《电路》（英文版）8-3 Phasor diagrams

§8-3 Phasor diagrams The phasor diagram is a name given to a sketch in the complex plane of the phasor voltages and currents throughout a specific circuit. 1=2 V1=6+j8=10∠531°V V2=3-j4=5∠-53.1°V V1+V2 J1+V2=9+j4=9.85∠24°V +1 1-V2=V1+(-2)=3+12=124∠76°

§8-3 Phasor diagrams The phasor diagram is a name given to a sketch in the complex plane of the phasor voltages and currents throughout a specific circuit. V j V  1 = 6 + 8 = 1053.1 • V j V  2 = 3 − 4 = 5 − 53.1 • V V j V  1+ 2 = 9 + 4 = 9.8524 • • V V V V j V  1− 2 = 1+ (− 2 ) = 3 + 12 = 12.476 • • • • + j + 1 1 2 • • V +V 2 • V 1 • V 1 2 • • V −V

s. The series RLC circuit--lhe phasor diagram is constructed most sily by employing the single current as the reference phasor. 5 40 VR=RI 十p 十 -i20 VL=JOL I L L C 3 Vs=Vr+VL+Yc r+y Vx=v+yc

The series RLC circuit--The phasor diagram is constructed most easily by employing the single current as the reference phasor. • • V R = R I • • V L = jL I • • = − I C VC j  1 V C • V s •  • I V R • V L • • I V R • V L • V C • V s •  V X • V s V R V L V C • • • • = + + V X V L V C • • • V s V R V X = + • • • = +

The parallel circuit--employing the voltage as the reference phasor. LetI=1∠0° C 5 10 IR=1/5=0.2A ⅠL=1/j4 0.254 l/(一10)=j0.1A Is=/R+L+IC 0.2-j0.25+0.1 0.2-j0.15 0.25∠-36.9°A

The parallel circuit--employing the voltage as the reference phasor. I R • I L • I C • I s • • V I R = 1/ 5 = 0.2A • I L = 1/ j4 = − j0.25A • I C = 1/(− j10) = j0.1A • A j j j Is I R I L I C  0.25 36.9 0.2 0.15 0.2 0.25 0.1 =  − = − = − + = + + • • • • Let V V  = 10 •

The first circuit complete response when sinusoidal input. f(t)=∫(t)+Jn(t)=∫(t)+Ae f(0)=∫(0)+A A=f(0)-f(0+) f(t)=∫(t)+f(1)-J(川e ①D= Vcos(m+y)(Vn∠v5joL ∠ Mayn- R+jOL 讠() Im cos(at -q)

The first circuit complete response when sinusoidal input.  t f t ff t fn t ff t Ae − ( ) = ( )+ ( ) = ( )+ f = f f + A + + (0 ) (0 ) (0 ) (0 ) + + = − f A f f  t f t ff t f ff e − + + ( ) = ( )+[ (0 )− (0 )]       =  − +  = • m m m I R j L V I ( ) cos(  ) i f t = I m t +  −

8-15 . i si ri 1u8 SHS.O 6=1000rad/s s=IXtla C =0.411=-00.5 Ix=I+I1=0.4-10.5 R j0.8 s=Ix+lc=0.4+10.3 L

CI • L I • R I •  250 100 0 o V s I • H2. 0 F  8 x I • =1000 rad/s 0.4 0.3 0.8 0.4 0.5 0.4 0.5 I I I j I j I I I j I I j S X C C X R L R L = + = + = = + = − = = − • • • • • • • • • • I R • LI • I C • I X • • • I S = I X + I C 8-15