Ch11slides

# Ch11slides - Chapter 11 AC and DC Equivalent Circuit...

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Fundamentals of Power Electronics 1 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode Chapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode Introduction 11.1. DCM Averaged Switch Model 11.2. Small-Signal AC Modeling of the DCM Switch Network 11.3. High-Frequency Dynamics of Converters in DCM 11.4. Summary of Key Points

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Fundamentals of Power Electronics 2 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode We are missing ac and dc equivalent circuit models for the discontinuous conduction mode DC CCM DCM + 1 : M(D) V g R + V + V g R + V + + 1 : M(D) L e C R + v ( s ) e ( s ) d ( s ) j ( s ) d ( s ) AC + R v g ( s ) + v ( s ) v g ( s ) ? ?
Fundamentals of Power Electronics 3 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode Change in characteristics at the CCM/DCM boundary l Steady-state output voltage becomes strongly load-dependent l Simpler dynamics: one pole and the RHP zero are moved to very high frequency, and can normally be ignored l Traditionally, boost and buck-boost converters are designed to operate in DCM at full load l All converters may operate in DCM at light load So we need equivalent circuits that model the steady-state and small- signal ac models of converters operating in DCM The averaged switch approach will be employed

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Fundamentals of Power Electronics 4 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode 11.1 Derivation of DCM averaged switch model: buck-boost example + L CR + v v g i L + v L Switch network + v 1 v 2 + i 1 i 2 • Define switch terminal quantities v 1 , i 1 , v 2 , i 2 , as shown • Let us find the averaged quantities v 1 , i 1 , v 2 , i 2 , for operation in DCM, and determine the relations between them
Fundamentals of Power Electronics 5 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode d 1 T s T s t i 1 (t) i pk Area q 1 i 1 ( t ) T s v 1 (t) 0 v g – v v 1 ( t ) T s v g i 2 (t) i pk Area q 2 v 2 (t) 0 v g – v – v i 2 ( t ) T s v 2 ( t ) T s d 2 T s d 3 T s DCM waveforms t i L (t) 0 i pk v g L v L v L (t) v g v 0 + L CR + v v g i L + v L Switch network + v 1 v 2 + i 1 i 2

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Fundamentals of Power Electronics 6 Chapter 11: AC and DC equivalent circuit modeling of the discontinuous conduction mode Basic DCM equations: i pk , v L , and d 2 (Approximate method) d 1 T s T s t i 1 (t) i pk Area q 1 i 1 ( t ) T s v 1 (t) 0 v g – v v 1 ( t ) T s v g i 2 (t) i pk Area q 2 v 2 (t) 0 v g – v – v i 2 ( t ) T s v 2 ( t ) T s d 2 T s d 3 T s i pk = v g L d 1 T s v L ( t ) T s = d 1 v g ( t ) T s + d 2 v ( t ) T s + d 3 0 Peak inductor current: Average inductor voltage: In DCM, the diode switches off when the inductor current reaches zero. Hence, i (0) = i ( T s ) = 0 , and the average inductor voltage is zero. This is true even during transients.
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## This note was uploaded on 07/15/2011 for the course EEL 4244 taught by Professor Lee during the Spring '09 term at FSU.

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Ch11slides - Chapter 11 AC and DC Equivalent Circuit...

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