buck-boost变换器的建模与仿真

题目：Vg1.5VQ135mΩ100uH100uFR5ΩVD0.5V图1buck-boost变换器电路图一、开关模型的建模与仿真图2buck-boost变换器的开关模型01234567占空比由0.806变化到0.7的电感电流波形00.0050.010.0150.020.0250.030.0350.040.0450.05-10123456占空比由0.806变化到0.7的电容电压波形图3buck-boost变换器的开关模型的仿真二、大信号模型与仿真1、开关导通时：Vg1.5VRon35mΩ100uH100uFViciig+-图4开关导通时的工作状态此时，电感电压和电容电流方程：(t)v(t)v(t)(t)(t)(t)(t)LgoncdiLiRdtdvviCdtR2、开关断开时：100uH100uFVic+-0.5Vi图5开关断开时的工作状态此时，电感电压和电容电流方程：(t)v(t)(t)(t)(t)(t)(t)LDcdiLVvdtdvviCidtR3、平均方程电源电压、电感电流、电容电压变化的不大均为低频信号，则(t)(t)ggvv；(t)(t)ii；v(t)v(t)又因为：(t)v(t)LdiLdt(t)(t)cdviCdt则有，电感电压平均方程：'v(t)d(t)v(t)(t)+d(t)(t)LgonDiRVv电容电流平均方程：''(t)(t)(t)(t)d(t)()d(t)((t))=d(t)(t)cvvviiiRRR输入电流平均方程：g(t)d(t)(t)ii4、大信号模型：''g(t)d(t)v(t)(t)+d(t)(t)d(t)(t)=d(t)(t)(t)d(t)(t)gonDdiLiRVvdtvvCidtRii由方程可得到三个等效电路：-+-+-+g(t)iv(t)g(t)vD(t)i'D(t)id(t)vCdt(t)diLdt'(0.5D)VonDR'(t)Dvv(t)gD图6buck-boost变换器的大信号模型的等效电路大信号模型的仿真电路：图7大信号模型仿真电路图大信号模型的仿真波形：0.650.70.750.80.850.9占空比随时间变化的波形-6-4-202468电感电流随占空比变化的波形00.0050.010.0150.020.0250.030.0350.040.0450.05-20246电容电压随占空比变化的波形图8大信号模型仿真波形图三、小信号模型假设，gv(t)=V+v(t)d(t)=D+d(t)(t)=(t)v(t)=V+v(t)(t)=(t)gggggiIiiIi且各变量的扰动值远小于其稳态值。则，对大信号模型在静态工作点处施加扰动并线性化：''(t)D+d(t)V+v(t)(t)+Dd(t)Vv(t)dV+v(t)V+v(t)=Dd(t)(t)(t)D+d(t)(t)ggonDggdIiLIiRVdtCIidtRIiIi整理得到小信号模型：''(t)Dv(t)(t)Dv(t)+Vd(t)dv(t)1=v(t)D(t)d(t)(t)D(t)+d(t)gongDongdiLDRiVVIRdtCiIdtRiiI小信号模型的等效电路图：-+-+-+onDR(t)diLdtdv(t)Cdt+Vd(t)gDonVVIRDv(t)g'Dv(t)d(t)I'D(t)id(t)ID(t)i(t)giv(t)gv(t)-+onDR(t)diLdtdv(t)Cdt+Vd(t)gDonVVIRd(t)I'D(t)id(t)I(t)giv(t)gv(t)D’:11:D