大学电路理论课程教案-线性直流电路6

3.10不含独立源的单口网络不含独立源的单口网络N+U—I3.10不含独立源的单口网络不含独立源的单口网络N+U—IR=U/I+U••对于有唯一解的线性电路,各独立源一致增大（或缩小）K倍，则任一支路电压或电流,也相应地增大（或缩小）K倍。回顾--齐次定理：称端口等效电阻比例系数：3.10不含独立源的单口网络不含独立源的单口网络N+U—IU=RI+U—IR等效电路例3.11R1R5R2R3R4)]//([R32451eRRRRRqqeR例：R1R5R2R3R4R6R7qeR例：R1R5R2R3R4R6R7+IUII2I3R1+R2+R3+R5-R2-R3IU-R2R2+R4+R6–R4I20-R3-R4R3+R4+R7I30=R=U/I•例2.12+-rI1ßI2I1I2R1R1R3qeR•例2.12+-rI1ßI2I1I2R2R1R3I+U+U2G1+G2-G1UI-G1G1+G3U2rI1G3-ßI2=U-U2=I1R1U=I2R2rRRRRrRRIUq321331e)1()(R3.11含独立源的单口网络•含独立源的单口网络N+u—iABi•含独立源的单口网络Req+-uocN+u—iABiN+—iABi=0NiABiu’u=uoc+u’=uoc-Reqi3.11含独立源的单口网络•含独立源的单口网络Req-ui+-uoc+ABN+u—iABu=uoc-Reqi含独立源的单口网络•Thevenin定理:–任一含独立源的单口网络,可以等效为一个独立电压源和一个电阻串联电路。独立电压源的电压等于该单口网络的开路电压；串联电阻等于该单口网络内部的各独立电源置零后的端口等效电阻。•例：R2R1+-+-e1i2ABuiR2R1+-+-e1i2ABui。。Req=R1//R2•例：R2R1+-+-e1i2ABuiR2R1+-e1i2ABuoci=0R1uoc(1/R1+1/R2)=e1/R1+i2uoc=e1+i2R2R1R2R1+R2R1+R2KCL：含独立源的单口网络•Norton定理:–任一含独立源的单口网络,可以等效为一个独立电流源和一个电阻并联电路。独立电流源的电流等于该单口网络的短路电流；并联电路等于该单口网络内部的各独立电源置零后的端口等效电阻。含独立源的单口网络•含独立源的单口网络iiscR+-uR-ui+-+ABABN+u—iuociiscR+-uR-ui+-+ABABuocRiuscocRuiocscsciocuNorton定理•例：R2R1+-+-e1i2ABuiR2R1+-e1i2ABii3iscNorton例.R2R1+-e1i2ABii3R2R1+-e1i2ABiai3R2R1+-e1i2ABibi3isc=ia+ib=e1/R1+i2含独立源的单口网络•含独立源的单口网络iiscR+-uR-ui+-uoc+ABABN+u—i等效电源之间的转换•转换关系iiscR+-uocR-ui+-uoc+ABABuoc=Riscisc=R/uocR=uoc/iscisc3.12不含独立源双口网络N+u1—i1+u2—i2N+u1-i1+u2-i2+u2+u1i1i2nnnnnnRRRRRRRRR212222111211niii210021uu=网孔法KVL：解的形式:2121111uui2221212uui记：2121111uui2221212uui1111G1212G2121G2222G2221212uGuGi2121111uGuGi这是双口网络自身固有的参数，与外界的激励无关双口网络的端口伏安关系•G参数的物理意义2221212uGuGi2121111uGuGiN+u1—i1+u2—i21111uiG2112uiG1221uiG2222uiG02u02u01u01u•G11参数的物理意义N+u1—i1+u2—i21111uiG02u=0G11端口2短路时，端口1的等效电导•G22参数的物理意义N+u1—i1+u2—i22222uiG01u=0G22端口1短路时，端口2的等效电导•G21参数的物理意义N+u1—i1+u2—i21221uiG02u=0端口2短路时，两端口间的转移电导•G12参数的物理意义N+u1—i1+u2—i22112uiG01u=0端口1短路时，两端口间的转移电导1、G参数方程及等效电路N+u1—i1+u2—i2i1G11G12u1i2G21G22u2=+u1-i1+u2-G11u1i2G11u1G11G222221212uGuGi2121111uGuGi•例：图3.52(P35)g12g31g23123已知:g12,g12,g12求:G参数g12g31g23123方法一：根据定义求1111uiG02uG113112ggg31g23123G222222uiG01u2312ggg12g12g31g23123+u11221uiG02ui212gg31g23123i1g12+u22112uiG01u12g方法二：列G参数方程g12g31g23123+u2+i2i1u1231212123112gggggg21uu21ii=2221212uGuGi2121111uGuGi22211211GGGG21ii21uu=21ii21uu22211211RRRR=2121111iRiRu2221212iRiRu22211211GGGG22211211RRRR=-1R参数的物理意义21ii21uu22211211RRRR=2121111iRiRu2221212iRiRu1111iuR2112iuR1221iuR2222iuR02i02i01i01i•R11参数的物理意义N+u1—i1+u2—i2=0R11端口2开路时，端口1的等效电阻1111iuR02i•R22参数的物理意义N+u1—i1+u2—i22222iuR01i=0R22端口1开路时，端口2的等效电阻•R21参数的物理意义N+u1—i1+u2—i2=0端口2开路时，两端口间的转移电阻1221iuR02i•R12参数的物理意义N+u1—i1+u2—i22112iuR01i=0端口1开路时，两端口间的转移电阻不含独立源双口网络2、R参数方程及等效电路N+u1—i1+u2—i2+u1-i1+u2-R21i1i2R12i2R11R22+-+-21ii21uu22211211RRRR=2121111iRiRu2221212iRiRu•例3.15（P73）+u2+i1u111216I3I3求：R参数方法一：根据定义求++u111216I3I3i1I3411231Ii316Iu=R11=1.91111iuR02i1221iuR02ii1++u111216I3I3i1I3411231Ii316Iu=+u23321IIu13101iI1221iuR02i=0.1i2++u211216I3I3I’i22222iuR01i11142iI236uI=IiI232222iuR01i=0.32112iuR01ii2++u211216I3I3I’i211142iI236uI=IiI23+u1IIu112107iI2112iuR01i=0.7•例3.15（P73）+u2+i2i1u111216I3I31126I3I31i1i-i211014101221iii2316uIu=23iiI11014101221iii2316uIu=23iiI3.01.07.09.121ii21uu=2221212uGuGi2121111uGuGi22211211GGGG21ii21uu=21ui21iu22211211HHHH=2121111uHiHu2221212uHiHiH参数的物理意义1111iuH2112uuH1221iiH2222uiR02u02u01i01i22211211HHHH=2121111uRiHu2221212uHiHi21iu21ui•H11参数的物理意义N+u1—i1+u2—i2=0H11端口2短路时，端口1的等效电阻1111iuH02u•H22参数的物理意义N+u1—i1+u2—i22222uiH01i=0H22端口1开路时，端口2的等效电导•H21参数的物理意义N+u1—i1+u2—i21221iiH02u=0端口2短路时，两端口的电流比•H12参数的物理意义N+u1—i1+u2—i22112uuH01i=0端口1开路时，两端口的电压比不含独立源双口网络3、H参数方程及等效电路N+u1—i1+u2—i2+u1-i1H12u2H11+-+u2-H21i1i2H2222211211HHHH=2121111uHiHu2221212uHiHi21iu21ui不含独立源双口网络3、A参数方程N+u1—i1+u2—i222211211AAAA=)(2122111iAuAu)(2221211iAuAi11iu22iu2111uuA2112iuA2121uiA2122iiA02i02i02u02u不含独立源双口网络4、其他参数方程N+u1—i1+u2—i222211211HHHH=21ui21iu22211211AAAA=22iu11iu•例3.16求A参数G1βIG2i1i2I+u2+u1G1βIG2i1i2I+u2+u1021iIIi2221)1(iuGi22uGIKCL:VA:G1βIG2i1i2I+u2+u1KVL：01)(2121uGiIu2121211)1(iGuGGu22uGIVA：2221)1(iuGi1)1(112112GGGGA：