An operational-amplifier circuit that may be used as a controller is shown inFigure Qla.Q1(а)C1R4wwR2wwR1wwe¡R3eFigure QlaR1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume bothop-amps are ideal and their input/output voltages are ei, e and eo, as shown inthe Figure. Using the impedance approach:(i)obtain the transfer function for each op-amp, i.e. E(s)/E:(s) andEo(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 andC1=1 F, C2=2 F.(b)Consider the closed-loop control system shown in Figure Qlb.1ΣK.D(s)(s + 2)Figure QlbK 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 valueof K, by considering the angle criterion at this point.(c)Briefly summarise the steps, which need to be taken to linearise a nonlinearsystem.

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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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Digital to Analog Converters

Digital to analog converters are commonly known as DAC, digital analog converter, D2A, or Digital-to-Analog converters. DACs are one of the important devices used in the electronics and electrical domain. DACs are the systems that convert a digital signal into an analog signal, whereas an analog to digital converter or ADC performs the opposite function. Digital signals are those signals that can represent the information or data as a set of discrete values. At a particular instant of time, a digital signal can only take a particular value of data. A digital signal is characterized by two unique values; zeros and ones, or true and false, represented by the Boolean domain. These are also known as binary signals or logic signals. Unlike digital signals, an analog signal is represented by continuous values, where at any time instant, the analog signal is represented by a real number.

Question

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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Analogue 2
An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. (a) R4 ww R1 R3 e Co 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). (ii) hence obtain the complete transfer function for the system, i.e. Eo(s)/Ei(s). (iii) Determine D(s) = Eo(s)/E:(s) when R1 = R2 = R3 = R4 = 1 N and C1=1 F, C2= 2 F. %3D (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. [. Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (ii) (c) Briefly summarise the steps, which need to be…
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