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Ch2slides

# Ch2slides - Chapter 2 Principles of Steady-State Converter...

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Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 1 Chapter 2 Principles of Steady-State Converter Analysis 2.1. Introduction 2.2. Inductor volt-second balance, capacitor charge balance, and the small ripple approximation 2.3. Boost converter example 2.4. Cuk converter example 2.5. Estimating the ripple in converters containing two- pole low-pass filters 2.6. Summary of key points

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Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 2 2.1 Introduction Buck converter SPDT switch changes dc component Switch output voltage waveform complement D : D = 1 - D Duty cycle D: 0 D 1 + R + v ( t ) 1 2 + v s ( t ) V g v s ( t ) V g DT s D ' T s 0 t 0 DT s T s Switch position: 12 1
Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 3 Dc component of switch output voltage v s = 1 T s v s ( t ) dt 0 T s v s = 1 T s ( DT s V g )= DV g Fourier analysis: Dc component = average value v s ( t ) V g 0 t 0 DT s T s v s = DV g area = DT s V g

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Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 4 Insertion of low-pass filter to remove switching harmonics and pass only dc component v v s = DV g + L CR + v ( t ) 1 2 + v s ( t ) V g V g 0 0 D V 1
Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 5 Three basic dc-dc converters Buck Boost Buck-boost M ( D ) D 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 D 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 D –5 –4 –3 –2 –1 0 0 0.2 0.4 0.6 0.8 1 (a) (b) (c) + L CR + v 1 2 + L + v 1 2 + L + v 12 M ( D )= D M ( D 1 1– D M ( D D D i L ( t ) V g i L ( t ) V g i L ( t ) V g

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Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 6 Objectives of this chapter ! Develop techniques for easily determining output voltage of an arbitrary converter circuit ! Derive the principles of inductor volt-second balance and capacitor charge (amp-second) balance ! Introduce the key small ripple approximation ! Develop simple methods for selecting filter element values ! Illustrate via examples
Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 7 2.2. Inductor volt-second balance, capacitor charge balance, and the small ripple approximation Buck converter containing practical low-pass filter Actual output voltage waveform v ( t )= V + v ripple ( t ) Actual output voltage waveform, buck converter + L CR + v ( t ) 1 2 i L ( t ) + v L ( t ) i C ( t ) V g v ( t ) t 0 V Actual waveform v ( t ) = V + v ripple ( t ) dc component V

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Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 8 The small ripple approximation In a well-designed converter, the output voltage ripple is small. Hence, the waveforms can be easily determined by ignoring the ripple: v ( t ) V v ( t )= V + v ripple ( t ) v ( t ) t 0 V Actual waveform v ( t ) = V + v ripple ( t ) dc component V v ripple < V
Fundamentals of Power Electronics Chapter 2: Principles of steady-state converter analysis 9 Buck converter analysis: inductor current waveform original converter switch in position 2 switch in position 1 + L

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Ch2slides - Chapter 2 Principles of Steady-State Converter...

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