大学电路理论课程教案-线性直流电路7

3.13Y-电阻网络的等效变换回顾：单口网络的相互等效如果两个单口网络的端口伏安关系相同，则它们对外界所产生的作用和影响也是相同的。称这两个单口网络相互等效。不含独立源双口网络的相互等效如果两个不含独立源双口网络的端口伏安关系相同，则它们对外界所产生的作用和影响也是相同的。称这两个双口网络相互等效。伏安关系相同，即双口网络参数相同双口网络参数方程相同Y形电阻网络和形电阻网络R1R2R3r12r13r23112233R1R2R3r12r13r23112233R1R2R3r12r13r23112233+u1+u2+u1+u2R参数：323321RRRRRRG参数323321RRRRRR-1231212121213ggggggG参数=323321RRRRRR-1231212121213gggggg=323321RRRRRR231212121213gggggg=10013212112RRRRRr1323223RRRRRr2131331RRRRRr31231231121rrrrrR31231223122rrrrrR31231231233rrrrrR等效条件•如果：rrrr312312YRRRR321则：YRr3rRY31R3R1R2R5R4R3R1R2R5R4r13r35r15例：R3R1R2R5R4r13r35r15R2R4r13r35r15不含独立源的互易双口网络N+u1—i1+u2—i2N+u1-i1+u2-i2+u2+u1i1i2由两端电阻构成例：：nnnnnnRRRRRRRRR212222111211niii210021uu=网孔法KVL：解的形式:2121111uui2221212uui因不含受控源，系数矩阵对称nnnnnRRRRuRRu22222112100nnnnnnRRRRRRRRR212222111211niii210021uu=nnnnnRRRuRRuR0012221111111i212111uu11i222121uunnnnnRRRRuRRu2222211210011i212111uunnnnnnRRRRRRRRRRR324342333321131212nnnnnRRRRuRRu22222112100nnnnnRRRuRRuR0012221111112i222121uunnnnnnnRRRRRRRRRRRR3144341333312232121nnnnnRRRuRRuR00122211111nnnnnnRRRRRRRRRRR324342333321131212nnnnnnnRRRRRRRRRRRR314434133331223211221121111G1212G2121G2222G2112GG回顾：互易定理（P64）•对于只含二端线性电阻的双口网络N+u1—i1+u2—i2作如下图两种形式的连接：NUSi1i2+I’NUSi1+I’’i2则I’=I’’•回顾：双口网络的G参数方程NUSi1i2+I’NUSi1+I’’i2I’=I’’2221212uGuGi2121111uGuGi(a)(b)对图(a)SUGIi212对图(b)SUGIi121因此：2112GG回顾：互易定理（P64）•对于只含二端线性电阻的双口网络N+u1—i1+u2—i2作如下图两种形式的连接：NISi1i2+U’NISi1+U’’i2则U’=U’’•回顾：双口网络的R参数方程(a)(b)对图(a)SIRUu212对图(b)SIRUu121因此：2112RRNISi1i2+U’NISi1+U’’i2U’=U’’2121111iRiRu2221212iRiRu•回顾：H参数意义1111iuH2112uuH1221iiH2222uiR02u02u01i01i2221212uGuGi2121111uGuGiG参数方程2112uuH01i1112GG1221iiH02u1121GG2112HH回顾：A参数意义：2111uuA2112iuA2121uiA2122iiA02i02i02u02u2121111iRiRu2221212iRiRuR参数方程2121uiA02i211R2111uuA02i2111RR2122iiA02u2122RR2112iuA02u2121122211RRRRR2111uuA02i2121uiA02i211R2111RR2122iiA02u2122RR2112iuA02u2121122211RRRRR22212112221121221121122211RRRRRRRRAAAA2112RR因：2112RR所以：121122211AAAA定理•对于互易的双口网络，下列关系成立：2112GG2112RR2112HH121122211AAAA•满足下列关系的的双口网络，是互易网络2112GG2112RR2112HH121122211AAAA*只含二端线性电阻的双口网络，是互易网络*由二端线性电阻和受控源构成的双口网络，可能是互易网络。但一般不是互易网络。不含独立源双口网络的等效电路+u1-i1+u2-G21u1i2G12u1G11G22G参数等效电路R参数等效电路H参数等效电路+u1-i1+u2-R21i1i2R12i2R11R22+-+-+u1-i1H12u2H11+-+u2-H21i1i2H22不含独立源双口网络的等效电路R参数方程2121111iRiRu2221212iRiRu2121121121111iRiRiRiRu)()(211211211iiRiRR2122221121212121122iRiRiRiRiRiRu21222112212112)()()(iRRiRRiiR)()(2112112111iiRiRRu212221122121122)()()(iRRiRRiiRu+u1-+u2-i1i21211RRR121222RR+11221)(iRR+u1-+u2-i1i21211RRR121222RR对互易网络：不含独立源双口网络的等效电路•G参数方程2221212uGuGi2121111uGuGi))(()(2112112111uuGuGGi212221122112122)()())((uGGuGGuuGi+u1-+u2-i1i21211GG-G121222GG11221)(uGG+u1-i11211GG-G121222GG+u2-i2对互易网络：