例求如图电路阻抗Z设信号频率R,LaeR, =R, =1Q L=0.2H C=1F解：Zab=R+joLcR11jocR(の)：等效电阻。7Acb11X(の)：等效电抗。+jocR2joc-joc/+Z=R + joL - +(oc)1/ROCR0+(oC)100= R(@)+ jX(@)0-1+01+075ircuitAnallyBeijing JiaotongUniversity
Circuit Analysis by Beijing Jiaotong University 求如图电路阻抗Zac 设信号频率ω 解： R(ω)：等效电阻。 X(ω)：等效电抗。 例 Zab = R1 + jwL j C R j C R j C R Y Z cb cb w w w 1 1 1 1 1 2 2 2 + = + = = Zac = Zab + Zbc ( ) 2 2 2 2 1 1 1 C R j C R R j L w w w + − = + + ( ) ( ) ( ) 2 2 2 2 2 2 2 1 1 1 1 C R C j L C R R R w w w w + + − + = + a c R1 L R2 b C R1 = R2 =1 L = 0.2H C =1F ) ( ) j ( ) 5 1 j( 1 1 ( ) 1 ac 2 2 w w w w w w Z w = R + X + + − + = + 75
10Q= R(の)+ jX(@)1+(51 +R,Lha阻抗与の有关Rc.纯阻0=0Zac(0)= R(0) =1+1= 2Q容性Z(1) = 1.5 +=1.5- j0.3(Q)0=1122纯阻Z(2):1.2- j0(2)0=255133Z(3) =1.1 + j0.3(2)感性0=3101076CircuitAnalvsisbvBeiline liaotoncUniversits
Circuit Analysis by Beijing Jiaotong University ) ( ) j ( ) 5 1 j( 1 1 ( ) 1 ac 2 2 w w w w w w Z w = R + X + + − + = + w = 0 Zac (0) = R(0) =1+1= 2 w =1 ) 1.5 j0.3( ) 2 1 5 1 Z(1) =1.5 + j( − = − w = 2 ) 1.2 j0( ) 5 2 5 2 j( 5 1 Z(2) =1+ + − = − w = 3 ) 1.1 j0.3( ) 10 3 5 3 j( 10 1 Z(3) =1+ + − = + 容性 纯阻 感性 纯阻 76 a c R1 L R2 b C 阻抗与ω有关
关于阻抗的讨论(1）无源二端网络的阻抗与导纳取决于+V网络结构，元件参数和信号源频率NoC(2）N。的性质（感性或容性）随α变化(3)当Φ,=0～90°或=-90°～0 时为感性(4）当Φ,=-90°～0或Φ=0～90°时为容性77Circuit Analysis by Beijing Jiaotong University
Circuit Analysis by Beijing Jiaotong University 77 (1) 无源二端网络的阻抗与导纳取决于 网络结构，元件参数和信号源频率 (3) 当 0 ~ 90 90 ~ 0 z = 或 Y = − 时为感性 (4) 当 = −90 ~ 0 = 0 ~ 90 z 或 Y 时为容性 (2) N0的性质（感性或容性）随ω变化 V N0 & I & 关于阻抗的讨论
四：阻抗导纳分析举例例证明图示相移电路的输出电压导前输入电压相位900-j10Q-j102Z=10l(10-j10)HHHH0++10(10-j10)=6- j2(2)文%10210 +(10- j10)102-00分压公式Lz6-j25101Z-j106- j12210- j10/2F5L45°V13U23378CircuitAnalysisbyBeijing JiaotongUniversity
Circuit Analysis by Beijing Jiaotong University 78 证明图示相移电路的输出电压 导前输入电压 相位90 例 0 Vi & Z − j10 − j10 10 V & 1 10 V0 & 6 j2( ) 10 (10 j10) 10(10 j10) 10 || (10 j10) = − + − − = Z = − i 1 i i 45 3 2 6 j12 6 j2 j10 V V V Z Z V o & & & & = − − = − = 1 1 10 2 45 10 j10 2 V V V o = = − 0 i i 2 2 1 45 45 j 2 3 3 V V V = = 分压公式 四．阻抗导纳分析举例
四、谐振电路1YYX=X, +XjoLjoc串联谐振RLC串联组合，可写出其阻抗为X与有关Z=R+ j(oLR+iX0当外加的信号频率使得电抗X=0时，称电路发生串联谐振1谐振频率0oLC81Circuit Analysis by Beljing Jiaotong University
Circuit Analysis by Beijing Jiaotong University 81 Vs & I & jwL VL & VC & jwC 1 VR & R 0 w 0 XL XC X=XL +XC 串联谐振 RLC串联组合，可写出其阻抗为 R X C Z R L ) j 1 = + j( − = + w w X与w有关 当外加的信号频率使得电抗X=0时，称电路发生串联谐振 谐振频率 LC 1 w0 = 四、谐振电路