电路基础 英文教学 9.ppt

1、Chapter 9 Sinusoids and Phasors,要求深刻理解与熟练掌握的重点内容有： 1正弦量，相量法的基础，有效值和相位差的概念。 2电路定律的相量形式。 3阻抗与导纳。 4电路的相量图表示法，参考正弦量的概念，会用相量图法分析串联电路、并联电路。 难点：相量图表示,9-1 Introduction,9-2 Sinusoids,9-3 Phasors,9-4 Phasor Relationships for Circuit Elements,9-5 Impedance and Admittance,9-6 Kirchhoffs Laws in the Frequency Do

2、main,9-7 Impedance Combinations,9-10 Summary and Review,9.1 Introduction,A sinusoid is signal that has the form of the sine or cosine function.,Circuits driven by sinusoidal current or voltage sources are called ac (alternating current) circuits.,sinusoidal variation 正弦振动,ripple 波动,economic fluctuat

3、ion 经济波动,derivative 导数,Fourier analysis 傅立叶分析,periodic signal 周期信号,impedance 阻抗,admittance 导纳,trigonometric identity 三角恒等式,the horizontal axis 横轴,the vertical axis 纵轴,polar coordinate 极坐标,vector 向量,complex plane 复平面,imaginary part 虚部,conjugate 共轭,velocity 速度,the time domain 时域,the phasor domain 频域,r

4、eactance 电抗,susceptance 电纳,trigonometric identity 三角恒等式,1、Characteristics of Sinusoids,9.2 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； 幅角,2、The Sine Wave,T：the period of the sinus

5、oid f：frequency Heinrich Rudorf Hertz (1857-1894)：赫兹,工频：f=50Hz，=2f=314rad/s,While is in radians per second (rad/s), f is in hertz (Hz),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+), =,0 in phase同

6、相,/2 orthogonal intersection 正交, in phase opposition 反相,AVERAGE AND EFFECTIVE VALUE,The average current is the average of the instantaneous current over one period.,1、Average Value 平均值,The effective value of a periodic current is the dc current that delivers the same average power to a resistor as t

7、he periodic current.,rms：root-mean-square, the square root of the mean (or average),2、Effective Value 有效值,3、Effective Value of Sinusoid,Rectangular form： z=x+jy ，x = Re(z)，y=Im(z),1、Complex Number 复数,9.3 phasors相量,A phasor is a complex number that represents the amplitude and phase of a sinusoid.,A

8、complex number z can be written in rectangular form as,z=x+jy,Where,x is the real part of z;,y is the imaginary part of z.,magnitude：,phase：,Exponential form：,Polar form：,If A= a+jb ，a = Re(A)，b=Im(A),A1A2 =(a1+a2)j(b1b2),Addition and subtraction:,Multiplication:,A1A2 =(a1+jb1)(a2+jb2)=(a1a2b1b2)+ j

9、(a1b2+a2b1),Reciprocal:,Square root:,Complex conjugate:,Division:,2、Phasor Idea,It is a complex number containing the amplitude and phase of the sinusoid.,Phasor-domain representation Time-domain representation The differences between u(t) and,1u(t) is the instantaneous or time-domain representation

10、, while is the frequency or phasor-domain representation.,2u(t) is time dependent, while is not.,3u(t) is always real while is generally complex.,Rotating point in the complex plane,振幅相量,旋转因子,The derivative of i(t) is transformed to the phasor domain,The integral of i(t) is transformed to the pasor

11、domain,3、 Phasor Diagram,Example：,Find u。,Solution： u = u1+u2,Phasor diagram:,To draw a phasor diagram.,Solution：,Example：,Using the phasor approach, determine the current i(t) in a circuit described by the integrodifferential equation,Example：,Solution：,We obtain the phasor form of the given equati

12、on as,But =2 rad/s, so,Converting this to the time domain,9.4 Phasor relationships for circuit elements,RESISTORS,1、Ohms Law,Ohms law in the time domain (时域),Ohms law holds true both in the time domain and in the frequency domain.,We will assume the passive sign convention.,Ohms law in the frequency

13、 domain (频域),Instantaneous power：瞬时功率,Average power：平均功率/有功功率,INDUCTORS,1、The voltage-current characteristics of an inductor in time domain,2、The voltage-current characteristics of an inductor in frequency domain,3、Energy Storage,Average power：,Stored magnetic energy：贮存的磁能,Instantaneous power：,CAPAC

14、ITORS,1、The voltage-current characteristics of a capacitor in time domain,2、The voltage-current characteristics of a capacitor in frequency domain,3、Energy Storage,Instantaneous power：,Average power：,Stored electric energy：,Table Summary of voltage-current relationships.,Element,Time domain,Frequenc

15、y domain,R,L,C,9.5 Impedance and admittance,1、The impedances and admittances of passive elements,or,Where Z is a frequency-dependent quantity known as impedance, measured in ohms.,The impedance Z of a circuit is the ratio of the phasor voltage to the phasor current .,The admittance Y is the reciproc

16、al of impedance, measured in siemens (s).,Table,Element,Impedance,Admittance,R,L,C,2、The impedances and admittances of one-port passive networks,Where R=Re(Z) is the resistance and X=Im(Z) is the reactance.,R,L,inductive reactance 感抗,C,capacitive reactance 容抗,We say that the impedance is inductive w

17、hen X is positive or capacitive when X is negtive or resistive when X is zero.,Where G=Re(Y) is called the conductance and B=Im(Y) is called the susceptance.,Admittance, conductance, and susceptance are all expressed in the unit of siemens (or mhos).,R,L,inductive susceptance 感纳,C,capacitive suscept

18、ance 容纳,We say that the admittance is capacitive when B is positive or inductive when B is negtive or resistive when B is zero.,Model For A Real Inductor,Find uL。,Example：,Solution：,Series And Parallel Inductors,The equivalent inductance of series-connected inductors is the sum of the individual ind

19、uctances.,The equivalent inductance of parallel-connected inductors is the reciprocal of the sum of the reciprocals of the individual inductances.,求i。,Example：,Solution：,Or：,Example：,Solution：,Find iC.,The equivalent capacitance of series-connected capacitors is the reciprocal of the sum of the reci

20、procals of the individual capacitances.,The equivalent capacitance of N parallel-connected capacitors is the sum of the individual capacitances.,Series And Parallel Capacitors,u(t) = u1(t)+u2(t)+un(t),u(t) = u1(t) = u2(t) = un(t),C= C1+C2+Cn,6、Model For A Real Capacitor,A Real Capacitor, G=0.00312S，with a sinusoidal voltage