# Problems br wileyrazavi fundamentals of

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 769 (1) Sec. 14.6 Chapter Summary 769 1. Determine the type of response (low-pass, high-pass, or band-pass) provided by each net- work depicted in Fig. 14.54. in V in V in V out V out V out V in V out V in V out V (d) (c) (a) (b) (e) Figure 14.54 2. Derive the transfer function of each network shown in Fig. 14.54 and determine the poles and zeros. 3. We wish to realize a transfer function of the form (14.198) where and are real and positive. Which one of the networks illustrated in Fig. 14.54 can satisfy this transfer function? 4. In some applications, the input to a filter may be provided in the form of a current. Compute the transfer function, , of each of the circuits depicted in Fig. 14.55 and determine the poles and zeros. out V out V out V out V out V (d) (c) (a) (b) (e) I in I in I in I in I in Figure 14.55 5. For the high-pass filter depicted in Fig. 14.56, determine the sensitivity of the pole and zero frequencies with respect to and . 6. Consider the filter shown in Fig. 14.57. Compute the sensitivity of the pole and zero fre- quencies with respect to , , and .
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 770 (1) 770 Chap. 14 Analog Filters R C 1 in V 1 out V Figure 14.56 C 1 out V in V C R 1 2 Figure 14.57 7. We wish to achieve a pole sensitivity of in the circuit illustrated in Fig. 14.58. If exhibits a variability of , what is the maximum tolerance of ? R in V 1 out V L 1 Figure 14.58 8. The low-pass filter of Fig. 14.59 is designed to contain two real poles. R in V 1 L 1 C 1 out V Figure 14.59 (a) Derive the transfer function. (b) Compute the poles and the condition that guarantees they are real. (c) Calculate the pole sensitivities to , , and . 9. Explain what happens to the transfer functions of the circuits in Figs. 14.17(a) and 14.18(a) if the pole and zero coincide. 10. For what value of do the poles of the biquadratic transfer function, (14.23), coincide? What is the resulting pole frequencies? 11. Prove that the response expressed by Eq. (14.25) exhibits no peaking (no local maximum) if . 12. Prove that the response expressed by Eq. (14.25) reaches a normalized peak of if . Sketch the response for , 4, and 8. 13. Prove that the response expressed by Eq. (14.28) reaches a normalized peak of at . Sketch the response for , 4, and 8. 14. Consider the parallel RLC tank depicted in Fig. 14.26. Plot the location of the poles of the circuit in the complex plane as goes from very small values to very large values while and remain constant. 15. Repeat Problem 14 if and remain constant and varies from very small values to very large values.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 771 (1) Sec. 14.6 Chapter Summary 771 16. With the aid of the observations made for Eq. (14.25), determine a condition for the low-pass filter of Fig. 14.29 to exhibit a peaking of 1 dB ( ).
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