I(s)?Ur(s)11 其中：Z??1/Cs?//Z1 Z1?R1??R1Cs?1?代入Z?Z?R2CsCS11?R1Cs?1?1RCs?1CsCs1中，则Z? ?11CsR1Cs?2??R1Cs?1?CsCs11Cs I1(s)?I(s)?I(s)11R1Cs?2?R1?CsCsU(s)111Ur(s)Uc(s)?I1(s)?I(s)R2?r?R2CsZ?R2R1Cs?2CsZ?R2?Ur(s)Ur(s)11?R2RCs?11R1Cs?11RCs?2Cs1?R21?R2CsR1Cs?2CsR1Cs?2

?所以：

Ur(s)Ur(s)?R1Cs?2?Cs?R2R1Cs?1?R2?R1Cs?2?CsR1Cs?1?R2?R1Cs?2?CsUc(s)R2?R1Cs?2?Cs1??Ur(s)R1Cs?1?R2?R1Cs?2?CsR1Cs?1?R2?R1Cs?2?Cs?R1R2Cs?2R2Cs?1R1R2C2s2?R1Cs?2R2Cs?122

解法2：首先将上图转换为复阻抗图（如解法1图）

I1(s)?Ur(s)?Uc(s)

R11??I2(s)?I1(s)?R1??Cs?I1(s)?R1Cs?1?

Cs??I(s)?I1(s)?I2(s)

Uc(s)?I1(s) 1?I(s)R2 Cs1 Cs 画出其结构图如下：

Ur(s) － 1 I1 R1 R1Cs+1 I2 I Uc(s) R2

化简上面的结构图如下： 1 Cs Ur(s) － 1 I1 R1 R1Cs+2 I Uc(s) R2

应用梅逊增益公式：

Uc(s)1n??Tk?k

Ur(s)?k?1其中：??1?La?Lb

La??R2?R1Cs?2?、Lb??1 R1R1CsR2?R1Cs?2??1?R1Cs?R2Cs?R1Cs?2??1 R1R1CsR1Cs所以??1?T1?R2?R1Cs?2?、?1?1 R11、?2?1 R1CsT2?所以：

R2?R1Cs?2??1Uc(s)R1R1CsR2Cs?R1Cs?2??1??Ur(s)R1Cs?R2Cs?R1Cs?2??1R1Cs?R2Cs?R1Cs?2??1R1CsR1R2C2s2?2R2Cs?1?R1R2C2s2?R1Cs?2R2Cs?1解：(c) 解法与(b)相同，只是参数不同。

2-14 试求出图P2-2中各有源网络的传递函数W(s)=Uc(s)/Ur(s)。

R1 C1 ur R0 (b) uc C0 R1 C1 uc R0 (a) 解：（a）

Uc(s)Z??1Ur(s)Z0 其中：

Z1?R1?11?R1C1s?1??1?T1s?1? ?C1sC1sC1s R1 C1 R2 C2 ur R0 uc (c) 1C0sR0R01Z0?//R0??? 其中：T1?R1C1、T0?R0C0

1C0sR0C0s?1T0s?1R0?C0sR0所以：

Uc(s)1?T0s?1??T1s?1? ??Ur(s)R0C1sR1 C1 C0 uc R0 (a) 解：（b）如图：

R1 C1 R3 I1 R2 ur I0 uc R0 (b) 将滑动电阻分为R2和R3，

I0?I1 Ir(s)s)R30?UR，

I1??Uc(0Z，其RR13?1?C1sR11Z?RC1sR1R?R1C1s?1??R12?R1?R2?R?1?2R

1?1C1s1C1s?1C1sZ?所以：

Uc(s)R??R3?R1?1??3?C1s????R1?R3?C1s?1?U(s)??R??RR22?R2?R1C1s?1??R1?r00R13C1s解：（c）解法与（b）相同。

2-15 求图P2-3所示各机械运动系统的传递函数。

(1)求图(a)的Xc(s)Xs)?? (2)求图(b)的

Xc(s)s)?? r(Xr((3)求图(c)的X2(s)X?? (4)求图(c)的 1(s)

中