Operational Amplifiers 1

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith2 Figure 2.1 Circuit symbol for the op amp.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith3 Figure 2.2 The op amp shown connected to dc power supplies.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith4 Figure 2.3 Equivalent circuit of the ideal op amp. TABLE 2.1 Characteristic of the ideal Op Amp 1.Infinite input impedence 2.Zero output impedence 3.Zero common-mode gain or, equivalently, infinite common-mode rejection 4.Infinite open-loop gain A 5.Infinite bandwidth

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith5 Figure 2.4 Representation of the signal sources v 1 and v 2 in terms of their differential and common-mode components.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith6 Figure E2.3

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith7 Figure 2.5 The inverting closed-loop configuration. Virtual short circuit

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith8 Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith9 Figure 2.7 Analysis of the inverting configuration taking into account the finite open-loop gain of the op amp.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith10 EXAMPLE 2.1 R 1 =1 k  R 2 =100 k 

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith11 Figure 2.8 Circuit for Example 2.2. The circled numbers indicate the sequence of the steps in the analysis. Ideal op-amp Gain 100 Input impedance lM 

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith12 EXAMPLE 2.2

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Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith14 Figure 2.9 A current amplifier based on the circuit of Fig The amplifier delivers its output current to R 4. It has a current gain of (1 + R 2 /R 3 ), a zero input resistance, and an infinite output resistance. The load (R 4 ), however, must be floating (i.e., neither of its two terminals can be connected to ground).

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith15 Figure E2.5 Transresistance amplifier Input resistance Ri Output resistance Ro Transresistance Rm

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith16 Figure E2.6

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith17 Figure 2.10 A weighted summer.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith18 Figure 2.11 A weighted summer capable of implementing summing coefficients of both signs.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith19 Figure 2.12 The noninverting configuration.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith20 Figure 2.13 Analysis of the noninverting circuit. The sequence of the steps in the analysis is indicated by the circled numbers.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith21 Figure 2.14 (a) The unity-gain buffer or follower amplifier. (b) Its equivalent circuit model.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith22 Figure E2.9

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith23 Figure E2.13

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith24 Figure 2.15 Representing the input signals to a differential amplifier in terms of their differential and common-mode components.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith25 Figure 2.16 A difference amplifier.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith26 Figure 2.17 Application of superposition to the analysis of the circuit of Fig

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith27 Figure 2.18 Analysis of the difference amplifier to determine its common-mode gain A cm ; v O / v Icm.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith28

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith29 Figure 2.19 Finding the input resistance of the difference amplifier for the case R 3 = R 1 and R 4 = R 2.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith30 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 R 1 and R 1 lumped together. This simple wiring change dramatically improves performance; (c) Analysis of the circuit in‘ (b) assuming ideal op amps.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith31

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith32 Figure 2.21 To make the gain of the circuit in Fig. 2.20(b) variable, 2R 1 is implemented as the series combination of a fixed resistor R 1f and a variable resistor R 1 v. Resistor R 1f ensures that the maximum available gain is limited. EXAMPLE 2.3

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith33 Figure 2.22 Open-loop gain of a typical general-purpose internally compensated op amp.

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Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith36 EXAMPLE 2.4

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith37 Figure 2.23 Frequency response of an amplifier with a nominal gain of +10 V/V.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith38 Figure 2.24 Frequency response of an amplifier with a nominal gain of –10 V/V.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith39 Large Signal Operation Output Voltage Saturation Rated Output Voltage Output Current Limit Maximum Allowed Output Current

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith40 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. EXAMPLE V p =1 V, R L = 1 k  2.V p =1.5 V, R L = 1 k 

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith41 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 ( v t V) is smaller than or equal to SR.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith42

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith43 Figure 2.27 Effect of slew-rate limiting on output sinusoidal waveforms.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith44 Figure 2.28 Circuit model for an op amp with input offset voltage V OS.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith45 Figure E2.23 Transfer characteristic of an op amp with V OS = 5 mV.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith46 Figure 2.29 Evaluating the output dc offset voltage due to V OS in a closed-loop amplifier.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith47 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.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith48 Figure 2.31 (a) A capacitively coupled inverting amplifier, and (b) the equivalent circuit for determining its dc output offset voltage V O.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith49 Figure 2.32 The op-amp input bias currents represented by two current sources I B1 and I B2.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith50 Figure 2.33 Analysis of the closed-loop amplifier, taking into account the input bias currents.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith51 Figure 2.34 Reducing the effect of the input bias currents by introducing a resistor R 3.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith52

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith53 Figure 2.35 In an ac-coupled amplifier the dc resistance seen by the inverting terminal is R 2 ; hence R 3 is chosen equal to R 2.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith54 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 R 3.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith55 Figure 2.37 The inverting configuration with general impedances in the feedback and the feed-in paths.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith56 Figure 2.38 Circuit for Example 2.6. EXAMPLE 2.6

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Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith58 Figure 2.39 (a) The Miller or inverting integrator. (b) Frequency response of the integrator.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith59

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith60 Figure 2.40 Determining the effect of the op-amp input offset voltage V OS on the Miller integrator circuit. Note that since the output rises with time, the op amp eventually saturates.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith61 Figure 2.41 Effect of the op-amp input bias and offset currents on the performance of the Miller integrator circuit.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith62 Figure 2.42 The Miller integrator with a large resistance R F connected in parallel with C in order to provide negative feedback and hence finite gain at dc.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith63 EXAMPLE 2.7

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith64 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 R F connected across integrator capacitor.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith65

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith66 Figure 2.44 (a) A differentiator. (b) Frequency response of a differentiator with a time-constant CR.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith67

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith68 Figure 2.45 A linear macromodel used to model the finite gain and bandwidth of an internally compensated op amp.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith69 Figure 2.46 A comprehensive linear macromodel of an internally compensated op amp.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith70

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith71 Figure 2.47 Frequency response of the closed-loop amplifier in Example 2.8. EXAMPLE 2.8

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Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith73 Figure 2.48 Step response of the closed-loop amplifier in Example 2.8.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith74 EXAMPLE 2.9

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith75 Figure 2.49 Simulating the frequency response of the µA741 op-amp in Example 2.9.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith76 Figure 2.50 Frequency response of the µA741 op amp in Example 2.9.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith77 Figure 2.51 Circuit for determining the slew rate of the µA741 op amp in Example 2.9.

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith78 Figure 2.52 Square-wave response of the µA741 op amp connected in the unity-gain configuration shown in Fig

Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith79 Figure P2.2

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Copyright  2004 by Oxford University Press, Inc. Microelectronic Circuits - Fifth Edition Sedra/Smith110 Figure P2.126