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LLC串联谐振半桥拓扑的分析与设计

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Simplified Analysis and Design of Seriesresonant LLC Half-bridge Converters MLD GROUP INDUSTRIAL & POWER CONVERSION DIVISION Off-line SMPS BU Application Lab I&PC Div. - Off-line SMPS Appl. Lab Presentation Outline • LLC series-resonant Half-bridge: operation and significant waveforms • Simplified model (FHA approach) • 300W design example I&PC Div. - Off-line SMPS Appl. Lab Series-resonant LLC Half-Bridge Topology and features Q1 Cr Ls Vin Half-bridge Driver Q2 Lp LLC tank circuit Preferably integrated into a single magnetic structure 3 reactive elements, 2 resonant frequencies 1 fr1 2⋅π⋅ Ls⋅Cr f r1 > f r2 1 fr2 2⋅π⋅ (Ls + Lp)⋅Cr Center-tapped output with fullwave rectification (low voltage and high current) Vout Vout Single-ended output with bridge rectifiication (high voltage and low current) Multi-resonant LLC tank circuit Variable frequency control Fixed 50% duty cycle for Q1 & Q2 Dead-time between LG and HG to allow MOSFET’s ZVS @ turn-on fsw ≈ fr, sinusoidal waveforms: low turn-off losses, low EMI Equal voltage & current stress for secondary rectifiers; ZCS, then no recovery losses No output choke; cost saving Integrated magnetics: both L’s can be realized with the transformer. High efficiency: >96% achievable I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Waveforms at resonance (fsw = fr1) Dead-time Tank circuit current is sinusoidal Magnetizing current is triangular Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents CCM operation Output current Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Switching details at resonance (fsw = fr1) Dead-time ZVS ! Tank circuit current >0 Magnetizing current V(D1)<0 I(D1)=0 ZCS ! I&PC Div. - Off-line SMPS Appl. Lab Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents LLC Resonant Half-bridge Operating Sequence at resonance (Phase 1/6) 1/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON; V(D1)=-2·Vout Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears Output energy comes from Cr and Ls Phase ends when Q2 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence at resonance (Phase 2/6) 2/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=V(D2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS2 and discharges COSS1, until V(COSS2)=Vin; Q1’s body diode starts conducting, energy goes back to Vin I(D2) is exactly zero at Q2 switch off Phase ends when Q1 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence at resonance (Phase 3/6) 3/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) back to Vin (Q1 is working in the 3rd quadrant) Phase ends when I(Ls)=0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence at resonance (Phase 4/6) 4/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) from Vin to ground Energy is taken from Vin and goes to Vout Phase ends when Q1 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence at resonance (Phase 5/6) 5/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=VD(2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS1 and discharges COSS2, until V(COSS2)=0; Q2’s body diode starts conducting I(D1) is exactly zero at Q1 switch off Phase ends when Q2 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence at resonance (Phase 6/6) 6/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q2’s RDS(on) (Q2 is working in the 3rd quadrant) Output energy comes from Cr and Ls Phase ends when I(Ls)=0, Phase 1 starts I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Waveforms above resonance (fsw > fr1) Dead-time Tank circuit current Magnetizing current is triangular Sinusoid @ f=fr1 ~ Linear portion CCM operation Output current Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Switching details above resonance (fsw > fr1) Dead-time ZVS ! Tank circuit current >0 Slope ~ -(Vc-n·Vout)/Ls Magnetizing current ZCS ! V(D1)<0 I(D1)=0 Output current Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 1/6) 1/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON; V(D1)=-2·Vout Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears Output energy comes from Cr and Ls Phase ends when Q2 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 2/6) 2/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=V(D2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS2 and discharges COSS1, until V(COSS2)=Vin; Q1’s body diode starts conducting, energy goes back to Vin V(D2) reverses as I(D2) goes to zero Phase ends when Q1 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 3/6) 3/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) back to Vin (Q1 is working in the 3rd quadrant) Phase ends when I(Ls)=0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 4/6) 4/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) from Vin to ground Energy is taken from Vin and goes to Vout Phase ends when Q1 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 5/6) 5/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=VD(2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS1 and discharges COSS2, until V(COSS2)=0; Q2’s body diode starts conducting Output energy comes from Cout Phase ends when Q2 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence above resonance (Phase 6/6) 6/6 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q2’s RDS(on) (Q2 is working in the 3rd quadrant) Output energy comes from Cr and Ls Phase ends when I(Ls)=0, Phase 1 starts I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Waveforms below resonance (fsw < fr1) Dead-time Tank circuit current Magnetizing current Sinusoid @ f=fr2 Sinusoid @ f=fr2 DCM operation Output current Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Switching details below resonance (fsw < fr1) Dead-time Gate-drive signals ZVS ! HB mid-point Voltage Resonant cap voltage Tank circuitcurrent = Magnetizing current >0 Portion of sinusoid @ f=fr2 I(D1)=0 ZCS ! Output current V(D1)<0 Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 1/8) 1/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON; V(D1)=-2·Vout Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears Output energy comes from Cr and Ls Phase ends when I(D2)=0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 2/8) 2/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q2 is ON, Q1 is OFF D1 and D2 are OFF; V(D1)=V(D2)=0; transformer’s secondary is open Cr resonates with Ls+Lp, fr2 appears Output energy comes from Cout Phase ends when Q2 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 3/8) 3/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=V(D2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS2 and discharges COSS1, until V(COSS2)=Vin; Q1’s body diode starts conducting, energy goes back to Vin Phase ends when Q1 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 4/8) 4/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) back to Vin (Q1 is working in the 3rd quadrant) Energy is recirculating into Vin Phase ends when I(Ls)=0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 5/8) 5/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 is ON, D2 is OFF; V(D2)=-2·Vout Lp is dynamically shorted: V(Lp) = n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q1’s RDS(on) from Vin to ground Energy is taken from Vin and goes to Vout Phase ends when I(D1)=0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 6/8) 6/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is ON, Q2 is OFF D1 and D2 are OFF; V(D1)=V(D2)=0; transformer’s secondary is open Cr resonates with Ls+Lp, fr2 appears Output energy comes from Cout Phase ends when Q1 is switched off I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 7/8) 7/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 and Q2 are OFF (dead-time) D1 and D2 are OFF; V(D1)=VD(2)=0; transformer’s secondary is open I(Ls+Lp) charges COSS1 and discharges COSS2, until V(COSS2)=0, then Q2’s body diode starts conducting Output energy comes from Cout Phase ends when Q2 is switched on I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Operating Sequence below resonance (Phase 8/8) 8/8 Q1 OFF Q2 ON Q1 ON Q2 OFF Q1 OFF Q2 ON Q1 Coss1 Cr Ls Vin n:1:1 D1 Cout Coss2 Lp Q2 Vout D2 Q1 is OFF, Q2 is ON D1 is OFF, D2 is ON Lp is dynamically shorted: V(Lp) =-n·Vout. Cr resonates with Ls, fr1 appears I(Ls) flows through Q2’s RDS(on) (Q2 is working in the 3rd quadrant) Output energy comes from Cr and Ls Phase ends when I(Ls)=0, Phase 1 starts I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Capacitive mode (fsw ~ fr2): why it must be avoided Capacitive mode is encountered when fsw gets close to fr2 Although in capacitive mode ZCS can be achieved, however ZVS is lost, which causes: Hard switching of Q1 & Q2: high switching losses at turn-on and very high capacitive losses at turn-off Body diode of Q1 & Q2 is reverse-recovered: high current spikes at turn-on, additional power dissipation; MOSFETs will easily blow up. High level of generated EMI Large and energetic negative voltage spikes in the HB midpoint that may cause the control IC to fail Additionally, feedback loop sign could change from negative to positive: In capacitive mode the energy vs. frequency relationship is reversed Converter operating frequency would run away towards its minimum (if MOSFETs have not blown up already!) I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Waveforms in capacitive mode (fsw ~ fr2) Dead-time Tank circuit current is piecewise sinusoidal Sinusoid @ f=fr2 Sinusoid @ f=fr1 Magnetizing current Output current Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Switching details in capacitive mode (fsw ~ fr2) HARD SWITCHING ! Very high voltage on Cr! Magnetizing current Tank circuit current is <0 Current is flowing in Q1’s body diode Q1’s body diode is recovered Output current Gate-drive signals HB mid-point Voltage Resonant cap voltage Transformer currents Diode voltages Diode currents I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Approximate analysis with FHA approach: Basics BASIC PRINCIPLES Input source CSN (Controlled Switch Network) Resonant tank Ideal transformer Uncontrolled rectifier Low-pass filter Load CSN provides a square wave voltage at a frequency fsw, dead times are neglected Resonant tank responds primarily to its fundamental component, then: Vin Tank waveforms are approximated by their fundamental components Uncontrolled rectifier + low-pass filter’s effect is incorporated into the load. Half-bridge Driver Q1 Cr Ls a:1 Lp Q2 Cout R Vout Vin Vin Q1 OFF Q2 ON 2 π Vin Note: Cr is both resonant and dc blocking capacitor 2 Q1 ON Its ac voltage is superimposed on a dc component Q2 OFF equal to Vin/2 (duty cyle is 50% for both Q1 and Q2) 0 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Equivalent model with FHA approach The actual circuit turns into an equivalent controlled switch M (jω) linear circuit where the ac resonant tank is dc input excited by an effective sinusoidal input source and drives an effective resistive load. Iin Standard ac analysis can be used to solve the Vin circuit iS ⇒ vS Zin (jω) ac resonant tank Functions of interest: Input Impedance Zin(jω) and Forward Transfer Function M(jω). It is possible to show that the complete conversion ratio Vout/Vin is: vS = 2 π Vin ⋅sin(2π ⋅ fs ⋅ t) rectifier with low-pass filter dc output iR Iout vR Re R Vout Re = 8 π2 a2 R Vout = M( jω) Vin Iin = 2 π is cos(ϕS ) = 2 π vS Re 1 Zi Iout = 2 a π iR This result is valid for any resonant topology I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Transformer model (I) Physical model LL1 Prim. leakage inductance Magnetizing inductance Ideal Transformer n:1:1 Lµ LL2a LL2b Sec. leakage inductance Sec. leakage inductance All-Primary-Side equivalent model used for LLC analysis Ls Ideal Transformer a:1:1 Lp Results from the analysis of the magnetic structure (reluctance model appraach) n is the actual primary-to-secondary turn ratio Lµ models the magnetizing flux linking all windings LL1 models the primary flux not linked to secondary LL2a and LL2b model the secondary flux not linked to primary; symmetrical windings: LL2a = LL2b APS equivalent model: terminal equations are the same, internal parameters are different a is not the actual primary-to-secondary turn ratio Ls is the primary inductance measured with all secondaries shorted out Lp is the difference between the primary inductance measured with secondaries open and Ls NOTE: LL1 +Lµ = Ls + Lp = L1 primary winding inductance I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Transformer model (II) Ls Lp Ideal Transformer a:1:1 LL1 Prim. leakage inductance Ideal Transformer LL2 n:1:1 Lµ Magnetizing LL2 inductance We need to go from the APS model to the physical model to determine transformer specification Undetermined problem (4 unknowns, 3 conditions); one more condition needed (related to the physical magnetic structure) Only n is really missing: L1 = Ls + Lp = LL1 + Lµ is known and measurable, Ls is measurable Magnetic circuit symmetry will be assumed: equal leakage flux linkage for both primary and secondary ⇒ LL1 = n2·LL2; then: Sec. leakage inductance Sec. leakage inductance n = a Lp Lp + Ls I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Transformer model (III) Example of magnetically symmetrical structure Slotted bobbin Primary winding Air gap symmetrically placed between the windings Ferrite E-half-cores Top view Secondary winding Like in any ferrite core it is possible to define a specific inductance AL (which depends on air gap thickness) such that L1 = Np2·AL In this structure it is also possible to define a specific leakage inductance ALlk such that Ls=Np2·ALlk. ALlk is a function of bobbin’s geometry; it depends on air gap position but not on its thickness I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Numerical results of ac analysis The ac analysis of the resonant tank leads to the following result: Input Impedance: Z in(x, k, Q) Z R⋅Q⋅ 1 + x2⋅k2 x2⋅k2⋅Q2 + j⋅ x − 1 x + 1+ x⋅k x2⋅k2⋅Q2 Module of the Forward transfer function (voltage conversion ratio): M(x, k, Q) 1⋅ 1 2 1 + 1 k ⋅ 1 − 1 2 x2 + Q2⋅ x − 1 x 2 where: f r1 1; 2⋅π⋅ Ls⋅Cr Z x R f Ls f r1 ; k Lp Ls ; Z R Ls ; Re Cr 8 ⋅a2⋅R π2 ; Q ZR Re NOTES: x is the “normalized frequency”; x<1 is “below resonance”, x>1 is “above resonance” ZR is the characteristic impedance of the tank circuit; Q, the quality factor, is related to load: Q=0 means Re=∞ (open load), Q=∞ means Re=0 (short circuit); one can think of Q as proportional to Iout I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Resonant Tank Input Impedance Zin(jω) Above resonance (x>1) Zin(jω) is always inductive; current lags voltage, so when vS=0, iS is still >0: ZVS 10 a Below fr2 (x< 1 1 + k ), Zin(jω) is always capacitive; current leads voltage, so when vS=0, iS is already <0: ZCS ( ) Zi x, kC, Qmax Below the first resonance ( ( ) 1 1+ k Qm(x) it is capacitive ⇒ ZCS. Zix, kZCi,n10(6x, k, Q) ( ) ZR Zi x, kC, 0.5⋅Qmax 1 In general, the ZVS-ZCS borderline (iZsi x, kC, ) 2⋅Qmax defined by Im(Zin(jω))=0 For x> 2 |Zin(jω)| is concordant with 2+ k the load: the lower the load the lower 1 1+ k 2 2+ k Q=0.19 Iout Q=0.38 k=5 Q=0.76 Iout Q=∞ (shorted output) Q=0 (open output) Capacitve region Current leading (always ZCS) Inductive region Current lagging (always ZVS) the input current 0.1 0.1 1 10 For x< 2 |Zin(jω)| is discordant with 2+ k the load: the lower the load the higher the input current! f = f r2 x Inductive (ZVS) for QQm(x) f = f r1 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Voltage conversion ratio ||M(jω)|| All curves, for any Q, touch at x=1, 3 M=0.5, with a slope -1/k; a The open output curve (Q=0) is the 2.5 upper boundary for converter’s ( ) M x, kC, 0 operating points in the x-M plane; ( ) M x, kC, 0.5⋅Qmax 2 M = 1× k 2 1+ k for x→∞; M → ∞ for x = 1 1+ k MMM((xx,,=kkCCa,, 2Q⋅⋅VmQVamixona)xu) t 1.5 All curves with Q>0 have maxima Mx, kC, 101 that fall in the capacitive region. B(x, kC) 1 Above resonance it is always M<0.5 1 C 1+ k Capacitve region Current leading (ZCS) Q=0 (open output) ZVS-ZCS borderline Q=0.38 Q=0.19 Iout M>0.5 only below resonance ZVS below resonance at a given frequency occurs if M> Mmin>0.5; if M> Mmin>0.5 is fixed, it occurs if Q>Qm. 0.5 0 0.1 f = f r2 Q=0.76 1 x Inductive region Current lagging (ZVS) k=5 Resonance: Load-independent point All curve have slope = -1/ k 1× k 2 1+k Q=10 10 f = f r1 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Effect of k on ||M(jω)|| 2 1.5 M (x, 1, 0) M (x, 1, 0.5) M (x, 1, 1) 1 M (x, 1, 2) 0.5 k=1 2 1.5 M (x, 2, 0) M (x, 2, 0.5) M (x, 2, 1) 1 M (x, 2, 2) 0.5 0 0.1 2 1.5 M (x, 5, 0) M (x, 5, 0.5) M (x, 5, 1) 1 M (x, 5, 2) 0.5 0 1 10 0.1 x 2 k=5 1.5 M (x, 10, 0) M (x, 10, 0.5) M (x, 10, 1) 1 M (x, 10, 2) 0.5 0 0 0.1 1 10 0.1 x I&PC Div. - Off-line SMPS Appl. Lab k=2 1 10 x k=10 1 10 x LLC Resonant Half-bridge Operating region on ||M(jω)|| diagrams 1 a ( ) M x, kC, 0 0.75 ( ) M x, kC, 0.5⋅Qmax MMM((xx,,=kkCCa,, 2Q⋅⋅VmQVamixona)xu) t 0.5 M x, kC, 101 M-axis of Vin: can be Vout is rescaled in regulated teBr(mx, ksC) 0.25 Given the input voltage range (Vinmin÷Vinmax), 3 types of possible operation: 1. always below M<0.5 (step-down) 0 0.1 2. always above M>0.5 (step-up) 3. across M=0.5 (step-up/down, shown in the diagram) 1 1+ k C Q=0 Operating region Q=Qm 1 x min x x max I&PC Div. - Off-line SMPS Appl. Lab k=5 a⋅ Vout Vin min a⋅ Vout Vin max 1× k 2 1+ k 10 LLC Resonant Half-bridge Full-load issue: ZVS at min. input voltage Zin(jω) analysis has shown that ZVS occurs for x<1, provided Q≤Qm, i.e. Im[Zin(jω)] ≥ 0. If Q=Qm (Im[Zin(jω)] = 0) the switched current is exactly zero, This is only a necessary condition for ZVS, not sufficient because the parasitic capacitance of the HB midpoint, neglected in the FHA approach, needs some energy (i.e. current) to be fully charged or depleted within the dead-time (i = C dv/dt) A minimum current must be switched to make sure that the HB midpoint can swing rail-to-rail within the dead-time. Then, it must be Q≤QZ> fr1 Cr disappears and the output voltage is given by the inductive divider made up by Ls and Lp If the minimum voltage conversion ratio is greater than the inductive divider ratio, regulation will be possible at some finite frequency This links the equivalent turn ratio a and the inductance ratio k: a⋅ Vout > 1 ⋅ k Vin max 2 1 + k This is equivalent to the graphical constraint that the horizontal line a·Vout/Vinmax must cross the Q=0 curve Equivalent schematic of LLC converter for x →∞ Ls a:1 V1 Lp V2 V2 V 1⋅ 1 a ⋅ Lp Ls + Lp I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge No-load issues: ZVS Zin(jω) analysis has shown that ZVS always occurs for x>1, even at no load (Q=0) x>1 is actually only a necessary condition for ZVS, not sufficient because of the parasitic capacitance of the HB midpoint neglected in the FHA approach A minimum current must be ensured at no load to let the HB midpoint swing rail-to-rail within the dead-time. This poses an additional constraint on the maximum value of Q at full load: ( ) Q ≤ π ⋅ 1 ⋅ Td 4 (1 + k)⋅x max Re⋅ 2⋅Coss + C stray Tdead Hard Switching at no load I&PC Div. - Off-line SMPS Appl. Lab ( ) 2⋅Coss + C stray ⋅Vin max Td LLC Resonant Half-bridge No-load issues: Feedback inversion Parasitic intrawinding and interwinding capacitance are summarized in Cp Cj is the junction capacitance of the output rectifiers; each contributes for half cycle Under no-load, rectifiers have low reverse voltage applied, Cj increases. The parasitic tank has a high-frequency resonance that makes M increase at some point: feedback becomes positive, system loses control Cure: minimize Cp and Cj, limit max fsw. Ls a:1 Lp Cp Cj ≡ Cj 3 2.5 ( ) MM x, kC, 0, p 2 MM MM=M (ax, (x, ⋅kCV,q0o.0u5t, p ) kVC,i0n.1, p ) 1.5 ( ) MM x, kC, 0.2, p 1 0.5 0 0.1 Ls Lp CD 41 x k⋅λ2 λ =0.08 d M <0 dx region d M >0 dx region 1 10 x CD Cp + C j a2 λ CD Cr I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design procedure. General criteria. DESIGN SPECIFICATION Vin range, holdup included (Vinmin ÷ Vinmax) Nominal input voltage (Vinnom) Regulated Output Voltage (Vout) Maximum Output Power (Poutmax) Resonance frequency: (fr) Maximum operating frequency (fmax) ADDITIONAL INFO Coss and Cstray estimate Minimum dead-time The converter will be designed to work at resonance at nominal Vin Step-up capability (i.e. operation below resonance) will be used to handle holdup The converter must be able to regulate down to zero load at max. Vin Q will be chosen so that the converter will always work in ZVS, from zero load to Poutmax There are many degrees of freedom, then many design procedures are possible. We will choose one of the simplest ones I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design procedure. Proposed algorithm (I). 1. Calculate min., max. and nominal conversion ratio with a=1: Vout Mmin Vinmax Vout Mmax Vinmin Vout Mnom Vinnom 2. Calculate the max. normalized frequency xmax: f max x max f r 3. Calculate a so that the converter will work at resonance at nominal voltage 1 a 2⋅M nom 4. Calculate k so that the converter will work at xmax at zero load and max. input voltage: k 2⋅a⋅M min ⋅ 1 − 1 1 − 2⋅a⋅M min x 2 max 5. Calculate the max. Q value, Qmax1, to stay in the ZVS region at min. Vin and max. load: Q max1 1⋅ 1 ( ) ⋅ 2⋅a⋅M max 2 + k ( ) k 2⋅a⋅M max 2⋅n⋅M max 2 − 1 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design procedure. Proposed algorithm (II). 6. Calculate the effective load resistance: Re 8 ⋅a2⋅R 8 ⋅a2⋅ Vout2 π2 π2 Pout max 7. Calculate the max. Q value, Qmax2, to ensure ZVS region at zero load and max. Vin: ( ) Q max2 π⋅ 1 ⋅ Td 4 (1 + k)⋅x max Re⋅ 2⋅Coss + C stray 8. Choose a value of Q, QS, such that QS ≤ min(Qmax1, Qmax2) 9. Calculate the value xmin the converter will work at, at min. input voltage and max. load: x min 1 1 + k⋅1 − 1 ( ) 2⋅ n⋅M max 1+ Q S Q max1 4 10. Calculate the characteristic impedance of the tank circuits and all component values: ZR Re⋅QS 1 Cs 2⋅fr⋅ZR⋅π ZR Ls 2⋅π⋅fr Lp k⋅Ls I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design example. 300W converter Vin range Nominal input voltage Regulated ouput voltage Maximum output Current Resonance frequency Maximum switching frequency Start-up switching frequency HB midpoint estimated parasitic capacitance Minimum dead-time (L6599) ELECTRICAL SPECIFICATION 320 to 450 Vdc 320V after 1 missing cycle; 450 V is the OVP theshold of the PFC pre-regulator 400 Vdc Nominal output voltage of PFC 24 V 12 A Total Pout is 300 W 90 kHz 180 kHz 300 kHz 200 pF 200 ns I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design example. 300W converter 1. Calculate min. and max. and nominal conversion ratio referring to 24V output: Vout 24 Mmin Vinmax 450 0.053 Vout 24 Mmax Vinmin 320 0.075 Vout 24 Mnom Vinnom 0.06 400 2. Calculate the max. normalized frequency xmax: f max 180 x max f r 2 90 3. Calculate a so that the converter will work at resonance at nominal voltage 1 a 2⋅M nom 1 8.333 2⋅ 0.06 4. Calculate k so that the converter will work at xmax at zero load and max. input voltage: k 2⋅a⋅M min ⋅ 1 − 1 6 1 − 2⋅a⋅M min x 2 max 5. Calculate the max. Q value, Qmax1, to stay in the ZVS region at min. Vin and max. load: Q max1 1⋅ 1 ⋅ k 2⋅a⋅M max ( ) 2⋅a⋅M max 2 + k ( ) 2⋅n⋅M max 2 − 1 0.395 I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design example. 300W converter 6. Calculate the effective load resistance: Re 8 ⋅a2⋅R 8 ⋅a2⋅ Vout 2 108.067 Ω π2 π2 Pout max 7. Calculate the max. Q value, Qmax2, to ensure ZVS at zero load: ( ) Q max2 π⋅ 1 ⋅ Td 4 (1 + k)⋅x max Re⋅ 2⋅Coss + C stray 0.519 8. Choose a value of Q, QS, such that QS ≤ min(Qmax1, Qmax2) Considering 10% margin: QS =0.9·0.395=0.356 9. Calculate the value xmin the converter will work at, at min. input voltage and max. load: 1 xmin 1 + k⋅1 − 1 0.592 ( ) 2⋅n⋅M max 1+ QS Q max1 4 fmin 90⋅0.592 53.28 kHz 10. Calculate the characteristic impedance of the tank circuits and all component values: ZR Re⋅QS 38.472 Ω Cs 1 46 nF 2⋅ fr⋅ Z R ⋅ π Ls ZR 68 µH 2⋅ π⋅ fr Lp k⋅Ls 408 µH I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Design example. 300W converter 11. Calculate components around the L6599: Oscillator setting. Choose CF (e.g. 470 pF as in the datasheet). Calculate RFmin: RFmin = 1 3 ⋅ CF ⋅ fmin = 1 3 ⋅ 470 ⋅10−12 ⋅ 53.28 ⋅103 = 13.3 kΩ Calculate RFmax: RFmax = RFmin fmax − 1 = 13.3 ⋅103 180 −1 = 5.54 kΩ fmin 53.28 Calculate Soft-start components: RSS = RFmin fstart − 1 = 13.3 ⋅103 300 − 1 = 2.87 kΩ fmin 53.28 CSS = 3 ⋅10−3 RSS = 3 ⋅10−3 2.87 ⋅10−3 = 1 µF I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Comparison with ZVS Half-bridge (I) Primary Conduction Losses (W) 1.8 AHB LLC 1.6 1.4 1.2 1 Primary Switching Losses (W) 1.6 AHB LLC 1.4 1.2 1 0.8 0.6 Secondary Conduction Losses 3.5 3 2.5 2 1.5 1 0.5 0.8 0.4 280 300 320 340 360 380 400 420 280 300 320 340 360 380 400 420 0 Input Voltage (V) Input Voltage (V) AHB LLC ELECTRICAL SPECIFICATION Input Voltage: 300 to 400(*) Vdc Output voltage: 20 Vdc Output power: 100 W Switching frequency: 200 kHz (*) 300 V holdup, 400 V nominal voltage AHB Primary Conduction Losses 0.97 W Primary Switching Losses 1.38 W Secondary Conduction Losses 3.15 W Secondary Switching Losses ? Total Losses 5.92 + ? W LLC 0.95 W 0.61 W 2.25 W 0W 3.81 W I&PC Div. - Off-line SMPS Appl. Lab LLC Resonant Half-bridge Comparison with ZVS Half-bridge (II) Efficiency (%) 96 95.5 95 94.5 94 93.5 93 92.5 92 0 20 40 60 80 Output Power (W) Efficiency (%) 96 95 AHB 94 LLC 93 AHB optimized for 400 V AHB LLC 92 Nominal voltage 91 100 120 280 300 320 340 360 380 400 420 Input Voltage (V) ZVS Half-bridge MOSFETs: high turn-off losses; ZVS at light load difficult to achieve Diodes: high voltage stress ⇒ higher VF ⇒ higher conduction losses; recovery losses Holdup requirements worsen efficiency at nominal input voltage LLC resonant half-bridge MOSFETs: low turn-off losses; ZVS at light load easy to achieve Diodes: low voltage stress (2·Vout) ⇒ lower VF ⇒ low conduction losses; ZCS ⇒ no recovery losses Operation can be optimized at nominal input voltage I&PC Div. - Off-line SMPS Appl. Lab

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