本論文利用能量守恆定理推導交錯式功率因數修正器(interleave power factor correctors)之等效電路模型,所推導的模型包括開路交錯式功率因數修正器的小訊號等效電路以及含寄生元件效應之小訊號轉移函數。此外,本論文亦推導包括漣波電壓、輸出阻抗、輸入阻抗與聲頻感受度等常用轉移函數公式。 由於交錯式功率因數修正器主要架構由兩個昇壓型轉換器(boost converter)並接組成,此兩個主電路架構間元件值的不同將影響以上所述模型與公式的複雜度,因此本論文將討論各模組的元件特性均一時,建立系統的模式。根據能量守恆定理,分別將各個元件上的等效阻抗求出,進而得到整個電路的小訊號電路,再使用反射定理(reflection rules),將所有元件的等效平均電阻等效成ㄧ個電阻以方便電路分析。為了得到交錯式功率因數修正器電路的小訊號電路,因此使用電路分析技巧,將兩個昇壓型電路的主架構簡化成單一小訊號電路,進而求出簡化電路的小訊號模型。利用此模型便可推導輸出阻抗、輸入阻抗與聲頻感受度等轉移函數公式。 最後,本論文將分別使用Matlab與電路模擬軟體Ispice來模擬交錯式功率因數修正器的輸出阻抗、輸入阻抗與聲頻感受度等轉移函數的頻率響應,並且求出所推導出的漣波性能指標,以驗證所推導的模型與性能公式的正確性。
In this thesis, by means of the principle of energy conservation, the small-signal transfer functions of interleave boost power factor correctors (PFC) are derived. The transfer functions include the open-loop transfer function of interleave PFC and the transfer function of small-signal circuit with parasitic elements. Also, the output ripple voltage, output impedance, input impedance, and audio-susceptibility are considered. Because the interleave PFC is composed of two paralleled boost converter, to derive the model of the circuit, it is assumed that the characteristics of two boost converters are the same to reduce the complication of the circuit. According to the principle of energy conservation, equivalent averaged resistances of circuitry components are firstly calculated. Using the reflection rules, all equivalent resistances can be integrated into a lumped resistance. Consequently, the small-signal models of the paralleled boost converters can be obtained and the whole model can be conducted by means of circuit analysis techniques. From derived the model, transfer functions of output impedance, input impedance, and audio-susceptibility are obtained. Finally, Matlab and Ispice are used respectively to simulate the frequency responses of the derived transfer functions of interleave PFC. The simulation results indicate that the derived model and formula are correct.
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