Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

104 cascode differential amplifiers recall from

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10.4 Cascode Differential Amplifiers Recall from Chapter 9 that cascode stages provide a substantially higher voltage gain than simple CE and CS stages do. Noting that the differential gain of differential pairs is equal to the single-
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 502 (1) 502 Chap. 10 Differential Amplifiers ended gain of their corresponding half circuits, we surmise that cascoding boosts the gain of differential pairs as well. We begin our study with the structure depicted in Fig. 10.37(a), where and serve as cascode devices and and are ideal. Recognizing that the bases of and are at ac ground, we construct the half circuit shown in Fig. 10.37(b). Equation (9.51) readily gives the gain as Q Q 1 2 I EE V in1 V in2 Q V b 4 Q V CC V out 3 Q 1 in1 Q 3 (a) (b) I 2 I 1 v out1 v Figure 10.37 (a) Bipolar cascode differential pair, (b) half circuit of (a). (10.166) confirming that a differential cascode achieves a much higher gain. The developments in Chapter 9 also suggest the use of cascodes for current sources and in Fig. 10.37(a). Illustrated in Fig. 10.38(a), the resulting configuration can be analyzed with the aid of its half circuit, Fig. 10.38(b). Utilizing Eq. (9.61), we express the voltage gain as Q Q 1 2 I EE V in1 V in2 Q 4 Q V CC V out 3 Q 1 in1 Q 3 out1 (a) (b) Q Q 5 6 V V b1 b2 Q Q V 7 8 b3 Q 5 Q 7 v v Figure 10.38 (a) Bipolar cascode differential pair with cascode loads, (b) half circuit of (a). (10.167)
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 503 (1) Sec. 10.4 Cascode Differential Amplifiers 503 Called a “telescopic cascode,” the topology of Fig. 10.38(b) exemplifies the internal circuit of some operational amplifiers. Example 10.25 Due to a manufacturing defect, a parasitic resistance has appeared between nodes and in the circuit of Fig. 10.39(a). Determine the voltage gain of the circuit. Q Q 1 2 I EE V in1 V in2 Q 4 Q V CC V out 3 Q 1 in1 Q 3 out1 (a) (b) Q Q 5 6 V V b1 b2 Q Q V 7 8 b3 Q 5 Q 7 R 1 A B R 1 2 v v Figure 10.39 Solution The symmetry of the circuit implies that the midpoint of is a virtual ground, leading to the half circuit shown in Fig. 10.39(b). Thus, appears in parallel with , lowering the output impedance of the cascode. Since the value of is not given, we cannot make approxima- tions and must return to the original expression for the cascode output impedance, Eq. (9.1): (10.168) The resistance seen looking down into the cascode remains unchanged and approximately equal to . The voltage gain is therefore equal to (10.169) Exercise If and V for all transistors and mA, what value of degrades the gain by a factor of two? We now turn our attention to differential MOS cascodes. Following the above developments for bipolar counterparts, we consider the simplified topology of Fig. 10.40(a) and draw the half
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 504 (1) 504 Chap. 10 Differential Amplifiers circuit as depicted in Fig. 10.40(b). From Eq. (9.69), M 1 I SS DD M 2 V V in1 V in2 M 3 V b1 V out M 4 M 1 in1 M 3 out1 (a) (b) v v Figure 10.40 (a) MOS cascode differential pair, (b) half circuit of (a).
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