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Cuk变换器设计

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Cuk变换器设计

Motivation for boost-buck converter topology

 Cuk convertter iin Conttiinuous Conducttiion Mode operattiion

 Critical inductors for Cuk converter in Border Current Mode

 Cuk convertter iin CCM wiitth couplled iinducttors

 Zero-ripple technique for both input and output currents

 Cuk convertter iin CCM wiitth diiscrette ttransformer

 Leakage reducing in the isolating transformer

 Mullttii-outtputt zero-riipplle iisollatted Cuk convertter

 Single magnetic realization of multi-output Cuk converter

 Augmentt of tthe lleakage iinducttance iin ttransformer

 Cuk converter in Discontinuous Conduction Mode operation

 Three swiittched nettworks and iinducttor currentts iin DCM

 Derivation of the Voltage Transfer Function in DCM

 Equiivallentt iinducttance requiired for DCM

 Lossless resistor emulated by Cuk DCM converter

 The desiign of tthe iinttermediiatte capaciittor

 Using of non-linear intermediate capacitor

 Hybriid swiittched capaciittor Cuk convertter

 Soft-switching technique applying to the converter

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Course: Problems in circuit design Lecturer: Prof. Sam Ben-Yaakov Student: Alex Kushnerov Ben-Gurion University of the Negev 2006 Content ▪ Motivation for boost-buck converter topology ▪ Ćuk converter in Continuous Conduction Mode operation ▪ Critical inductors for Ćuk converter in Border Current Mode ▪ Ćuk converter in CCM with coupled inductors ▪ Zero-ripple technique for both input and output currents ▪ Ćuk converter in CCM with discrete transformer ▪ Leakage reducing in the isolating transformer ▪ Multi-output zero-ripple isolated Ćuk converter ▪ Single magnetic realization of multi-output Ćuk converter ▪ Augment of the leakage inductance in transformer ▪ Ćuk converter in Discontinuous Conduction Mode operation ▪ Three switched networks and inductor currents in DCM ▪ Derivation of the Voltage Transfer Function in DCM ▪ Equivalent inductance required for DCM ▪ Lossless resistor emulated by Ćuk DCM converter ▪ The design of the intermediate capacitor ▪ Using of non-linear intermediate capacitor ▪ Hybrid switched capacitor Ćuk converter ▪ Soft-switching technique applying to the converter Motivation for Boost-Buck converter topology ☺ A capacitor instead of an inductor is used for storing and transferring energy from input to the output. ☺ Energy transfer occurs during both on and off gated switch intervals. ☺ Operation is performed at almost zero ripple current at both the input and output. ☺ These characteristics make the Ćuk converter the closest to an ideal DC power supply of any topology Ćuk converter in Continuous Conduction Mode operation Boost : Vc = 1 Vin Doff   ⇒ Vout = − Don Buck : Vout Vc = − Don   Vin Doff Q Q is shorted : is broken : Vc Vc = = −Vout ⋅Ton Vin ⋅Toff    ⇒ Vout Vin = − Don Doff Critical inductors for Ćuk converter in Border Current Mode For 100% efficiency I out =− Doff Don ⋅ Iin IˆL1 = I in = I out ⋅ Don Doff I in min = IˆL1 − Vin L1cr ⋅ Ton 2 =0 I out min = I out − Vin Lc2r ⋅ Ton 2 =0 ( ) L1cr = Vin ⋅ 1 − Don 2 ⋅ I out ⋅ f Lc2r = Vin ⋅ Don 2 ⋅ I out ⋅ f Ćuk converter in CCM with coupled inductors Negative inductance condition Leq1 = L1 ⋅ 1− k 2 1− k ; Leq1 <0 if n 1 k   VL1 = L1 ⋅ di1 dt + M ⋅ di2 dt  VL2 = L2 ⋅ di2 dt + M ⋅ di1 dt n = w2 ≈ w1 L2 ; k = L1 Lm1 ⋅ Lm2 L1 ⋅ L2 For toroidal core: M = k n ⋅ L1 = k ⋅ n ⋅ L2 = Lm1 Lm2 Zero - ripple current at input : di1 = 0 → n = 1 dt k output : di2 = 0 → n = k dt Zero-ripple technique for both input and output currents For CCM mode : ∆U C1 = 8⋅ Vin ⋅ Don Lm1 ⋅ C1 ⋅ f 2 ⋅n1 ∆UC 2 = 8⋅ Vin ⋅ Don Lm2 ⋅ C2 ⋅ f 2 ⋅ n2 In the case of double core must be perfomed ratio n1 = 1 k1 ; n2 = k2 Ćuk converter in CCM with discrete transformer n′ = L2 ; n = w2 and inductors : L1 w1 Leq1 = L1 ⋅ 1− k 2 1− k ⋅n n′ ; Leq 2 = L2 ⋅ 1− k 1− k ⋅ 2 n′ n Zero - ripple current at input : k ⋅n n′ = 1 → Leq2 = L2 output : k ⋅ n′ n = 1 → Leq1 = L1 Both sides zero-ripple converter Reflection of the parameters to primary or secondary windings : Z ′ 2 = Z2 n2 ; Z1′ = n2 ⋅ Z1 • Capacitors C1 and C2 ensure that no DC voltage is applied to transformer primary or secondary windings • Transformer functions in conventional manner, with small magnetizing current and negligible energy storage within the magnetizing inductance Leakage reducing in the isolating transformer Zero - leakage inductance : Leq = L⋅1− k2 1− k n L ⋅ 1− k2 1−k ⋅n ⇒ n=k n= 1 k In the case of ready transformer an additional inductors should be included series to improve the compensation effect Multi-output zero-ripple isolated Ćuk converter Single magnetic realization of multi-output zero-ripple isolated Ćuk converter Augment of the leakage inductance in transformer by collinear windings E – storing energy I – current in entire turn N=2 – number of turns l = π·D – turn length Ls = 2⋅ E ⋅l I2⋅N LSpread legs = 7.4 LSame leg Ćuk converter in Discontinuous Conduction Mode operation Advantages ☺ Input current follows the input voltage (no current loop is needed) ☺ Ripple is defined by the correct choice of magnetic components ☺ Zero-Current turn-on in the switch and ZC turn-off in the diode ☺ Start-up and output short circuit currents are reduced ☺ Input-output galvanic isolation is easily obtained ☺ Theoretical power factor is unity Disadvantages High RMS current and voltage, which limits application range Inherent problems caused by an isolation transformer Three switched networks and inductor currents in DCM Derivation of the Voltage Transfer Function in DCM Average current in the secondary inductor S2 = S21 + S22 T2 = V1 V2 ⋅ T1 S1 − S2 = St − Ib ⋅(T −T3 ); Iˆ 2 = 1 T ⋅ (S1 − S2 − S3 ) Iˆ2 = Vˆ2 R = V1 2 ⋅ L2 ⋅ 1 + V1 V2  ⋅ T12 T − Ib Charge balance of the intermediate capacitor Q∑ = S1 − S2 + S3 = 0 ; S1 − S2 = Ib ⋅T − St S3 = Ib ⋅ (T − T1 )+ I pk1 2 ⋅T2 ; Le = L1 | | L2 Ib = V1 2 ⋅ L2 ⋅ T12 T ⋅ 1 − V1 V2 ⋅ L2 L1  ; Ke = 2 ⋅ Le R ⋅T ; V2 = − V1 D1 Ke Equivalent inductance required for DCM    Vo Vin Vo  Vin = − Don 1− Don = − Don Ke ; ; for CCM for DCM As result from both equations DCM condition : Ke(max) < (1− Don )2 It should be noticed that : ( ) M max +1= Don + 1 − Don 1− Don =1 1− Don For changing DC input voltage or in the case of arbitrary AC, M max occurs at minimum input ( ) Ke(max) < 1 M max +1 2 If a maximum load have place then conduction parameter is : K e (max ) = 2 ⋅ Le Rmin ⋅T ( ) Le(min) < Rmin ⋅T 2 ⋅ 1+ M max 2 Lossless resistor emulated by Ćuk DCM converter   Iˆ 1 = V1 2 ⋅ L1 ⋅ D1 ⋅T ⋅ (D1 + D2 )+ Ib   Iˆ 2 = V1 2 ⋅ L2 ⋅ D1 ⋅T ⋅ (D1 + D2 )− Ib Iˆ1 + Iˆ2 = V1 2 ⋅ Le ⋅ D1 ⋅T ⋅ (D1 + D2 ) For 100% efficiency Iˆ 1 = D1 D2 ⋅ Iˆ2 A surprising result is : Rem = viˆˆ11((tt)) = 2 ⋅ Le Do2n ⋅ f Input current waveforms for Ćuk converter For Flyback converter Rem = 2⋅L Do2n ⋅ f Input current waveforms for Flyback The design of the intermediate capacitor When Ćuk converter operates as a PFC, the capacitor voltage should be: ● Nearly constant value on a switching period ● Following the input alternating voltage profile The usual approach to practical design ■ Assume that switching voltage ripple on the C is about 20% of output voltage ■ With this capacitance of the C is very much smaller than output capacitor Co The resonant frequency approach ■ It is remarkable result by using the conventional formula: C = (2 ⋅ π ⋅ 1 f sw )2 ⋅ Leq ■ For isolated converter it is necessary to reflect one of the inductors to second ☺ Short circuit and in-rush currents during start-up are reduced about 30 times The transformer magnetizing inductance causes for additional resonance Using of non-linear intermediate capacitor The capacitance varies between C/2 and 2C by changing of the current direction. During T(off) the capacitors are connected in series. Thus, each capacitor is charged to the half of the applied voltage. During T(on) the energy that stored in the capacitors releases in parallel. In this way load voltage becomes half of the conventional circuit output. Hybrid switched capacitor Ćuk converter During T(off) the capacitors are connected in parallel. During T(on) the capacitors are discharged in series with load. By using a voltage balance : ( ) Vin ⋅ Don = Vc −Vin ⋅ Doff ( ) ( ) 2 ⋅Vc −Vout ⋅ Don = Vout −Vc ⋅ Doff Vout = 1+ Don Vin Doff Soft-switching technique applying to the converter ZVS in automatic current shaper with fast output regulation. The converter works in two completely new and decoupled DCM. ZVS Active-Clamping Class “D” Zero-Voltage Transition Passive Lossless Soft-Switching Simplest visual simulation with discrete inductors Comparative simulation for discrete and coupled inductors Comparative simulation for isolated converter Comparative simulation for non-linear capacitance REFERENCES: Polikarpov A., Sergienko E., Single-Ended Voltage Converters in Power Supplies (in Russian) Moscow: Radio and Communication, 1989. - 160 p. Erickson R. W., Maksimovic D., Fundamentals of Power Electronics New-York: Kluwer Academic Publishers, 2001. - 912 p. http://ece-www.colorado.edu/~pwrelect/book/solutions/prob5p6.pdf Bryant B., Kazimierczuk M., Derivation of the Ćuk PWM DC-DC converter circuit topology Ćuk S., A New Zero-Ripple Switching DC-to-DC Converter and Integrated Magnetics Patent US4327348 Hirayama H., Variable leakage transformer Patent SU1277315 Polikarpov A., Sergienko E., Transformer for voltage converters Brkovic M., Ćuk S., Input current shaper using Ćuk converter Patent US5442539 Ćuk S., Brkovic M., Ćuk DC-to-DC switching converter with input current shaping for unity power factor operation Takahashi I., Sato T., Takeda M., Applications of Nonlinear Impedance Circuit Composed of Diodes and Capacitors or Inductors Axelrod B., Berkovich Y., Ioinovici A., Hybrid Switched - Capacitor Ćuk / ZETA / SEPIC Converters in Step-Up Mode IEEE International Symposium on Circuits and Systems, (ISCAS) 2005, Vol. 2, pp.1310 - 1313 Brkovic M., Ćuk S., Automatic current shaper with fast output regulation and soft switching Smith K.M., Smedley K., Properties and Synthesis of Passive Lossless Soft-Switching PWM Converters IEEE Transactions on Power Electronics, Vol. 14, No5, Sep. 1999 Costa D., Duarte C., The ZVS-PWM Active-Clamping CUK Converter IEEE Transactions on Industrial Electronics, Vol. 51, No1, Feb. 2004

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