# Does the result depend on the bias current 27 due to

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Does the result depend on the bias current? 27. Due to a manufacturing error, a bipolar cascode amplifier has been configured as shown in Fig. 9.57. Determine the voltage gain of the circuit. 28. Writing and , express Eq. (9.72) in terms of the device parameters and plot the result as a function of . 29. The MOS cascode of Fig. 9.20(a) must provide a voltage gain of 200. If and for both transistors, determine the required value of . 30. The MOS cascode of Fig. 9.20(a) is designed for a given voltage gain, . Using Eq. (9.79) and the result obtained in Problem 28, explain what happens if the widths of the transis- tors are increased by a factor of while the transistor lengths and bias currents remain

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 456 (1) 456 Chap. 9 Cascode Stages and Current Mirrors V Q Q b1 1 2 in v out v Q V b2 3 V CC Q 4 Figure 9.57 unchanged. 31. Repeat Problem 30 if the lengths of both transistors are increased by a factor of while the transistor widths and bias currents remain unchanged. 32. Due to a manufacturing error, a CMOS cascode amplifier has been configured as shown in Fig. 9.58. Calculate the voltage gain of the circuit. M M in out M 1 2 3 V V M V 4 V DD V V V b1 b2 b3 b4 Figure 9.58 33. In the cascode stage of Fig. 9.20(b), . If , and , , and , calculate the bias current such that the circuit achieves a voltage gain of 500. 34. Determine the voltage gain of each circuit in Fig. 9.59. Assume . M M M 1 2 3 V V M V 4 V DD b2 b3 b4 R P out V M M 1 3 V V M V 4 V DD b2 b3 b4 R P out V M 2 M M 1 3 V V M V 4 V DD V b1 b2 b3 b4 out V M 2 M 5 in V in V in V M M 1 3 V V M V 4 V DD V b1 b2 b3 b4 out V M 2 M 5 in V (d) (c) (a) (b) Figure 9.59
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 457 (1) Sec. 9.3 Chapter Summary 457 35. From Eq. (9.83), determine the sensitivity of to , defined as . Explain intuitively why this sensitivity is proportional to the transconductance of . 36. Repeat Problem 35 for Eq. (9.85) (in terms of ). 37. The parameters and in Eq. (9.85) also vary with the fabrication process. (In- tegrated circuits fabricated in different batches exhibit slightly different parameters.) Deter- mine the sensitivity of to and explain why this issue becomes more serious at low supply voltages. 38. Having learned about the logarithmic function of the circuit in Fig. 9.23(b), a student re- members the logarithmic amplifier studied in Chapter 8 and constructs the circuit depicted in Fig. 9.60. Explain what happens. R 1 Q 1 V REF I X Q 2 V 1 Figure 9.60 39. Repeat Problem 38 for the topology shown in Fig. 9.61. R 1 Q V REF I X Q 2 V 1 1 Figure 9.61 40. Due to a manufacturing error, resistor has appeared in series with the emitter of in Fig. 9.62. If is half of its nominal value, express the value of in terms of other circuit Q I V CC REF REF Q 1 I R P 1 Figure 9.62 parameters. Assume and are identical and .

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