摘要
功因校正電路主要可分被動式與主動式，被動式使用電感、電容組合成濾波電路，改善輸入電流波形與相角；主動式功因校正係利用電力轉換器加入在整流級與穩壓級中間，以獲得良好功率因數，相較於被動式功因校正，主動式具有體積小、重量輕、效率高等優點。
某些電力轉換器操作在不連續導通模式，天生就具有功因校正能力，無須設計功因校正控制器。本文中，首先探討基本電力轉換器之功因校正能力，利用輸入電壓/平均電流之輸入特性曲線與LFR (Loss-Free Resistor)兩種方法，分別分析基本電力轉換器功因校正能力，由分析可知zeta電力轉換器，在三種操作模式1.DCMLm>Lo 2.DCMLm<Lo 3.DCMLm<<Lo，皆具有優良功因校正能力(PF=1)。在不改變電路的動作情形下，為了電氣隔離與開關驅動容易，可將zeta電力轉換器修改成隔離式，並將浮接開關改為接地開關。
吾人針對隔離式zeta電力轉換器操作在DCMLm>Lo模式下，利用線電壓週期 輸入平均電流與輸出平均電流，畫出小訊號等效電路，推導其小訊號數學模式，並使用頻譜分析儀與模擬軟體IsSpice，以驗證模式推導之正確性。最後根據所推導之數學模式來設計古典控制器，由實作結果顯示，加入控制器能抵抗負載變動，達到穩壓的效果，並維持原有的功因校正能力(PF=1)。

Abstract
The power factor correction (PFC) circuits are primarily divided into passive and active types. For the passive type, a filter composed of inductor and capacitor is used to improve the phase lag of the input current. On the other hand, a power converter is added between the rectifier and the voltage regulation stage to achieve a good power factor for the active type. In comparison with the two types of PFC circuits, the active PFC circuit exhibits the advantages of small volume, light weight and high efficiency.
Some power converters, operating in discontinuous conduction mode, has the gift of PFC without any controller. First of all, the PFC capabilities of the basic power converters are discussed in this thesis. Two approaches, including the characteristic curve plotting of input voltage/averaging current and LFR (Loss-Free Resistor), are applied to analyze the PFC capabilities for these basic power converters. Among them, it is worthy to note that the zeta power converter, operating in three modes of DCMLm>Lo, DCMLm<Lo and DCMLm<<Lo, are all verified to have excellent PFC with PF=1. In addition, for the sake of electrical isolation and easily switch driving, the zeta power converter is modified into an isolated mode with a grounded switch without effecting the operation of the converter.
By perturbation of the averaged input/output current under the period of line voltageTL, a small-signal model is derived for the proposed isolated zeta power converter operating in DCMLm>Lo mode. Then the equivalent circuit related to the derived small-signal model can be obtained. In addition, the proposed model is also verified by the measurements of spectral analyser and simulation results of IsSpice. Finally, a PI controller is designed for the derived model. It is shown from the experimental results that the variations of load are insensitive to the closed-loop system, and excellent voltage regulation can also be exhibited. The PFC capability with unity power factor of the converter can still be maintained.

參考文獻
[DSU93] Dos Reis, F. S., J. Sebastian and J. Uceda, “Characterization of Conduction Noise Generation for Sepic, Cuk and Boost Converters Working as Power Factor Preregulators,” IEEE IECON, pp. 965-970, 1993.
[Eri97] Erickson, R. W., Fundamentals of Power Electronics, Kluwer Academic Publishers, 1997.
[GeL96] Gegner, J. R. and C. Q. Lee, “Linear Peak Current Mode Control: A Simple Active Power Factor Correction Control Technique for Continuous Conduction Mode,” IEEE PESC, pp. 196-202, 1996.
[HeM86] Henze, C. P. and N. Mohan, “A Digitally Controlled AC to DC Power Conditioner that Draws Sinusoidal Input Current”, IEEE PESC, pp. 531-540, 1986.
[HLC92] Huliehel, F. A., F. C. Lee and B. H. Cho, “Small-Signal Modeling of Single-Phase Boost High Power Factor Converter with Constant Frequency Control,” IEEE PESC, pp. 475-482, 1992.
[HuJ97] Huber, L. and M. M. Jovanovic, “Single-Stage, Single-Switch Isolated Power Supply Technique with Input-Current Shaping and Fast Output-Voltage Regulation for Universal Input-Voltage-Range Applications,” IEEE APEC, pp. 272-280, 1997.
[JTL94] Jovanovic, M. M., D. M. Tsang and F. C. Lee, “Reduction of Voltage Stress in Integrated High-Quality Rectifier-Regulators by Variable Frequency Control,” IEEE APEC, pp. 569-575, 1994.
[KRS91] Kislovski, A. S., R. Redl and N. O. Sokal, Dynamic Analysis of Switching-Mode DC/DC Converters,Van Nostrand Reinhold, 1991.
[KSV91] Kassakian, J. G., M. F. Schlecht and G. C. Verghese, Principles of Power Electronics, Addison Wesley, 1991.
[LeC98] Lee, K. C. and B. H. Cho, “Design of the Loop for Single Controller Power Factor Correction Converter,” IEEE PESC, pp. 889-904, 1998.
[LiL00] Lin, J. L. and Z. H. Liu, Modeling and Controller Design for Single-Stage Isolated High Power Factor Converters, NCKU Master Thesis, 2000.
[LiT01] Lin, J. L. and T. H. Tsai, Modelimg for Single-Stage Isolated High Power Factor Converters with Magnetic Switch, NCKU Master Thesis, 2001.
[LiY00] Lin, J. L. and C. H. Yu, Modeling and Controller Design for Zero-Voltage-Transition Soft-Switching of Active High Power Factor Correction, NCKU Master Thesis, 2000.
[MEI92] Madigan, M., R. Erickson and E. Ismail, “Integrated High-Quality Rectifier-Regulators,” IEEE PESC, pp. 1043-1051, 1992.
[MJE95] Maksimovic, D., Y. Jang and R. Erickson, “Nonlinear-Carrier Control for High Power Factor Boost Rectifiers,” IEEE APEC, pp. 635-641, 1995.
[MUF84] Mohan, N. T., M. Undeland and R. J. Ferraro, “Sinusoidal Line Current Rectification with a 100 kHz B-SIT Step-Up Converter,” IEEE APEC, pp. 92-98, 1984.
[QiL96] Qian, J. and F. C. Lee, “A Novel Single Stage High Power Factor Rectifier with a Coupling Inductor,” VPEC Seminar, pp. 1-7, 1996.
[QZL97] Qian, J., Q. Zhao and F. C. Lee, “Single-Stage Single-Switch Power Factor Correction (S4-PFC) AC/DC Converters with DC Bus Voltage Feedback for Universal Line Applications,” VPEC Seminar, pp. 29-35, 1997.
[RaU99] Ranganathan, G. and L. Umanand “Power Factor Improvement Using DCM Cuk Converter with Coupled Inductor,” IEE Proceedings, part B, Electric Power Application , Vol. 146, No. 2, pp. 231-236, March 1999.
[RBS94] Redl, R., L. Balogh and N. O. Sokal, “A New Family of Single-Stage Isolated Power-Factor Corrector with Fast Regulation of the Output Voltage,” IEEE PESC, pp. 1137-1144, 1994.
[ReE94] Redl, R. and B. P. Erisman, “Reducing Distortion in Peak-Current-Controlled Boost Power-Factor Corrector,” IEEE PESC, pp. 576-583, 1994.
[RLN97] Rajagopalan, J., F. C. Lee and P. Nora, “A Generalized Technique for Derivation of Average Current Mode Control Laws for Power Factor Correction without Input Voltage Sensing,” IEEE APEC, pp. 81-87, 1997.
[ScC97] Schenk, K. and S. Cuk “A Single-Switch Active Power Factor Corrector with High Quality Input and Output Line,” IEEE APEC, pp. 234-241, 1980.
[SCGU92] Sebastian, J., J. A. Cobos, P. Gil and J. Uceda, “The Determination of the Boundaries between Continuous and Discontinuous Conduction Modes in PWM DC-to-DC Converters Used as Power Factor Prepegulators,” IEEE PESC, pp. 1061-1070, 1992.
[Sch80] Schlecht, M. F., “A Line Interfaced Inverter with Active Control of the Output Current Waveform,” IEEE APEC, pp. 234-241, 1980.
[SiE92] Singer, S. and R. W. Erickson, “Canonical Modeling of Power Processing Circuits Based on the POPI Concept”, IEEE Transactions on Power Electronics, Vol. 7, No. 1, pp. 37-43, January 1992
[SSU97] Simonetti, D. S. L., J. Sebastian and J. Uceda, “The Discontinuous Conduction Mode Sepic and Cuk Power Factor Preregulators: Analysis and Design,” IEEE Trans. on Industrial Electronics, Vol. 44, No. 5, pp. 630-637, 1997.
[SuG92] Sun, J. and H. Grotstollen, “Averaged Modeling of Switching Power Converters: Reformulation and Theoretical Basis,” IEEE PESC, pp. 1162-1172, 1992.
[SuG93] Sun, J. and H. Grotstollen, “Averaged Modeling and Analysis of Resonant Converters,” IEEE PESC, pp. 707-713, 1993.
[TMW96] Tsai, F., P. Markowski and E. Whitcomb, “Off-Line Flyback Converter with Input Harmonic Correction,” IEEE INTELEC, pp. 120-124, 1996.
[WeB98] Wei, H. and I. Batarseh, “Comparison of Basic Converter Topologies for Power Factor Correction,” IEEE PESC, pp. 348-353, 1998.
[WuC99] Wu, T. F. and Y. K. Chen, “Modeling of Single-Stage Converter with High Power Factor and Fast Regulation,” IEEE PESC, pp. 585-593, 1999.
[鄭99] 鄭培璿，IsSpice在電力電子與電子轉換器上的應用，全華科技圖書股份有限公司，1999年9月初版。