulling terminals. The wiper of the potentiometer is connected to the negative supply of the op amp.
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Figure 2.31 (a) A capacitively coupled inverting amplifier, and (b) the equivalent circuit for determining its dc output offset voltage VO.
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Figure 2.32 The op-amp input bias currents represented by two current sources IB1 and IB2.
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Figure 2.33 Analysis of the closed-loop amplifier, taking into account the input bias currents.
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Figure 2.34 Reducing the effect of the input bias currents by introducing a resistor R3.
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Figure 2.35 In an ac-coupled amplifier the dc resistance seen by the inverting terminal is R2; hence R3 is chosen equal to R2.
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Figure 2.36 Illustrating the need for a continuous dc path for each of the op-amp input terminals. Specifically, note that the amplifier will not work without resistor R3.
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Figure 2.37 The inverting configuration with general impedances in the feedback and the feed-in paths.
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Figure 2.38 Circuit for Example 2.6.
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Figure 2.39 (a) The Miller or inverting integrator. (b) Frequency response of the integrator.
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Figure 2.40 Determining the effect of the op-amp input offset voltage VOS on the Miller integrator circuit. Note that since the output rises with time, the op amp eventually saturates.
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Figure 2.41 Effect of the op-amp input bias and offset currents on the performance of the Miller integrator circuit.
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Figure 2.42 The Miller integrator with a large resistance RF connected in parallel with C in order to provide negative feedback and hence finite gain at dc.
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Figure 2.43 Waveforms for Example 2.7: (a) Input pulse. (b) Output linear ramp of ideal integrator with time constant of 0.1 ms. (c) Output exponential ramp with resistor RF connected across integrator capacitor.
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Figure 2.44 (a) A differentiator. (b) Frequency response of a differentiator with a time-constant CR.
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Figure 2.45 A linear macromodel used to model the finite gain and bandwidth of an internally compensated op amp.
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Figure 2.46 A comprehensive linear macromodel of an internally compensated op amp.
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Figure 2.47 Frequency response of the closed-loop amplifier in Example 2.8.
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Figure 2.48 Step response of the closed-loop amplifier in Example 2.8.
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Figure 2.49 Simulating the frequency response of the µA741 op-amp in Example 2.9.
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Figure 2.50 Frequency response of the µA741 op amp in Example 2.9.
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Figure 2.51 Circuit for determining the slew rate of the µA741 op amp in Example 2.9.
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Figure 2.52 Square-wave response of the µA741 op amp connected in the unity-gain configuration shown in Fig. 2.51.
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Figure P2.2
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 115
Figure P2.8
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 116
Figure P2.16
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Figure P2.22
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 118
Figure P2.25
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 119
Figure P2.30
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 120
Figure P2.31
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 121
Figure P2.32
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Figure P2.33
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 123
Figure P2.34
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Figure P2.35
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Figure P2.43
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith 126
Figure P2.46
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Figure P2.47
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Figure P2.49
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Figure P2.50
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Figure P2.51
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Figure P2.59
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Figure P2.62
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Figure P2.68
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Figure P2.69
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Figure P2.70
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Figure P2.71
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Figure P2.77
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Figure P2.78
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Figure P2.108
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Figure P2.117
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Figure P2.118
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Figure P2.119
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Figure P2.122
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Figure P2.125
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Figure P2.126
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Table 1.1 The Four Amplifier Types