第7讲电路的定理(CircuitTheorems)1叠加定理重点2戴维南定理和诺顿定理重点3替代定理1叠加定理(SuperpositionTheorem)i1由回路法其中R11=R1+R2R=R=-RR1R2R3Ri+Ri=u12212i11a12bs11+a+ib+R22=R2+R3R21ia+R22ib=us22u=u-uus1us2us3s11s1s2–––us22=us2-us3u-uR11R12uRs1s2u-u∆=s1112s2s3RRuRR−R2122i=s2222=22u+12uas11s22=R11R22−R12R21R11R12∆∆R21R22RR+RR=22u−1222u+12u∆s1∆s2∆s3PrinciplesofElectricCircuitsLecture7TsinghuaUniversity20051i11i12i13R1R2R3R1R2R3R1R2R3iiii+a1b1a2+ib2a3ib3+us1us2us3–––uS2和uS3不作用uS1和uS3不作用uS1和uS2不作用R11ia2+R12ib2=-us2R11ia3+R12ib3=0R11ia1+R12ib1=us1Ri+Ri=uRi+Ri=-uRi+Ri=021a222b2s221a322b3s321a122b10R−us2R1212us1R12uR−us3R22s222i=0R22ia2=a3i=RRR11R12a1RR11121112RRR21R222122R21R22R−RR122212=−(−u)R22=(−us2)+us2s3=us1∆∆∆∆RR12+R2212=−u=us3∆s2∆us11R12us22R22R22−R12R22R12+R22R12ia==us11+us22=us1−us2+us3R11R12∆∆∆∆∆R21R22ia=ia1+ia2+ia30R12us1R12−us2R12−us3R220R22us2R22ia3=ia1=ia2=R11R12R11R12R11R12R21R22R21R22R21R22R12R22R22−R12=u=(−u)+u=−(−us3)∆s1∆s2∆s2∆RR12+R2212=−u=us3∆s2∆PrinciplesofElectricCircuitsLecture7TsinghuaUniversity20052i1R1R2R3i+a+ib+us1us2us3–––ia=ia1+ia2+ia3i11i12i13R1R2R3R1R2R3R1R2R3iiii+a1b1a2+ib2a3ib3+us1us2us3–––uS2和uS3不作用uS1和uS3不作用uS1和uS2不作用3个独立电源作用的效果与单个独立电源作用的效果之和相同PrinciplesofElectricCircuitsLecture7TsinghuaUniversity2005叠加定理在线性电路中，任一支路电流(或电压)都是电路中各个独立电源单独作用时，在该支路产生的电流(或电压)的代数和。单独作用：一个电源作用，其余电源不作用。电压源（us=0)短路不作用电流源(is=0)开路PrinciplesofElectricCircuitsLecture7TsinghuaUniversity20053推广到l个回路,第j个回路的回路电流：第j列R11il1+R12il1+…+R1lill=uS11R11Lus11LR1lR21il1+R22il1+…+R2lill=uS22…MMMMMRl1il1+Rl2il1+…+Rllill=uSllRj1LusjjLRjlMMMMMRuR代数余子式i=l1LsllLlllj∆∆∆∆∆=1ju+2ju++jju++lju∆s11∆s22L∆sjjL∆sll电压源（us=0)短路不作用电流源(is=0)开路PrinciplesofElectricCircuitsLecture7TsinghuaUniversity2005∆∆∆∆i=1ju+2ju++jju++ljulj∆s11∆s22L∆sjjL∆sll第l个回路电压源的电压升第b条支路上电把usi的系数合并为Gjius1Lusb压源的电压b第i个电压源单独作用时在us1-us2i=Guus11R12u-ulj∑jisi第j个回路中产生的回路电流s2s3