ECEN5817, ECEE Department, University of Colorado at BoulderAnalysis of quasi-square-wave ZVS convertersD1i1(t) i2(t)LrIV1Lr–V2Lri2(t)ZVS-QSW buck: single-transistor case+–CrVgD2Q1+v2(t)–+v1(t)–LCR+V–0Tsv2(t)V10t0Conductingdevices:D2XXQ1D1Resonant transitions but transistor and diode conduction intervals are similar to PWMPeak voltages applied to ECEN 58171similar to PWMTank capacitor is in parallel with all semiconductor devices, hence all semiconductors operate with ZVSPeak currents are increased, and are similar to DCMgppsemiconductors are same as PWMMagnetics are small, and are similar to DCMSingle-transistor ZVS-QSW waveforms and state-plane analysismc+V1_+V_LC+vci1iLD1D2Q1jlmcotoTs12345_ECEN 58172jlot Devices conductingECEN5817, ECEE Department, University of Colorado at BoulderA way to solve and plot the characteristicsECEN 58173Solving, p 2ECEN 58174ECEN5817, ECEE Department, University of Colorado at BoulderResults: Switch conversion ratio µ vs. FECEN 58175Switch conversion ratio µ vs. ECEN 58176Course website contains Excel spreadsheet (with function macros) that evaluates the above equations and can plot the above characteristics.ECEN5817, ECEE Department, University of Colorado at BoulderSummary of 1-transistor ZVS-QSW characteristicsµ vs. FECEN 58177ZVS-QSW switch cellQDConverter examplesHigh-frequency view of the switch networkDQDQQDBasic switch implementation optionsECEN 58178QDQ: current-bidirectional (e.g. MOSFET)D: single-quadrant (diode)Q: current-bidirectional (e.g. MOSFET)D: current-bidirectional synchronous rectifier (e.g. MOSFET)ECEN5817, ECEE Department, University of Colorado at BoulderTwo-transistor (synchronous-rectifier) ZVS-QSWD1Q1+i1(t) i2(t)+LrL+I+–CrVgD2Q1v2(t)–v1(t)–CRV–• Resonant transitions but transistor and conduction intervals are similar to PWM; peak voltages are the same as in hard-switched PWM • Tank capacitor is in parallel with all semiconductor devices, hence all semiconductors operate with ZVSECEN 58179• Peak currents are increased, and are similar to DCM• Constant-frequency duty-cycle control, similar to standard PWM, is possible• ZVS-QSW (resonant-transition) concept extends to a number of other important practical soft-switching converters2-transistor ZVS-QSW: state plane ECEN 581710ECEN5817, ECEE Department, University of Colorado at BoulderWaveforms and definition of duty cycle, 2 transistors•Here, the controller duty ,ycycle Dcis defined as the duty cycle that would be chosen by a conventional PWM chip• The resonant transitions are “dead times” that occur at the beginning of the DTsand ECEN 581711ggsD’TsintervalsConstant-frequency control characteristicsof the 2-switch ZVS-QSWECEN 581712Constant frequency, duty cycle control:Low output impedance, µ doesn’t depend much on JVery similar to conventional PWM CCM switch, but exhibits ZVS over a range of operating pointsECEN5817, ECEE Department, University of Colorado at Boulder2-switch ZVS-QSW: ZVS boundaryReducing F = fs/f0leads ZVS id to ZVS over a wider range of µ and JECEN 581713AC (small-signal dynamic) modeling of quasi-resonant convertersQuasi-resonant converters inherit properties of PWM parents, with switch conversion ratio  playing the role of the PWM switch duty cycle dAC modeling approach:• Start from (v,i,fs) found for the resonant switch• Perturb and linearizeECEN 581714• Replace d with  in the small-signal AC dynamic model of the PWM parent converter (from ECEN5797 Intro to PE)ECEN5817, ECEE Department, University of Colorado at BoulderExample 1: Full-wave ZCS-QR BuckECEN 581715Small-signal AC model of the PWM buck converterTextbook, Fig.7.17(a)ECEN 581716ECEN5817, ECEE Department, University of Colorado at BoulderSmall-signal AC model of the full-wave ZCS-QR buck ECEN 581717Example 2: Half-wave ZCS-QR buckECEN 581718ECEN5817, ECEE Department, University of Colorado at BoulderPerturb and linearize ECEN 581719Small-signal AC model of the half-wave ZCS-QR buckECEN 581720ECEN5817, ECEE Department, University of Colorado at BoulderECEN 581721Summary of the linearization/perturbation resultsECEN 581722ECEN5817, ECEE Department, University of Colorado at BoulderHow about 2-switch ZVS-QSW?ECEN