R₁ =CL -V 10-2 In using the open-circuit time-constants method, adapt the formula given in (a) for Red to obtain Red. By what factor is increased? Figure 10.5.2 == [12 points] (a) The MOSFET in the common-source amplifier in Fig. 10.5.1 (refer to Figure on previous page), where the de bias arrangement is not shown, is operating at g2 mA/V and ro 20 kn and has Raig RL-20k. The transistor capacitances are specified as Cgs = 40 fF and Cgd = Cdb = 10 ff. Also, there is an additional capacitance between the output node and ground, C = 10 fF. Find the overall de gain G = Vo/Vsig, the upper 3-dB fre- quency fit, and the gain-bandwidth product fi. To determine f, use the method of open-circuit time constants and recall that the resistance seen by Ced is given by Red = (1 + gm)Raig + R, where R=RL ||ro [18 points] (b) To increase fr, the common-source transistor is cascoded as shown in Fig. 10.5.2 (refer to Figure above), where the de bias arrangement is not shown. For the same values of Rsig, RL, and CL as in (a), assuming Q1 and Q2 are biased so that get gm2-2 mA/V and 701 F02 = 20 k2, and for the capacitances of 1 and 2 to have the same values as specified in (a) above, find GH, and fi for the cascode amplifier. Recall R that Rout (mo)ro and Rin2 + 22 Vpo 10.6 [30 minutes] The MOSFET in the common-source amplifier [29 points] in Fig. 10.6.1 (refer to Figure below) has g = 5mA/V, ro 20 kn, Cg 5pF, and Cgd 1 pF, and the total capacitance at the output node, CL, is 10 pF. (a) Find the value of the midband voltage gain. [5 points] (b) Use the method of short-circuit time constants (12 points] to determine the lower 3-dB frequency, ft. Which capacitor dominates the determination off? (c) Use the method of open-circuit time constants [12 points] to determine the upper 3-dB frequency, f. Which capacitor dominates the determination of fH? 10.7 [40 minutes] The amplifier in Fig. 10.7.1 (refer to Figure on fol- 135 points] lowing page) has Rsig=1 kn, Cg = 1 uF, C=10 uF, Cc = 1 uF, R₁ = 8 kQ, VBE = 0.7 V, and Vcc 15 V. (a) Assuming ẞoo, find Rgi, RB2, Rg, and Rc [5 points] to operate the BJT at a de bias point characterized by Ic ImA and VC-7 V. Design for Vg = 5 V and a voltage-divider current of 0.1 mA. (b) Find re. gm, and, assuming ẞ=100. (c) At midband frequencies, find Rin. Va/Vsig [7 points] Vo/V, and Vo/Vaig, assuming = 100. [3 points] (d) In the low-frequency band use the method of [12 points] short-circuit time constants to obtain an estimate of the 3-dB frequency, fz- (e) If C 10pF and C 1 pF, use the Miller [8 points] approximation to determine the input capacitance of the amplifier at high frequencies, and hence determine an estimate of the high-frequency 3 dB frequency. /н Vas Rai 2 ΜΠ RD 10 ΚΩ R = 200 k HH C₂-F ww H Qi R₁-10k C=0.1 F Rat 1 MA Rs 2 k HI =C₂ = 5 µF Figure 10.6.1

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