1

Single-Stage Integrated-Circuit Amplifiers

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Table 6.3

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Figure 6.1 The intrinsic gain of the MOSFET versus bias current ID. Outside the subthreshold region, this is a plot of for the case: nCox = 20 A/V2, V9A = 20 V/m, L = 2 m, and W = 20 m.0 2 /A Dn oxA V C WL I

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Figure 6.2 Frequency response of a CS amplifier loaded with a capacitance CL and fed with an ideal voltage source. It is assumed that the transistor is operating at frequencies much lower than fT, and thus the internal capacitances are not taken into account.

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Figure 6.3 Increasing ID or W/L increases the bandwidth of a MOSFET amplifier loaded by a constant capacitance CL.

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Figure 6.4 Circuit for a basic MOSFET constant-current source.

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Figure 6.5 Basic MOSFET current mirror.

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Figure 6.6 Output characteristic of the current source in Fig. 6.4 and the current mirror of Fig. 6.5 for the case Q2 is matched to Q1.

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Figure 6.7 A current-steering circuit.

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Figure 6.8 The basic BJT current mirror.

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Figure 6.9 Analysis of the current mirror taking into account the finite of the BJTs.

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Figure 6.10 A simple BJT current source.

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Figure 6.11 Generation of a number of constant currents of various magnitudes.

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Figure E6.8

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Figure 6.12 Frequency response of a direct-coupled (dc) amplifier. Observe that the gain does not fall off at low frequencies, and the midband gain AM extends down to zero frequency.

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Figure 6.13 Normalized high-frequency response of the amplifier in Example 6.5.

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Figure 6.14 Circuits for Example 6.6: (a) high-frequency equivalent circuit of a MOSFET amplifier; (b) the equivalent circuit at midband frequencies; (c) circuit for determining the resistance seen by Cgs; and (d) circuit for determining the resistance seen by Cgd.

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Figure 6.15 The Miller equivalent circuit.

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Figure 6.16 Circuit for Example 6.7.

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Figure E6.13

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Figure 6.17 (a) Active-loaded common-source amplifier. (b) Small-signal analysis of the amplifier in (a), performed both directly on the circuit diagram and using the small-signal model explicitly.

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Figure 6.18 The CMOS common-source amplifier; (a) circuit; (b) i–v characteristic of the active-load Q2; (c) graphical construction to determine the transfer characteristic; and (d) transfer characteristic.

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Figure 6.19 (a) Active-loaded common-emitter amplifier. (b) Small-signal analysis of the amplifier in (a), performed both directly on the circuit and using the hybrid- model explicitly.

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Figure 6.20 High-frequency equivalent-circuit model of the common-source amplifier. For the common-emitter amplifier, the values of Vsig and Rsig are modified to include the effects of r and rx; Cgs is replaced by C, Vgs by V, and Cgd by C.

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Figure 6.21 Approximate equivalent circuit obtained by applying Miller’s theorem while neglecting CL and the load current component supplied by Cgd. This model works reasonably well when Rsig is large and the amplifier high-frequency response is dominated by the pole formed by Rsig and Cin.

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Figure 6.22 Application of the open-circuit time-constants method to the CS equivalent circuit of Fig. 6.20.

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Figure 6.23 Analysis of the CS high-frequency equivalent circuit.

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Figure 6.24 The CS circuit at s 5 sZ. The output voltage Vo 5 0, enabling us to determine sZ from a node equation at D.

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Figure 6.25 (a) High-frequency equivalent circuit of the common-emitter amplifier. (b) Equivalent circuit obtained after the Thévenin theorem is employed to simplify the resistive circuit at the input.

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Figure 6.26 (a) High-frequency equivalent circuit of a CS amplifier fed with a signal source having a very low (effectively zero) resistance. (b) The circuit with Vsig reduced to zero. (c) Bode plot for the gain of the circuit in (a).

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Figure 6.27 (a) Active-loaded common-gate amplifier. (b) MOSFET equivalent circuit for the CG case in which the body and gate terminals are connected to ground. (c) Small-signal analysis performed directly on the circuit diagram with the T model of (b) used implicitly. (d) Operation with the output open-circuited.

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Figure 6.28 (a) The output resistance Ro is found by setting vi 5 0. (b) The output resistance Rout is obtained by setting vsig 5 0.

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Figure 6.29 The impedance transformation property of the CG configuration.

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Figure 6.30 Equivalent circuit of the CG amplifier illustrating its application as a current buffer. Rin and Rout are given in Fig. 6.29, and Gis 5 Avo (Rs/Rout) . 1.

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Figure 6.31 (a) The common-gate amplifier with the transistor internal capacitances shown. A load capacitance CL is also included. (b) Equivalent circuit for the case in which ro is neglected.

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Figure 6.32 Circuits for determining Rgs and Rgd.

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Figure 6.33 (a) Active-loaded common-base amplifier. (b) Small-signal analysis performed directly on the circuit diagram with the BJT T model used implicitly. (c) Small-signal analysis with the output open-circuited.

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Figure 6.34 Analysis of the CB circuit to determine Rout. Observe that the current ix that enters the transistor must equal the sum of the two currents v/r and v/Re that leave the transistor, that is; ix 5 v/r 1 v/Re.

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Figure 6.35 Input and output resistances of the CB amplifier.

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Figure 6.36 (a) The MOS cascode amplifier. (b) The circuit prepared for small-signal analysis with various input and output resistances indicated. (c) The cascode with the output open-circuited.

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Figure 6.37 (a and b) Two equivalent circuits for the output of the cascode amplifier. Either circuit can be used to determine the gain Av 5 vo/vi, which is equal to Gv because Rin 5 and thus vi 5 vsig. (c) Equivalent circuit for determining the voltage gain of the CS stage, Q1.

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Figure 6.38 The cascode circuit with the various transistor capacitances indicated.

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Figure 6.39 Effect of cascoding on gain and bandwidth in the case Rsig 5 0. Cascoding can increase the dc gain by the factor A0 while keeping the unity-gain frequency constant. Note that to achieve the high gain, the load resistance must be increased by the factor A0.

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Figure 6.40 (a) The BJT cascode amplifier. (b) The circuit prepared for small-signal analysis with various input and output resistances indicated. Note that rx is neglected. (c) The cascode with the output open-circuited.

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Figure 6.41 (a) Equivalent circuit for the cascode amplifier in terms of the open-circuit voltage gain Avo 5 –A0. (b) Equivalent circuit in terms of the overall short-circuit transconductance Gm . gm. (c) Equivalent circuit for determining the gain of the CE stage, Q1.

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Figure 6.42 Determining the frequency response of the BJT cascode amplifier. Note that in addition to the BJT capacitances C and C, the capacitance between the collector and the substrate Ccs for each transistor are also included.

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Figure 6.43 A cascode current-source.

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Figure 6.44 Double cascoding.

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Figure 6.45 The folded cascode.

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Figure 6.46 BiCMOS cascodes.

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Figure 6.47 (a) A CS amplifier with a source-degeneration resistance Rs. (b) Circuit for small-signal analysis. (c) Circuit with the output open to determine Avo. (d) Output equivalent circuit. (e) Another output equivalent circuit in terms of Gm.

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Figure 6.48 (a) The CS amplifier circuit, with a source resistance Rs, prepared for frequency-response analysis. (b) Determining the resistance Rgd seen by the capacitance Cgd.

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Figure 6.49 A CE amplifier with emitter degeneration: (a) circuit; (b) analysis to determine Rin; and (c) analysis to determine Avo.

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Figure 6.50 (a) An IC source follower. (b) Small-signal equivalent-circuit model of the source follower. (c) A simplified version of the equivalent circuit. (d) Determining the output resistance of the source follower.

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Figure 6.51 Analysis of the high-frequency response of the source follower: (a) Equivalent circuit; (b) simplified equivalent circuit; and (c) determining the resistance Rgs seen by Cgs.

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Figure 6.52 (a) Emitter follower. (b) High-frequency equivalent circuit. (c) Simplified equivalent circuit.

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Figure 6.53 (a) CD–CS amplifier. (b) CC–CE amplifier. (c) CD–CE amplifier.

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Figure 6.54 Circuits for Example 6.13: (a) The CC–CE circuit prepared for low-frequency small-signal analysis; (b) the circuit at high frequencies, with Vsig set to zero to enable determination of the open-circuit time constants; and (c) a CE amplifier for comparison.

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Figure 6.55 (a) The Darlington configuration; (b) voltage follower using the Darlington configuration; and (c) the Darlington follower with a bias current I applied to Q1 to ensure that its remains high.

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Figure 6.56 (a) A CC–CB amplifier. (b) Another version of the CC–CB circuit with Q2 implemented using a pnp transistor. (c) The MOSFET version of the circuit in (a).

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Figure 6.57 (a) Equivalent circuit for the amplifier in Fig. 6.56(a). (b) Simplified equivalent circuit. Note that the equivalent circuits in (a) and (b) also apply to the circuit shown in Fig. 6.56(b). In addition, they can be easily adapted for the MOSFET circuit in Fig. 6.56(c), with 2r eliminated, C replaced with Cgs, C replaced with Cgd, and V replaced with Vgs.

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Figure 6.58 A cascode MOS current mirror.

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Figure 6.59 A current mirror with base-current compensation.

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Figure 6.60 The Wilson bipolar current mirror: (a) circuit showing analysis to determine the current transfer ratio; and (b) determining the output resistance. Note that the current ix that enters Q3 must equal the sum of the currents that leave it, 2i.

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Figure 6.61 The Wilson MOS mirror: (a) circuit; (b) analysis to determine output resistance; and (c) modified circuit.

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Figure 6.62 The Widlar current source.

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Figure 6.63 Circuits for Example 6.14.

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Figure 6.64 Capture schematic of the CS amplifier in Example 6.15.

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Figure 6.65 Transistor equivalency.

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Figure 6.66 (a) Voltage transfer characteristic of the CS amplifier in Example 6.15.

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Figure 6.66 (Continued) (b) Expanded view of the transfer characteristic in the high-gain region. Also shown are the transfer characteristics where process variations cause the width of transistor M1 to change by +15% and –15% from its nominal value of W1 = 12.5 m.

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Figure 6.67 Capture schematic of the CS amplifier in Example 6.16.

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Figure 6.68 Frequency response of (a) the CS amplifier and (b) the folded-cascode amplifier in Example 6.16, with Rsig = 100 and Rsig = 1 .

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Figure 6.69 Capture schematic of the folded-cascode amplifier in Example 6.16.

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Figure P6.9

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Figure P6.25

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Figure P6.26

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Figure P6.28

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Figure P6.33

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Figure P6.34

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Figure P6.35

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Figure P6.37

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Figure P6.46

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Figure P6.54

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Figure P6.57

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Figure P6.61

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Figure P6.63

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Figure P6.65

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Figure P6.72

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Figure P6.73

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Figure P6.75

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Figure P6.76

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Figure P6.84

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Figure P6.85

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Figure P6.93

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Figure P6.96

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Figure P6.144

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Figure P6.145