Rin (b) -μ Ry Rel Section 11.7: The Stability Problem 11.14 An op amp designed to have a low-frequency gain of 104 V/V and a high-frequency response dom- inated by a single pole at 1000 rad/s acquires, through a manufacturing error, a pair of addi- tional poles at 100,000 rad/s. At what frequency does the total phase shift of the open-loop gain A reach 180°? At this frequency, for what value of ẞ, assumed to be frequency independent, does the loop gain at 180 reach a value of unity? What is the corresponding value of closed-loop gain at low frequencies? Figure 11.12.1 continued amplifier in The shunt-shunt feedback Fig. 11.12.1(b) utilizes an inverting amplifier with a gain having the equivalent circuit shown in Fig. 11.12.1(a), where ry-100 k2 and ro=1k0. It is required to design the feedback amplifier to obtain V-1 V/0.1 mA of input current Is. The amplifier transresistance gain is required to not deviate from this ideal value by more than 0.1%. Specify the required values of Rƒ and µ. Also, find the input resistance Rin and the out- put resistance Rout of the feedback transresistance amplifier. Section 11.8: Effect of Feedback on the Amplifier Poles 11.15 A de amplifier having a single-pole response with pole frequency 1 kHz and unity-gain frequency of 10 MHz is connected in a negative feedback loop to obtain a closed-loop low-frequency gain of 40 dB. What is the 3-dB frequency of the closed- loop gain. Sketch Bode plots for both the open- loop and closed-loop gains on the same diagram. D11.13 Ri Ro Section 11.9: Stability Study Using Bode Plots 11.16 An amplifier has an open-loop gain with a de value of 105 and poles at 102 Hz, 3.16 x 103 Hz, and 3.16 x 10 Hz. Construct Bode plots for [4] and 4. Use your plots to find f180 and the correspond- ing value of B, and A. What is the significance of these values of ẞ and A? Also, determine the values of ẞ and Af for which a 45° phase mar- gin is available. For this phase margin, what is the peaking in 14/? Figure 11.13.1 It is required to design the feedback current ampli- fier in Fig. 11.13.1 to obtain a current gain lo/I, of -10 A/A with a maximum error (due to finite loop gain) of 0.1%. Utilize R₁ = 1002 and assume that has gm 2 mA/V and ro 20 k2. Specify the values required for the resistance R2 and the gain . Also, give the values of Rin and Rout of the feedback current amplifier. Section 11.10: Frequency Compensation D11.17 For the amplifier specified in Problem 11.16, to what frequency must the pole fps (where fp] = 102 Hz) be shifted in order for the amplifier to be stable when connected in a closed-loop configu- ration with a gain Ayo of 40 dB? By what factor must the capacitance at the internal amplifier node where fp is produced be increased to shift the pole by the required amount?/n11.18 11-5 ww + HH =4 R₁ G V 8m R₂ C₂ V Figure 11.18.1 It is required to apply Miller compensation to the amplifier specified in Problem 11.16 to obtain stable closed-loop operation with gains as low as unity. Recall that the open-loop amplifier has a de gain of 100 dB and has three poles at 102 Hz, 3.16 x 103 Hz, and 3.16 x 104 Hz. It has been found that the first pole is introduced at the input of an amplifier stage such as that shown in Fig. 11.18.1, and the second pole is introduced at the output of this stage. Here Cy has been added to effect the frequency compensation. Assume that the effect of Cd has been included in C1 and C2. Let C₁ 100 pF, C2-10 pF, and gm-1 mA/V. Find the required value of Cy and the unity-gain frequency of the compensated amplifier.

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