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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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--- ### Problem 2. (Unidirectional DC/DC Boost Converter) #### Consider a Unidirectional DC/DC Boost Converter with the following parameters: - \( R = 50.0\Omega \) - \( C = 100.0\mu F \) - \( L = 100.0mH \) - \( f_s = 10.0kHz \) Let the input voltage be \( V_g = 10.0V \) and the duty cycle be \( D = 0.75 \). Call \( v_C(t), i_L(t) \) the voltage across the capacitor and the current through the inductor respectively. **Q1:** Determine the expected steady-state values for \( v_C(t), i_L(t) \), and also the expected ripples \( \Delta v_C(t), \Delta i_L(t) \). **Q2:** Assuming zero initial conditions \( v_C(0) = 0 \), \( i_L(0) = 0 \), sketch \( v_C(t), i_L(t) \) in the first three periods \( 0 \leq t \leq 3T_s \). In particular, use the Taylor series approximation in the notes and show the values for \( t = 0, DT_s, T_s, T_s + DT_s, 2T_s, 2T_s + DT_s, 3T_s \). **Q3:** Using the same state equations in the notes, compute the steady-state values for \( v_C(0), v_C(DT_s), i_L(0), i_L(DT_s) \), where \( t = 0 \) denotes the beginning of "switch on" and time \( t = DT_s \) denotes the beginning of "switch off" (Hint: in steady state \( v_C(0) = v_C(T_s) \) and \( i_C(0) = i_C(T_s) \)). 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: - \( R = 50.0\Omega \) - \( C = 100.0\mu F \) - \( L = 100.0mH \) - \( f_s = 10.0kHz \) Let the input voltage be \( V_g = 10.0V \) and the duty cycle be \( D = 0.75 \). Call \( v_C(t), i_L(t) \) the voltage across the capacitor and the current through the inductor respectively. **Q1:** Determine the expected steady-state values for \( v_C(t), i_L(t) \), and also the expected ripples \( \Delta v_C(t), \Delta i_L(t) \). **Q2:** Assuming zero initial conditions \( v_C(0) = 0 \), \( i_L(0) = 0 \), sketch \( v_C(t), i_L(t) \) in the first three periods \( 0 \leq t \leq 3T_s \). In particular, use the Taylor series approximation in the notes and show the values for \( t = 0, DT_s, T_s, T_s + DT_s, 2T_s, 2T_s + DT_s, 3T_s \). **Q3:** Using the same state equations in the notes, compute the steady-state values for \( v_C(0), v_C(DT_s), i_L(0), i_L(DT_s) \), where \( t = 0 \) denotes the beginning of "switch on" and time \( t = DT_s \) denotes the beginning of "switch off" (Hint: in steady state \( v_C(0) = v_C(T_s) \) and \( i_C(0) = i_C(T_s) \)). Verify that the ripples are close to what you expect. ---
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