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Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz %3D Let the input voltage be V, =10.0V and the duty cycle be D=0.75 . Call v.(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for v.(t),i, (1), and also the expected ripples Av (t), Ai, (1)

Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz %3D Let the input voltage be V, =10.0V and the duty cycle be D=0.75 . Call v.(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for v.(t),i, (1), and also the expected ripples Av (t), Ai, (1)

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
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Please help with Question 2. I also attached the notes that question 2 referred to.

Unidirectional Boost Converter di, (t) L dt -9(1)v(t) ee + v(t) - v(t) = q(t)i¿(t)- R dt C R V. - DT, q(t) I- VIR DT, - D'T, - - V/R ee i(t) +v,() - + + v,(0) - R Switch in 1 (q(t)= 0) : Switch in 2 (g(t) =1) : di, L = v, (1) = V, dt di, = v, (t) = V, -vc(1) dt cdvc dve = ic(t) = i,(1) dt dt R See the solution on any of the intervals. Assume RC «1 and use simple Taylor's series as solution of LDES. 1 2 DT, T f. Switch in 1: V. i,(DT.) = i_(0) + DT, di, dt L 0st< DT, vc(0) DT, = v(0) RC dve -vc(t) v(DT,) =v(0) –- dt RC Switch in 2: V,-vc(0) di, V -v.(t) i,(T,) =| i,(0)+ |(1- D)T, L DT, <t<T, dt L V,-(1-D)vc(0) i, (1) vc(t) dvc = =i, (0) + L dt C RC (i,(DT,) v (0) ve(T,) = vc(0) + C RC (1-D)T Ev(0) + ¿(DT,) -(1– D)T, C Therefore: i, (T.) > i,(0) vc(T,) > vc(0) ve(0)(1– D)<V½ if See the transient response: Smaller slope since the Inductor current is charging the capacitor i,(DT,) = i,(0) + 4 DT, i,(1) i, (T.) = i,(0) + V-(1-D)v (0), T,
Transcribed Image Text:Unidirectional Boost Converter di, (t) L dt -9(1)v(t) ee + v(t) - v(t) = q(t)i¿(t)- R dt C R V. - DT, q(t) I- VIR DT, - D'T, - - V/R ee i(t) +v,() - + + v,(0) - R Switch in 1 (q(t)= 0) : Switch in 2 (g(t) =1) : di, L = v, (1) = V, dt di, = v, (t) = V, -vc(1) dt cdvc dve = ic(t) = i,(1) dt dt R See the solution on any of the intervals. Assume RC «1 and use simple Taylor's series as solution of LDES. 1 2 DT, T f. Switch in 1: V. i,(DT.) = i_(0) + DT, di, dt L 0st< DT, vc(0) DT, = v(0) RC dve -vc(t) v(DT,) =v(0) –- dt RC Switch in 2: V,-vc(0) di, V -v.(t) i,(T,) =| i,(0)+ |(1- D)T, L DT, <t<T, dt L V,-(1-D)vc(0) i, (1) vc(t) dvc = =i, (0) + L dt C RC (i,(DT,) v (0) ve(T,) = vc(0) + C RC (1-D)T Ev(0) + ¿(DT,) -(1– D)T, C Therefore: i, (T.) > i,(0) vc(T,) > vc(0) ve(0)(1– D)<V½ if See the transient response: Smaller slope since the Inductor current is charging the capacitor i,(DT,) = i,(0) + 4 DT, i,(1) i, (T.) = i,(0) + V-(1-D)v (0), T,
Problem 2. (Unidirectional DC/DC Boost Converter). Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz Let the input voltage be V, = 10.0V and the duty cycle be D = 0.75 . Call vc(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for ve(t),i, (t), and also the expected ripples Av (1), Ai,(1) Q2: assuming zero initial conditions v.(0) = 0, i,(0) =0 sketch v.(t),i, (t) in the first three periods 0<tS 3T, . In particular use the Taylor series approximation in the notes and show the values for t = 0, DT,, T,, T,+DT, ,2T,, 2T,+DT,, 3T,. in Q3: using the same state equations in the notes, compute the steady state values for Vc(0), vc(DT,),i¿ (0),i¿(DT,), where time t = 0 denotes the beginning of "switch on" and time t = DT, denotes the beginning of "switch off" (Hint: in steady state v.(0) = v.(T,) and i.(0) = i.(T,) ). Verify that the ripples are close to what you expect.
Transcribed Image Text:Problem 2. (Unidirectional DC/DC Boost Converter). Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz Let the input voltage be V, = 10.0V and the duty cycle be D = 0.75 . Call vc(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for ve(t),i, (t), and also the expected ripples Av (1), Ai,(1) Q2: assuming zero initial conditions v.(0) = 0, i,(0) =0 sketch v.(t),i, (t) in the first three periods 0<tS 3T, . In particular use the Taylor series approximation in the notes and show the values for t = 0, DT,, T,, T,+DT, ,2T,, 2T,+DT,, 3T,. in Q3: using the same state equations in the notes, compute the steady state values for Vc(0), vc(DT,),i¿ (0),i¿(DT,), where time t = 0 denotes the beginning of "switch on" and time t = DT, denotes the beginning of "switch off" (Hint: in steady state v.(0) = v.(T,) and i.(0) = i.(T,) ). Verify that the ripples are close to what you expect.
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