Direct-Off-Line Single-Ended Forward Converters and The Right-Half-Plane ZeroDirect-Off-Line Single-Ended Forward ConverterForward converter with energy recovery windingOperating PrinciplesSlide 5Slide 6Slide 7Slide 8Output VoltageSlide 10Circuit SimulationThe Right-Half-Plane ZeroCauses of the RHP ZeroThe RHP Zero A simplified ExplanationEffects of Increasing Duty RatioSlide 16Duty Raito Control EquationsSlide 18Slide 19Current-Mode Control EquationsSlide 21Slide 22Slide 2312/06/200312/06/2003 11Direct-Off-Line Single-Ended Direct-Off-Line Single-Ended Forward ConvertersForward ConvertersandandThe Right-Half-Plane ZeroThe Right-Half-Plane ZeroPresented by:Presented by:Geetpal KaurGeetpal KaurEE136 StudentEE136 Student12/06/200312/06/2003 22Direct-Off-Line Single-Ended Direct-Off-Line Single-Ended Forward ConverterForward ConverterThe power stage of a typical The power stage of a typical single-ended forward convertersingle-ended forward converterLs carries a large DC current Ls carries a large DC current componentcomponentThe term “Choke” is used to The term “Choke” is used to describe this componentdescribe this componentThe general appearance of the The general appearance of the power stage is similar to the power stage is similar to the flyback unitflyback unit12/06/200312/06/2003 33Forward converter with energy Forward converter with energy recovery windingrecovery winding12/06/200312/06/2003 44Operating PrinciplesOperating PrinciplesWhen transistor Q1 turns onWhen transistor Q1 turns onSupply voltage Vcc is applied to Supply voltage Vcc is applied to the primary winding P1the primary winding P1As a result a secondary voltage As a result a secondary voltage Vs is developed and applied to Vs is developed and applied to output rectifier D1 and choke Lsoutput rectifier D1 and choke Ls12/06/200312/06/2003 55Operating PrinciplesOperating PrinciplesThe voltage across the choke Ls The voltage across the choke Ls will be Vs less the output voltage will be Vs less the output voltage VoutVoutThe current in Ls will increase The current in Ls will increase linearly linearly di / dt = (Vs – Vout) / Lsdi / dt = (Vs – Vout) / Ls12/06/200312/06/2003 66Operating PrinciplesOperating PrinciplesAt the end of an on periodAt the end of an on periodQ1 will turn ofQ1 will turn ofSecondary voltages will reverseSecondary voltages will reverseChoke current IChoke current ILL will continue to will continue to flow in the forward directionflow in the forward direction12/06/200312/06/2003 77Operating PrinciplesOperating PrinciplesAs a result diode D2 will turn onAs a result diode D2 will turn onD2 allows the current to D2 allows the current to continue circulating in the loop continue circulating in the loop D2, Ls, Co, and loadD2, Ls, Co, and loadThe voltage across the choke Ls The voltage across the choke Ls will reversewill reverse12/06/200312/06/2003 88Operating PrinciplesOperating PrinciplesThe current in Ls will decreseThe current in Ls will decrese-di / dt = Vout / Ls-di / dt = Vout / Ls12/06/200312/06/2003 99Output VoltageOutput VoltageVVoutout = (V = (Vss * t * tonon) / (t) / (tonon + t + tofof))Vs = secondary voltage, peak VVs = secondary voltage, peak Vton = time that Q1 is conduction, ton = time that Q1 is conduction, µsµs12/06/200312/06/2003 1010Output VoltageOutput Voltagetof = time that Q1 is of, µstof = time that Q1 is of, µsthe ratio:the ratio: ton / (ton + tof)ton / (ton + tof) is called the duty ratiois called the duty ratio12/06/200312/06/2003 1111Circuit SimulationCircuit Simulation12/06/200312/06/2003 1212The Right-Half-Plane ZeroThe Right-Half-Plane ZeroThe difficulty of obtaining a The difficulty of obtaining a good stability margin and good stability margin and high-frequency transient high-frequency transient performance from the performance from the continuous-inductor-mode continuous-inductor-mode flyback and boost convertersflyback and boost converters12/06/200312/06/2003 1313Causes of the RHP ZeroCauses of the RHP ZeroA negative zero in the small-A negative zero in the small-signal duty cycle control to signal duty cycle control to output transfer functionoutput transfer functionThe negative sign locates this The negative sign locates this zero in the right half of the zero in the right half of the complex frequency planecomplex frequency plane12/06/200312/06/2003 1414The RHP ZeroThe RHP ZeroA simplified ExplanationA simplified ExplanationThe right-half-plane (RHP) zero The right-half-plane (RHP) zero has the same 20dB/decade rising has the same 20dB/decade rising gain magnitude as a gain magnitude as a conventional zero, but with 90º conventional zero, but with 90º phase lag instead of lead phase lag instead of lead12/06/200312/06/2003 1515Effects of Increasing Duty RatioEffects of Increasing Duty RatioThe peak inductor current The peak inductor current increases in each switching cycleincreases in each switching cycleThe diode conduction time The diode conduction time decreasesdecreasesThis is the circuit efect which is This is the circuit efect which is mathematically the RHP Zeromathematically the RHP Zero12/06/200312/06/2003 1616The RHP ZeroThe RHP ZeroA simplified ExplanationA simplified Explanation12/06/200312/06/2003 1717Duty Raito Control EquationsDuty Raito Control EquationsThe equations for the flyback The equations for the flyback circuit are developed starting circuit are developed starting with the voltage VL across the with the voltage VL across the inductor:inductor:VVLL = V = ViiD–VD–Vo o (1-D) = (V(1-D) = (Vii+V+Vaa)D – V)D – Voo12/06/200312/06/2003 1818Duty Raito Control EquationsDuty Raito Control EquationsModulating the duty ratio D by a Modulating the duty ratio D by a small AC signal d whose small AC signal d whose frequency is much smaller than frequency is much smaller than the switching frequency the switching frequency generated an ac inductor voltage generated an ac inductor voltage ννLL::ννLL = (Vi + Va)d – = (Vi + Va)d – ννo(1-D) =o(1-D) = (Vi + Vo)d (Vi + Vo)d12/06/200312/06/2003 1919Duty Raito Control EquationsDuty Raito Control EquationsRHP zero frequency:RHP zero frequency: ωωz z = Vi / L IL= Vi / L IL12/06/200312/06/2003 2020Current-Mode Control EquationsCurrent-Mode Control EquationsIo = iL (1-D) – (j Io = iL (1-D) – (j ωω L IL iL) / (Vi + L IL iL) / (Vi + Vo) = Vi iL / (Vi + Vo) -
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