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1、工学工学电路理论电路理论 华科华科电气电气Chapter 9 Sinusoids and Phasors 22 INDUCTORS1、The v-i characteristics of an inductor in time domainU=jLI2)The v-I characteristics of an inductor in frequency domainU=jLI3)The Impedance of An Inductor自感电抗/感抗 Inductor reactance，measured in Ohms( )电感电纳/感纳 Inductor susceptance，measu
2、red in siemens(S). =0，XL=0；The reactance of an inductor varies linearly with frequency.3 CAPACITORS1)The v-i characteristics of a capacitor in time domainI=jCU2) The v-I characteristics of a capacitor in frequency domain2) The v-I characteristics of a capacitor in frequency domainI=jCU3) The Impedan
3、ce of A Capacitor电容电抗/容抗 Capacitor reactance，measured in Ohms( ).=0，XC=，XC =0电容电纳/容纳 Capacitor susceptance，measured in siemens(S).elementTime domainFrequency domainRV(t)=Ri(t)LCU=jLIOhms law in phasor form9.5 KIRCHHOFFS LAWS IN THE FREQUENCY DOMAIN1、KCL in the time domain:which is Kirchhoffs current
4、 law in the frequency domain.2、KVL in the frequency domain:10.2 Phasor DiagramA graphical representation of phasor is known as a phasor diagram.+-RU.I.U.I.+-j LU.I.I.U.+-U.I. 1j CI.U.90 phasor model of the circuit:Differential equationAlgebraic equationLCRuSiLiCiR+- -j L1/j CR+- -in time domainIn fr
5、equency domainPhasor model：voltage and current is represented by phasors；Circuit elements in the frequency domain.9.6 IMPEDANCE AND ADMITTANCEThe impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in ohms().Where,The admittance Y is the reciprocal of impe
6、dance, measured in siemens(S).9.6.1 PASSIVE ONE-PORT NETWORK1. RLC Series ConnectionThe voltage-current characteristics in frequency domain：Impedance：Z = R+jX Z is a frequency-dependent quantity known as impedance, R=Re(Z) is the resistance and X=Im(Z) is the reactance, they are all measured in ohms
7、.magnitude：phase：X0，0： The phasor voltage is resolved into two components, one in phase with the current, and one leads by 90.Active component：Reactive component：0，XXC ，X=XLXC 0，0，Current lags voltage, impedance is inductive.XLXC ，X=XLXC 0，0， 0： The phasor current is resolved into two components, on
8、e in phase with the voltage, and one lags by 90.phase：Active component：Reactive component：B0，BC，B = BLBC 0，0，Voltage leads current, admittance is inductive.BLBC，B = BLBC 0， 1/ C ，X0， 0，inductive； L1/ C ，X0， 1/ C ) Voltage triangleUXU L=1/ C ，X=0， =0，resistive。Voltage triangleUXU |Z|RX Impedance tria
9、ngleR+- -+- -+- -jX2. Admittance:Y+- -无源无源线性线性+- -resistorinductorcapacitorj LR+- -conductancesusceptance|Y|GB Susceptance triagle单位：单位：S导纳的模导纳的模导纳角导纳角The relationship between the impedance and admittance:Usually, G 1/R B 1/XZRjXGjBY4.Impedance combination:Drill: Z1=10+j6.28 Z2=20- -j31.9 Z3=15+j15.7 Calculate: ZabZ1Z2Z3ab
