第16章 b 二端口网络

BACKNEXT3端口1电源有内阻，端口2接负载US(S)NU1(S)U2(S)I1(S)I2(S)R+-R1已知Z参数求)()()(2SUSUSHS)()()(2SUSUSHS)()()()()()()()()()(22212122121111SISZSISZSUSISZSISZSU)()()(111SIRSUSUSRSISU)()(22)()())())((()(21122211121SZSZSZRSZRRSZ二端口的转移函数不仅和二端口参数有关而且和端接阻抗有关BACKNEXT§16-5二端口网络的联接一、级联（链联）设22211211][TTTTTT+T+1I1U2U2I+1UT+1I2I2U+1I1U+2U2I22211211][TTTTT222221121111IUTTTTIU222221121111IUTTTTIUBACKNEXTT+T+1I1U2U2I+1UT+1I2I2U+1I1U+2U2I得222221121111IUTTTTIU222221121122211211IUTTTTTTTTTT+2U2IT+1I1U+2U2I2I22IUBACKNEXT得结论：级联后所得复合二端口T参数矩阵等于级联的二端口T参数矩阵相乘。上述结论可推广到n个二端口级联的关系。22222112112221121111IUTTTTTTTTIUTTTT1T2......TnT=[T1][T2]….[Tn]BACKNEXT例10Ω411T1S25.0012T10Ω613T4644T12.5S0.25Ω1621061125.0011041][][][][321TTTT46T3T222222112122111ITUTIITUTUBACKNEXT二、并联：输入端口并联，输出端口并联212221121121UUYYYYII212221121121UUYYYYII+1I1U+2U2IY++1I1U2U2IY++2U1U2I1IY正规联接时：BACKNEXT212121IIIIII+1I1U+2U2IY++1I1U2U2IY++2U1U2I1IY21222112112122211211UUYYYYUUYYYY21212211121121][UUYUUYYYYIIYYY即：BACKNEXT结论：正规联接时，二端口并联所得复合二端口的Y参数矩阵等于两个二端口Y参数矩阵相加。注意：（1）两个二端口并联时，其端口条件可能被破坏此时上述关系式就不成立。(2)具有公共端的二端口，将公共端并在一起将不会破坏端口条件。Y'Y''BACKNEXT注意：(1)两个二端口并联时，其端口条件可能被破坏此时上述关系式就不成立。并联后端口条件破坏。1A2A1A1A4A1A2A2A0A0A1052.52.52.54A1A1A4A10V5V++2ABACKNEXT(2)具有公共端的二端口(三端网络形成的二端口)，将公共端并在一起将不会破坏端口条件。Y+++1I1U+2I2U++2IY1I2I1I2U1U1U2UBACKNEXT例.R4R1R2R3R1R2R3R4BACKNEXT例RfIaR1R2aIRf211'101RRRyffffRRRRy1111R2R1aIaIBACKNEXTfffffffRRRRRRRRRRRRRyyY221111'121111)11(URURRIff221112)11(1URRURRUIff211'101RRRyffffRRRRy1111RfIaR1R2aIBACKNEXT三、串联：联接方式如图，采用Z参数方便。Z++'1I'2I'2U'1U+1I1U+2I2UZ++''1I''2I''2U''1U21222112112121][IIZZZZIIZUU21222112112121][IIZZZZIIZUUBACKNEXT212121IIIIII212121UUUUUUZ++'1I'2I'2U'1U+1I1U+2I2UZ++''1I''2I''2U''1U2121212121][][IIZIIZUUUUUU2121][]}[]{[IIZIIZZBACKNEXT则][][][ZZZ即222112112221121122211211ZZZZZZZZZZZZ结论：串联后复合二端口Z参数矩阵等于原二端口Z参数矩阵相加。可推广到n端口串联。BACKNEXT注意：（1）串联后端口条件可能被破坏。22端口条件破坏][][]['ZZZ3¸1¸1¸1¸12222A2A1A1A3A1.5A1.5A1.5A1.5A1A2AZ”BACKNEXT端口条件破坏，不正规联接!23211121225225Z6336Z26222106610ZZZBACKNEXT（2）具有公共端的二端口，将公共端串联时将不会破坏端口条件。端口条件不会破坏1I2I3IZ'Z''213IIIBACKNEXT则ZZZ即222112112221121122211211ZZZZZZZZZZZZ结论正规联接时,串联后复合二端口Z参数矩阵等于原二端口Z参数矩阵相加。可推广到n端口串联。2121II])Z[]Z([UUBACKNEXT例.3I112+2I13I112+2I1BACKNEXT小结:(1)级联时端口条件总满足，用T参数方便。(2)串联和并联联接时端口条件可能被破坏。(3)正规联接时，串联用Z参数、并联用Y参数方便。(4)还有其它联接方式：串-并联联接、并-串联联接。BACKNEXT一、回转器1.回转器：回转器也是二端口.1221riuriu或1221guiguir称为回转电阻g称为回转电导i1u1+u2+i2电路符号特性：§16-6回转器和负阻抗变换器BACKNEXT其矩阵形式为：212100iirruu或212100uuggii注意u,i的方向!0000ggYrrZ令有1YZBACKNEXT2.回转器可以把一个端口的电流(或电压)回转成另一个端口的电压(或电流)。因此利用回转器可以把电容回转成电感。i1u1+u2+i2C21riuCrL21221riuriudtduCi22dtdurC2dtdiCr12dtdiL1BACKNEXT从端口1看，u1,i1关系为一等效电感关系，L=r2C.若r=50k,C=1F则等效电感L=2500H！3.回转器不消耗功率(能量)，也不储能。是线性无源元件。021122211iriiriiuiu4.回转器是非互易元件。0000ggYrrZBACKNEXT5回转器例子u2RuuRuuic1211RuuRuuiF2212ARRRRRFCaibi++––RR+–1u2u+–1i2iu11112uuRuuRucc122222uuuRuuRuuFFcBACKNEXT12uuc1222uuuFRu1回转器方程RuuRuuic1211RuuRuuiF2212Ru2u2ARRRRRFCaibi++––RR+–1u2u+–1i2iu1BACKNEXT二、负阻抗变换器1.电压反向型负阻抗变换器和电流反向型负阻抗变换器电压反向型22112121100iukiuiikuuT参数矩阵UNICi1+u1i2+u2BACKNEXT电流反向型22112121001iukiukiiuuT参数矩阵INICi1+u1i2+u2BACKNEXT2.阻抗变换关系(以INIC为例)INIC变换器ZLINIC++1U2U1I2I21UU21IkI22IZULBACKNEXT(3)代入(1)得(4)除以(2)得即输入端阻抗Li1ZkZ21UU21IkI22IZUL(1)(2)(3))4(21IZULLLZkIkIZIU12211BACKNEXT当k=1时，实现了负阻抗的变换！ZLINIC++1U2U1I2IZi与ZL差一负号。LiZZLi1ZkZBACKNEXT电路举例：2c221c11ca121RUUIRUURUUIUU21212211IRRIIRIRR2abcR1++1U1I+2U2IBACKNEXT212121IRRIUUR2abcR1++1U1I+2U2I12RRk221211001IURRIU电流反向型负阻抗变换器BACKNEXT当输出端口接阻抗Z