电路分析基础第二章(李瀚荪)

uS1uS2R1R2R3ba+–+–i2il1il2推广到l个回路其中Rjk:互电阻+:流过互阻两个回路电流方向相同-:流过互阻两个回路电流方向相反0:无关R11il1+R12il1+…+R1lill=uSl1…R21il1+R22il1+…+R2lill=uSl2Rl1il1+Rl2il1+…+Rllill=uSllRkk:自电阻(为正),k=1,2,,l网孔电流法:对平面电路,若以网孔为独立回路,此时回路电流也称为网孔电流,对应的分析方法称为网孔电流法。例1用回路法求各支路电流。解(1)设独立回路电流(顺时针)(2)列KVL方程(R1+R2)Ia-R2Ib=US1-US2-R2Ia+(R2+R3)Ib-R3Ic=US2-R3Ib+(R3+R4)Ic=-US4对称阵,且互电阻为负(3)求解回路电流方程,得Ia,Ib,Ic(4)求各支路电流:I1=IaIaIcIb+_US2+_US1I1I2I3R1R2R3+_US4R4I4(5)校核选一新回路U==E?,I2=Ib-Ia,I3=Ic-Ib,I4=-Ic_+Ui_+_US1US2R1R2R5R3R4IS+I1I2I3①将看VCVS作独立源建立方程;4Ia-3Ib=2-3Ia+6Ib-Ic=-3U2-Ib+3Ic=3U2①②找出控制量和回路电流关系。U2=3(Ib-Ia)②例2用回路法求含有受控电压源电路的各支路电流。4Ia-3Ib=2-12Ia+15Ib-Ic=09Ia-10Ib+3Ic=0③将②代入①,得各支路电流为:Ia=1.19AIb=0.92AIc=-0.51A解得*由于含受控源,方程的系数矩阵一般不对称。I1=Ia=1.19A,I2=Ia-Ib=0.27A,I3=Ib=0.92AI4=Ib-Ic=1.43A,I5=Ic=-0.52A+_2V3U2++3U2–1212I1I2I3I4I5IaIbIc