ECEN5817, ECEE Department, University of Colorado at BoulderChapter 19Resonant ConversionIntroduction19.1 Sinusoidal analysis of resonant converters19.2 ExamplesSeries resonant converterParallel resonant converter19.3 Soft switchingZero current switchingZero voltage switchingECEN 5817119.4 Load-dependent properties of resonant converters19.5 Exact characteristics of the series and parallel resonant convertersA class of resonant DC-to-AC invertersECEN 58172ECEN5817, ECEE Department, University of Colorado at BoulderA resonant DC-DC converterTransfer functionH(s)A resonant dc-dc converter:iR(t)vR(t)+–+–R+v(t)–Resonant tank networkis(t)dcsourcevg(t)vs(t)+–Switch networkLCsNSNTi(t)Rectifier networkNRNFLow-passfilternetworkdcloadECEN 58173networkIf tank responds primarily to fundamental component of switch network output voltage waveform, then harmonics can be neglectedSection 19.1: modeling based on sinusoidal approximationThe sinusoidal approximationSwitchoutputTank current and output fvoltagespectrumResonanttankresponseffs3fs5fsf3f5fTank current and output voltage are essentially sinusoids at the switching frequency fsNeglect harmonics of switch output voltage waveform, and model only the fundamental ECEN 58174fTankcurrentspectrumffs3fs5fsfs3fs5fscomponentRemaining ac waveforms can be found via standard phasor analysisECEN5817, ECEE Department, University of Colorado at Boulder19.1.1 Controlled switch network modelis(t)NS1+–vgvs(t)+–Switch network1212ECEN 58175Fourier series expansion of square-wave switch network output voltage vs(t):The fundamental component isSo model switch network output port with voltage source of value vs1(t)Model of switch network input portis(t)+NS1Find dc (average) component of the switch network input current+–vgvs(t)–Switch network212Fundamental component of the ECEN 58176output current:ECEN5817, ECEE Department, University of Colorado at BoulderSwitch network: equivalent circuit• Switch network converts dc to ac• Dc components of input port waveforms are modeledECEN 58177• Fundamental ac components of output port waveforms are modeled• Model is power conservative: predicted average input and output powers are equal19.1.2 Modeling the rectifier and capacitive filter networksiR(t)R+(t)i(t)+(t)| iR(t) |Rv(t)–Rectifier networkNRNFLow-passfilternetworkdcloadvR(t)–Assume large output filter it h i ll i lIf iR(t) is a sinusoid:ECEN 58178capacitor, having small ripple.vR(t) is a square wave, having zero crossings in phase with tank output current iR(t).Then vR(t) has the following Fourier series:ECEN5817, ECEE Department, University of Colorado at BoulderSinusoidal approximation: rectifierAgain, since tank responds only to fundamental components of applied waveforms, harmonics in vR(t) can be neglected. vR(t) becomesECEN 58179Rectifier dc output port modeliR(t)R+v(t)i(t)+vR(t)| iR(t) |Output capacitor charge balance: dc load current is equal to average rectified tank output currentRv(t)–Rectifier networkNRNFLow-passfilternetworkdcloadvR(t)–HenceECEN 581710ECEN5817, ECEE Department, University of Colorado at BoulderEquivalent circuit of rectifierRectifier input port:Fundamental components of current and voltage are iid h i hsinusoids that are in phaseHence rectifier presents a resistive load to tank networkEffective resistance ReisRectifier equivalent circuitECEN 581711With a resistive load R, this becomesLoss free resistor: all power absorbed by Reis transferred to the output port19.1.3 Resonant tank networkModel of ac waveforms is now reduced to a linear circuit. Tank k i i d b ff i i id l l ( i h k ECEN 581712network is excited by effective sinusoidal voltage (switch network output port), and is load by effective resistive load (rectifier input port)Can solve for transfer function via conventional linear circuit analysisECEN5817, ECEE Department, University of Colorado at BoulderSolution of tank network waveformsECEN 58171319.1.4 Solution of convertervoltage conversion ratio M = V/VgECEN 581714ECEN5817, ECEE Department, University of Colorado at Boulder19.2 Examples19.2.1 Series resonant converterECEN 581715Model: series resonant converterECEN 581716ECEN5817, ECEE Department, University of Colorado at BoulderConstruction of Zi– resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re= 10 ΩECEN 581717Construction of H = V / Vg– resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re= 10 ΩECEN 581718ECEN5817, ECEE Department, University of Colorado at BoulderModel: series resonant converterECEN 58171919.2.2 Subharmonic modes of the SRCExample: excitation of tank by third harmonic of switching frequencyCan now approximate vs(t) by its third harmonic:Result of analysis:ECEN 581720ECEN5817, ECEE Department, University of Colorado at BoulderSRC DC conversion ratio MECEN 581721Subharmonic modes19.2.3 Parallel resonant dc-dc converterDiffers from series resonant converter as follows:Different tank networkECEN 581722Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filterNeed a new model for rectifier and filter networksECEN5817, ECEE Department, University of Colorado at BoulderModel of uncontrolled rectifierwith inductive filter network – input portFundamental component of iR(t):ECEN 581723Model of uncontrolled rectifierwith inductive filter network – output portOutput inductor volt second balance: dc voltage is equal to average rectified tank output voltageECEN 581724ECEN5817, ECEE Department, University of Colorado at BoulderEffective resistance ReECEN 581725Equivalent circuit model of uncontrolled rectifierwith inductive filter networkECEN 581726Output port modeled as a dependent voltage source based on rectified tank voltage, in contrast to SRC where output port is modeled as dependent current source based on rectified tank currentECEN5817, ECEE Department, University of Colorado at BoulderEquivalent circuit modelParallel resonant dc-dc converterECEN 581727Ways to construct transfer function H in terms of impedancesECEN 581728ECEN5817, ECEE Department, University of Colorado at BoulderConstruction of Zo– resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re= 1 kΩECEN 581729Construction of H = V / Vg– resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re= 1 kΩECEN 581730ECEN5817, ECEE Department, University of Colorado at BoulderConstruction of HECEN 581731Dc conversion ratio of the PRCAt resonance, this becomesECEN 581732• PRC can step up the voltage, provided R > R0•