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# Ch5slide - Chapter 5 The Discontinuous Conduction Mode 5.1...

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Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 1 Chapter 5. The Discontinuous Conduction Mode 5.1. Origin of the discontinuous conduction mode, and mode boundary 5.2. Analysis of the conversion ratio M(D,K) 5.3. Boost converter example 5.4. Summary of results and key points

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Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 2 Introduction to Discontinuous Conduction Mode (DCM) Occurs because switching ripple in inductor current or capacitor voltage causes polarity of applied switch current or voltage to reverse, such that the current- or voltage-unidirectional assumptions made in realizing the switch are violated. Commonly occurs in dc-dc converters and rectifiers, having single- quadrant switches. May also occur in converters having two-quadrant switches. Typical example: dc-dc converter operating at light load (small load current). Sometimes, dc-dc converters and rectifiers are purposely designed to operate in DCM at all loads. Properties of converters change radically when DCM is entered: M becomes load-dependent Output impedance is increased Dynamics are altered Control of output voltage may be lost when load is removed
Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 3 5.1. Origin of the discontinuous conduction mode, and mode boundary Buck converter example, with single-quadrant switches + Q 1 L C R + V D 1 V g i L (t) i D (t) i L (t) t i L I 0 DT s T s conducting devices: Q 1 D 1 Q 1 i D (t) t 0 DT s T s i L I i L = ( V g V ) 2 L DT s = V g DD ' T s 2 L continuous conduction mode (CCM) Minimum diode current is (I – i L ) Dc component I = V/R Current ripple is Note that I depends on load, but i L does not.

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Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 4 Reduction of load current Increase R , until I = i L + Q 1 L C R + V D 1 V g i L (t) i D (t) i L = ( V g V ) 2 L DT s = V g DD ' T s 2 L CCM-DCM boundary Minimum diode current is (I – i L ) Dc component I = V/R Current ripple is Note that I depends on load, but i L does not. i L (t) t 0 DT s T s conducting devices: Q 1 D 1 Q 1 i L I i D (t) t 0 DT s T s I i L
Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 5 Further reduce load current Increase R some more, such that I < i L + Q 1 L C R + V D 1 V g i L (t) i D (t) i L = ( V g V ) 2 L DT s = V g DD ' T s 2 L Discontinuous conduction mode Minimum diode current is (I – i L ) Dc component I = V/R Current ripple is Note that I depends on load, but i L does not. The load current continues to be positive and non-zero. i L (t) t 0 DT s T s conducting devices: Q 1 D 1 Q 1 I X D 1 T s D 2 T s D 3 T s i D (t) t 0 DT s T s D 2 T s

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Fundamentals of Power Electronics Chapter 5: Discontinuous conduction mode 6 Mode boundary I > i L for CCM I < i L for DCM Insert buck converter expressions for I and i L : DV g R < DD ' T s V g 2 L 2 L RT s < D ' Simplify: This expression is of the form K < K crit ( D ) for DCM where K = 2 L RT s and K crit ( D ) = D '
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