2. Main Contents ： 1. Three key factors 2. The phasor model of sinusoidal 3. Compound resistance 4. The phasor model of KCL,KVL) chapter 8 Phasor Method Review complex numbers difficulty

3. in linear circuit,if all sources are the sinusoidal functions with the same frequency,so all of state responses are the sinusoidal functions with the same frequency. That kind of circuit is called sinusoidal AC circuit 。 The Merit of sinusoidal AC circuit ： transmit easily ； be good for electric device operation ； topical circuit..... Supplement: Sinusoidal Alternative Circuit

4. Including sin and cos 1. Three key factors of sinusoid ：  ------ initial phase, rad 、 degree （ ° ） F m ------ maximal value ω ------ angular frequency ， rad /s ImIm  t i(t)=I m cos(  t+  ) i waveform If i(t)=I m cos(  t+  )  T 一、 sinusoid ： §8.1 Phasor

5. * Power network frequency ) ： China 50 Hz American 、 Japan 60 Hz wire communication frequency : 300 - 5000 Hz Wireless communication) ： 30 kHz - 3×10 4 MHz Supplement: Common Sense

6. If u(t)=U m cos(  t+  u ), i(t)=I m cos(  t+  i ) phase difference  = (  t+   u ) - (  t+  i )=  u -  i  >0 ， u leading i ， or i lagging u  t t u, i u i uu ii  0  <0 ， i leading u ， or u lagging i 二 phasor Difference of The Same Sequence Sinusoidal

7.  = 0 ， u and I in phase ：  =   (  180 o ) ， 5.u or I opposite in phase ： regulate ： |  |   (180°)  t t u, i u i 0  t t u i 0  t t u i 0 5.  =  90° ， u and I intersect

8. Electric variable must use capital ： U 、 I Effective Value So whe n AC current Direct current Heat Effective The notions of effective value

9. appliance ~ 220V The tolerant voltage =300V if a electrical appliance’s tolerant voltage is 300V ， whether it is used in 220V circuit ? because this appliance ’ s tolerant voltage is low to source voltage ’ s maximal value,it is not used 。 Effective value U = 220V Maximal value U m = 220V = 311V Source’s voltage Questions and Discussions

10. §8. 2 Phasor Expression of Sinusoidal complex function the real part of A(t) ： A(t) also can be written 一、 Phasor Expression of Sinusoidal ： phasor

11. sin function: In the same circuit,sinusoid’s forms are identical Cos function ： Using the maximal value ： Transform phasor to sinusoid, distinguish the effective value or maximal value At the same time as sin function or cos function

12. Example 8-2 Try to express i 、 u in phasor 。 Solution ： example8-3 Try writing current instantaneous expressions solution ：

13. Link phasor Rotate factor phasor A(t)is rotate vector ), Rotate vector :the Reflection in Real Axis is cos function t 0 t1t1 t1t1 ＋1＋1 ＋j＋j 0  Geometry Meaning of phasor

14. 1. The same sequent sinusoid can add or minus In fact it is a transforming methods,from time-domain to phasor. “phasor” differ from “vector” 二、 Phasor Operation ： so

15. Time-domain ： when variable is the kind of functions changing with time, we research the net,and analyse the circuit under the condition that time is variable. Frequent-domain ： research the net under the condition that variable is transformed,and analyse the circuit under the condition that frequency is a variable. Phasor methods ： transform time–sin function to phasor,then analyse the circuit.it belongs to frequent-domain. i 1  i 2 = i 3 Time-domain phasor

16. Use the phasor diagram to do the add or minus operation the same sequent sinusoid 。 Phasor diagram play a important role in the sinusoid steady-state analysis,especially qualitative analysis. 。 Re Im Re Im Note ： when return to the form of sinusoid,notice the corresponding sinusoid Supplementary Example

17. 2. Sinusoid differential and integral operation solve ：

18. 一、 resistance ： Phasor form ： Effective value relationship of resistance ： U R = RI The relationship of phase ： u, i in phase + - Phasor model R Phasor relationship of resistance: Phasor diagram §8.3 Phasor Relationship of Voltage And Current of Resistance,Inductor And Capacitor + u R (t) i(t) R - Time-domain model  t t u i 0

19. Phasor form Effective value relationship U=  L I Phase relationship: u leading i 90° i lagging u 90° j Lj L Phasor model + - Phasor diagram i(t) u (t)L + - Time- domain Time-domain form  t t u, i u i 0 waveform Phasor relationship of inductive ： Inductive reactance X L =  L= 2  f L units: ohm 二 、 Inductance ：

20. Physical meaning of inductive reactance: (1)Reflect the capability of restricting current ； (2) Inductive reactance and frequent are positive ratio 。  XLXL (3) Because of inductive reactance,I lagging u 90° 。 U=  L I =X L I

21. Phasor form Effective value relationship I=  C U Phase relationship : i leading u 90° U lagging i 90° Time-domain form  t t u, i u i 0 waveform Time-domain model i (t) u(t)C + - Phasor diagram Phasor model + - Phasor relationship of capacitor Capacitive reactance X C =1/  C=1/ 2  f C 三 、 Capacitor

22. (1)Reflect the capability of restricting current ； (2) the absolute value of capacitive and frequent are 。 (3) Because of capacitive reactance,I leading u 90° 。  I=  C U Physics Meaning of capacitive reactance ：

23. For controlled source ， the relationship of voltage and current can be written to phasor form directly ， equations are same as that of time-domain 。 i k =0 + - + - ukuk ujuj ijij + - + - In phasor diagram ， KCL 、 KVL 、 circuit’s three analysis methods are also valid 四、 Controlled Source ：

24. 一、 Phasor form of Kirchhoff’s Law: 二、 Voltage Current Relation of phasor form of circuit component ： 8. 4 Phasor Form of Circuit Law And Phasor Model of Circuit

25. write differential equation in time-domain Phasor form Algebra equation Phasor model ： voltage 、 current in phasor ； component in complex impedance 。 L C RuSuS iLiL iCiC iRiR + - Time-domain circuit 1 2 j  L R + - Phasor model 1 2 三. Phasor Model :

26. 1. The Same Sequence Sinusoidal can be expressed in a phasor diagram ； 2. positive angle are couterclockwise ； 3. Choose a reference phasor (initial phase is zone 。 ) choose Ù R is reference phase j  L 1/j  C R + - + - + + - - assignment ： 7 、 11 、 12 、 13 、 15 、 16 、 17 四、 Notice about phase methods ：

27. 1.The base of relations between voltage and current in single parameter current Inductive component Base relation Complex impedance L Capacitance component Base relation C Resistance component R Base relation Complex impedance Conclusion

28. in sinusoidal AC circuit,if sinusoidal are expressed in phasor,and circuit parameters use complex impedance( ),so compound form ohm ’ s law is similar with that of directive current 。 resisrance circuit Inductive circuit capacitive Compound form ohm ’ s law 2. Compound Form Ohm’s Law of Single Parameter Circuit

29. * The relation between voltage and current instantaneous value is accordant to ohm’s law and kirchhoff’s law 。 uLuL i uRuR u R L 3. Relation of Simple Sinusoidal Alternating Current (Take R-L Circuit For Example)

30. R L *if Current and voltage phasor are accordant to the phasor form,they can use ohm’s law and kirchhoff’s law

31. In resistance circuit ： Judge right or wrong ： ？ ？ ？ Instantaneous value Effective value   Some problems in homework ： notice write

32. in inductive circuit Judge right or wrong ？ ？ ？ ？ ？ 