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An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. Q1 (a) C1 R4 R2 ww R1 ej R3 e eo Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). (i) (ii) hence obtain the complete transfer function for the system, i.e. Eo(s)/E:(s). (iii) Determine D(s) = Eo(s)/E:(s) when RI = R2 = R3 = R4 = 1 2 and Ci = 1 F, C2= 2 F.

An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. Q1 (a) C1 R4 R2 ww R1 ej R3 e eo Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). (i) (ii) hence obtain the complete transfer function for the system, i.e. Eo(s)/E:(s). (iii) Determine D(s) = Eo(s)/E:(s) when RI = R2 = R3 = R4 = 1 2 and Ci = 1 F, C2= 2 F.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. Q1 (а) C1 R4 ww R2 ww R1 ww e¡ R3 e Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: (i) obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). hence obtain the complete transfer function for the system, i.e. Eo(s)/E:(s). (ii) (ii) Determine D(s) = Eo(s)/E:(s) when R1 = R2 = R3 = R4 = 1 2 and C1=1 F, C2=2 F. (b) Consider the closed-loop control system shown in Figure Qlb. 1 Σ K.D(s) (s + 2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. (ii) Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (c) Briefly summarise the steps, which need to be taken to linearise a nonlinear system.
Transcribed Image Text:An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. Q1 (а) C1 R4 ww R2 ww R1 ww e¡ R3 e Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: (i) obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). hence obtain the complete transfer function for the system, i.e. Eo(s)/E:(s). (ii) (ii) Determine D(s) = Eo(s)/E:(s) when R1 = R2 = R3 = R4 = 1 2 and C1=1 F, C2=2 F. (b) Consider the closed-loop control system shown in Figure Qlb. 1 Σ K.D(s) (s + 2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. (ii) Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (c) Briefly summarise the steps, which need to be taken to linearise a nonlinear system.
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