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1、CHAPTER 4 AC CIRCUITS,4-1 INTRODUCTION,1、Characteristics of Sinusoids,where： A= the amplitude of the sinusoid (or maximum value)；振幅，最大值 = the angular frequency in radians/s；角频率 = phase；初相 t+= the argument of the sinusoid； 相位,2、The Sine Wave,T：the period of the sinusoid f：frequency Heinrich Rudorf He
2、rtz (1857-1894)：赫兹,工频：f=50Hz，=2f=314rad/s,3、Sinusoids with different phases,Leading, lagging and in phase. The reference：u=Umsin(t), then i=Imsin(t-) The reference：i=Imsin(t), then u=Umsin(t+),4-2 AVERAGE AND EFFECTIVE VALUE,The average current is the average of the instantaneous current over one pe
3、riod.,The effective value of a periodic current is the dc current that delivers the same average power to a resistor as the periodic current.,rms：root-mean-square, the square root of the mean (or average),1、Average Value 平均值,2、Effective Value 有效值,3、Effective Value of Sinusoid,4-3 REPRESENTING SINUSO
4、IDS WITH PHASORS,Rectangular form：A= a+jb ，a = Re(A)，b=Im(A),magnitude：,phase：,Exponential form：,Polar form：,1、Complex Number,A1A2 =(a1+a2)j(b1b2) A1A2 =(a1+jb1)(a2+jb2)=(a1a2b1b2)+ j(a1b2+a2b1),2、Phasor Idea,It is a complex number containing the amplitude and phase of the sinusoid.,Phasor-domain re
5、presentation Time-domain representation The differences between u(t) and,1u(t) is the instantaneous or time-domain representation, while is the frequency or phasor-domain representation.,Check Your Understanding,2u(t) is time dependent, while is not.,3u(t) is always real while is generally complex.,
6、？,Rotating point in the complex plane,振幅相量,旋转因子,3、 Phasor Diagram,例：,求u。,解：u = u1+u2,例：,画出相量图。,解：,4-4 RESISTORS,1、Ohms Law,Ohms law holds true both in the time domain and in the frequency domain. Ohms law in the time domain (时域),Ohms law in the frequency domain (频域),Instantaneous power：瞬时功率,Average
7、power：平均功率/有功功率,4-5 INDUCTORS,1、The voltage-current characteristics of an inductor in time domain,2、The voltage-current characteristics of an inductor in frequency domain,3、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).
8、,=0，XL=0；The reactance of an inductor varies linearly with frequency.,例：,解：,求uL。,4、Energy Storage,Instantaneous power：,Average power：,Stored magnetic energy：,5、Reactive Power,QL = ULI = I2XL ， VA，无功伏安，简称乏（var）,6、Model For A Real Inductor,阻抗 Impedance，measured in ohms(). R=Re Z is the resistance and
9、X=Im Z is the reactance.,导纳 Admittance，measured in siemens(S).,7、Series And Parallel Inductors,The equivalent inductance of series-connected inductors is the sum of the individual inductances.,The equivalent inductance of parallel inductors is the reciprocal of the sum of the reciprocals of the indi
10、vidual inductances.,例：,解：,求i。,Or：,Or：,4-6 CAPACITORS,1、The voltage-current characteristics of a capacitor in time domain,2、The voltage-current characteristics of a capacitor in frequency domain,3、The Impedance of A Capacitor,电容电抗/容抗 Capacitor reactance，measured in Ohms().,=0，XC=,电容电纳/容纳 Capacitor su
11、sceptance，measured in siemens(S).,例： 求iC（iC与uC参考方向一致）,解：,4、Energy Storage,Instantaneous power：,Average power：,Stored electric energy：,Reactive Power：QC = UCIC = IC2XC = UC2BC (无功伏安，乏),5、Series And Parallel Capacitors,The equivalent capacitance of N parallel-connected capacitors is the sum of the ind
12、ividual capacitances.,u(t) = u1(t)+u2(t)+un(t),The equivalent capacitance of series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.,u(t) = u1(t) = u2(t) = un(t),C= C1+C2+Cn,6、Model For A Real Capacitor,导纳 Admittance，measured in siemens(S).,例：一个非理想电容器，G=0.00312S，加上一个U=10V，=314 rad/s的正弦电压，I=0.1A。求C，i(t)。,解：,4-7 KIRCHHOFFS LAWS IN THE FREQUENCY DOMAIN,1、KCL Using Phasors,which is Kirchhoffs current law in the frequency domain.,2、KVL Using Phasors,The Kirchhoffs voltage law in the frequency domain：,
