高二物理竞赛课件运算电路电阻性网络各种解法的适用性

运算电路，电阻性网络各种解法的适用性

15SU3(S)=(5S+0.1)U1–0.1U2–2S·=–18+18S15

–0.1U1+(5S+0.1)U2–3S·=–18+18S15U1(S)=150S+7.5S(25S+1)U2(S)=S(25S+1)225S+7.5I(S)=0.1[U1(S)–U2(S)]==(25S+1)–7.5–0.3(S+)125i(t)=£–1(t>0)解法：节点分析+–9S6S12S13S12S13S6S9S+–+–+–+–15S123I(S)10运算电路，电阻性网络各种解法的适用性u1(0-)=15=9V

35u2(0-)=6V

UOC(S)=–+=–

9S6S3S例(见教材习题7-8)+–15V152F2F3F3Fi––++u2u1+–9S6S12S13S12S13S6S9S+–+–+–+–15S10I(S)解法一、应用戴维南定理+–9S6S12S13S12S13S6S9S+–+–+–+–15S–+U0Ci(t)=–0.04t–10I(S)+3S25S–13S12SZ0(S)=2=·13S12S+25S12S13S12S13SUOC(S)=–

3S+–9S6S12S13S12S13S6S9S+–+–+–+–15S10I(S)I(S)==

–=

–

3S–25S10+1550S+2312510(S+)讨论:是网络函数的一般定义对正弦稳态电路中定义的网络函数如何理解(2)讨论网络函数的意义H(S)与h(t)的关系网络或系统的稳定性与对应正弦稳态响应的关系7网络函数7定义与分类零状态响应的拉氏变换输入的拉氏变换网络函数H(S)=H(S)H(j)H

(j)=UR.U.+-U.RjC1jL+-UR.+-RSC1SL+-U(S)UR(S)H

(S)=UR(S)U(S)RR+SL+

SC1=jCRR+jL+

1=与对应正弦稳态响应的关系H(S)H(j)

£[u2(t)]

£[iS(t)]S1S+212(–)S1S+24H(S)===u2(t)=14.1sin(2t–45º)7网络函数7定义与分类

例

N0为线性定常松弛网络。在端口1施加电流源iS(t)=1(t)A

时，端口2电压的零状态响应为u2(t)=21(t)(1–e–2t

)V。

如果将电流源波形改为iS(t)=10sin2tA，求稳态响应u2(t)。+iS(t)N0Ru2(t)–11´2´2U2=H(j2)IS=10=14.1–45º

2+j24••2、网络函数的分类(1)策（驱）动点函数—输入和输出在同一端口（或支路）Zin(S)=U1(S)I1(S)Yin(S)=I1(S)U1(S)(分别具有阻抗导纳的量纲)Zin(S)=1/Yin(S)+N0Z2(S)U2(S)–I1(S)I2(S)+–U1(S)7网络函数7定义与分类HV(S)=U2(S)U1(S)(转移电压比)HI(S)=I1(S)I2(S)(转移电流比)(2)传输(传递、转移)函数—输入和输出不在同一端口（或支路）Z21(S)=U2(S)I1(S)(转移阻抗)Y21(S)=U1(S)I2(S)(转移导纳)2、网络函数的分类+N0Z2(S)U2(S)–I1(S)I2(S)+–U1(S)7网络函数7定义与分类7

网络函数的确定121R(+2SC)U1–Ui=012R=SCU2U12R1R(2SC+)U2–SCU0=0H(S)==U0(S)Ui(S)4R2C2S21

例求如图所示电路的传递函数H(S)=，并求对应的冲激响应。U0(S)Ui(S)u0ui-+2CR2R2RCC2SC1SC1SC1Ui(S)U0(S)h(t)=£–1[H(S)]=t1(t)14R2C2Zin=11Yin=112-13Z21=Y21=11Z212-13HV=1112-13Z2HI=12-137

网络函数的确定+N0Z2(S)U2(S)–I1(S)I2(S)+–U1(S)231Yn(S)E(S)=InS(S)InS(S)=I1(S)00T•••E1(S)=I1(S)11E2(S)=I1(S)12E3(S)=I1(S)13网络函数是复频率变量S的实系数有理函数H(S)=F1(S)F2(S)(S–zi)i=1m(S–pj)j=1n=H0网络函数的零点和极点Zin=11Yin=112-13Z21=Y21=