电子电工技术英文课件 (31).pdf

3.5 Analysis of AC Circuits 3.5.1 Calculation of Current and Voltage in AC Circuits The impedance of the resistor,inductor and capacitor of AC circuits are R=RRRVZI,j LLLLVZI=,1j CCCCVZI=respectively.You may notice that Ohms law applies to AC circuits.Similarly,KCL and KVL also apply to AC circuits.Lets take an example to show the process of calculating current and voltage in AC circuits.Fig.1 shows an AC circuit with a resistor and an inductor in series.SVILVRV Figure 1:Circuit for example 1.According to KVL and Ohms law,Rj L=+=+sRLVVVII(1)From(1),SRj LSVVIZ=+(2)The voltage of the resistor is SRRRj L=+RVIV(3)The voltage of the inductor is Sj Lj LRj L=+LVIV(4)Lets take another example to show the calculating process of AC circuits.Fig.2 shows an AC circuit with a resistor and a capacitor in parallel.SVICIRIR1j C Figure 2:Circuit for example 2.According to KCL and Ohms law,1j Cj CRR=+=+=+SRCSSVIIIVV(5)From above two examples,we can see that the complex operation will be used when analyzing AC circuits.Therefore,the analysis of AC circuits is more complex than the analysis of DC circuits.3.5.2 Phasor Diagrams Although we can analyze AC circuits through complex operation,it is difficult to distinguish relations among different phasors.A phasor diagram is a convenient and useful tool for geometrically presenting the relationships among the various voltages and currents in an AC circuit.A phasor diagram consists of a number of straight lines with arrows.Lets start by drawing the phasor diagrams for R,L and C.For a resistor shown in Fig.3,RRIRV Figure 3:A resistor in AC circuits.R=RRVI(6)The expression(6)shows that the phase difference of the voltage and the current of the resistor is zero.Thus,we can draw the phasor diagram for the resistor,as shown in Fig.4.RIRV Figure 4:Phasor diagram for the resistor.For an inductor shown in Fig.5,j LLILV Figure 5:An inductor in AC circuits.o90j LL=LLVI(7)The expression(7)shows that the phase difference of the voltage and the current of the inductor is 90 degree.Thus,we can draw the phasor diagram for the inductor,as shown in Fig.6.Note that we choose VL as a reference by selecting its phase angle to be zero.LILV Figure 6:Phasor diagram for the inductor.For a capacitor shown in Fig.7,1CjCICV Figure 7:A capacitor in AC circuits.o11190CCjj CCC=IV(8)The expression(8)shows that the phase difference of the voltage and the current of the capacitor is 90 degree.Thus,we can draw the phasor diagram for the capacitor,as shown in Fig.8.CICV Figure 8:Phasor diagram for the capacitor.If there is more than one circuit element in an AC circuit,we can also draw the phasor diagram.For example,the phasor diagram for the circuit in Fig.1 is shown in Fig.9.Note that we choose I as a reference in the series circuit for convenience.ILVSVRV Figure 9:Phasor diagram for the circuit in Fig.1.The phasor diagram for the circuit in Fig.2 is shown in Fig.10.Note that we choose Vs as a reference in the parallel circuit for convenience.ISVRICI Figure 10:Phasor diagram for the circuit in Fig.2.From the phasor diagrams drawn above,we can clearly see the relationships among the various voltages and currents in an AC circuit from a geometric point of view.