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，measured 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 Impedance 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 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 frequency 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 impedance, 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.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, one 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 triangleR+- -+- -+- -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