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Electrical Engineering
1. Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 R2 Vo FIGURE Q1 The equations based on electrical laws are the following: VR = İR R,, VR, = iR, di, ic = V =L- dt dt i=i, = İR, , VR =Vc=V. V =V +Vz +Vcs i=ig +i, Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. а. Solve a state space representation using the following variables as states: [VRI,İR2). b. Develop an s-domain transfer function for the system using the state space representation obtained in part (a).

1. Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 R2 Vo FIGURE Q1 The equations based on electrical laws are the following: VR = İR R,, VR, = iR, di, ic = V =L- dt dt i=i, = İR, , VR =Vc=V. V =V +Vz +Vcs i=ig +i, Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. а. Solve a state space representation using the following variables as states: [VRI,İR2). b. Develop an s-domain transfer function for the system using the state space representation obtained in part (a).

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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1. Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 L. Vi R2 Vo FIGURE Q1 The equations based on electrical laws are the following: Va = iR R, VR, = R dV i, =C dt dt i = i, = ig , VR =Vc=V• V =V½ +V; +V¢, i=ig, tig Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. а. Solve a state space representation using the following variables as states: [VRI,İR2]. b. Develop an s-domain transfer function for the system using the state space representation obtained in part (a). C. Select another set of variables as states. Justify your selection. Construct a state space representation for the same system using the new states. 2
Transcribed Image Text:1. Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 L. Vi R2 Vo FIGURE Q1 The equations based on electrical laws are the following: Va = iR R, VR, = R dV i, =C dt dt i = i, = ig , VR =Vc=V• V =V½ +V; +V¢, i=ig, tig Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. а. Solve a state space representation using the following variables as states: [VRI,İR2]. b. Develop an s-domain transfer function for the system using the state space representation obtained in part (a). C. Select another set of variables as states. Justify your selection. Construct a state space representation for the same system using the new states. 2
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