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# Prologue to Converter Examined Information Demonstrating.

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Prologue to Converter Sampled-Data Modeling . ECEN 5807 Dragan Maksimovic. Targets. Better comprehension of converter little flag progress, particularly at high frequenciesApplicationsDCM high-recurrence modelingCurrent mode controlDigital control. Case: A/D and D/A transformation. Demonstrating destinations.
Transcripts
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Introduction to Converter Sampled-Data Modeling ECEN 5807 Dragan Maksimovi ć

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Objectives Better comprehension of converter little flag flow, particularly at high frequencies Applications DCM high-recurrence demonstrating Current mode control Digital control

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v* ( t ) D/An A/D v ( t ) v o ( t ) Analog-to-computerized converter Digital-to-simple converter v ( t ) t v* ( t ) t v o ( t ) t nT ( n +1) T ( n +2) T = testing period 1/T = inspecting recurrence Example: A/D and D/A transformation

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Modeling targets Relationships: v to v * to v o Time space: v ( t ) to v *( t ) to v o ( t ) Frequency space: v ( s ) to v *( s ) to v o ( s ) v ( t ) t v* ( t ) t v o ( t ) t nT ( n +1) T ( n +2) T = examining period 1/T = testing recurrence

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Model v* ( t ) D/An A/D v ( t ) v o ( t ) Analog-to-advanced converter Digital-to-simple converter v* ( t ) H v ( t ) v o ( t ) T Sampler Zero-request hold

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Sampling v* ( t ) v ( t ) T Sampler v ( t ) t v* ( t ) t Unit motivation (Dirac)

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Unit drive d ( t ) zone = 1 s ( t ) t D t Properties Laplace change unit step

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Sampling in recurrence area

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Sampling in recurrence space: deduction

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Sampling in recurrence area: determination

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Aliasing

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Zero-request hold v* ( t ) H v o ( t ) Zero-request hold v* ( t ) t v o ( t ) t nT ( n +1) T ( n +2) T = examining period 1/T = examining recurrence

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Zero-request hold: time space H d ( t ) v o ( t ) Zero-request hold

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Zero-request hold: recurrence space H u ( t ) v o ( t ) Zero-request hold

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Sampled-information framework case: recurrence area v* ( t ) H v ( t ) v o ( t ) T Sampler Zero-request hold Consider just low-recurrence signals: System "exchange capacity" =

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Zero-request hold: recurrence reactions

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Zero-request hold: recurrence reactions f s = 1 MHz MATLAB record: zohfr.m

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Zero-request hold: 1 st - request estimate 1 st - request Pade guess

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Zero-request hold: recurrence reactions f s = 1 MHz MATLAB document: zohfr.m

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How does any of this apply to converter displaying?

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PWM is a little flag sampler! PWM examining happens at t p ( i.e. at dT s , occasionally, in every exchanging period)

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General examined information model Sampled-information model substantial at all frequencies Equivalent hold portrays the converter little flag reaction to the inspected obligation cycle bothers [Billy Lau, PESC 1986] State-space averaging or found the middle value of switch models are low-recurrence constant time approximations to this tested information model

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Application to DCM high-recurrence displaying i L c dT s d 2 T s T s

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Application to DCM high-recurrence demonstrating i L c dT s d 2 T s T s

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DCM inductor current high-recurrence reaction High-recurrence post because of the inductor current progression in DCM, see (11.77) in Section 11.3

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Conclusions PWM is a little flag sampler Switching converter is an inspected information framework Duty-cycle irritations go about as a series of motivations Converter reaction to the obligation cycle annoyances can be demonstrated as an identical hold Averaged little flag models are low-recurrence approximations to the proportional hold In DCM, at high frequencies, the inductor-current element reaction is depicted by a comparable hold that carries on as zero-request hold of length D 2 T s Approximate consistent time model taking into account the DCM examined information model corresponds with the investigation of Section 11.3: the same high-recurrence shaft at f s/( p D 2 ) is acquired Next: current-mode control (Chapter 12)

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