Bài giảng Electric circuit theory - Chapter IX: Sinusoid and Phasors - Nguyễn Công Phương

Nguyễn Công Phương Electric Circuit Theory Sinusoid & Phasors Contents I. Basic Elements Of Electrical Circuits II. Basic Laws III. Electrical Circuit Analysis IV. Circuit Theorems V. Active Circuits VI. Capacitor And Inductor VII. First Order Circuits VIII.Second Order Circuits IX. Sinusoid and Phasors X. Sinusoidal Steady State Analysis XI. AC Power Analysis XII. Three-phase Circuits XIII.Magnetically Coupled Circuits XIV.Frequency Response XV. The Laplace Transform XVI.Two-port Networks Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 2 Sinusoid & Phasors 1. Sinusoids 2. Complex Numbers 3. Phasors 4. Phasor Relationships for Circuit Elements Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 3 Sinusoids vt( ) Vm sin( t ) v(t) 2 Vm T  2π  π 0 1 ωt f   T –Vm Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 4 Complex Numbers (1) zxjyr    rej ;1 j  Imaginary axes y rxy22;tan  1 x y r xrcos ; yr sin  Real axes x Re(zy ); Im( z ) 0 x zxjyr   rej r(cos  j sin ) Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 5 Ex. 1 Complex Numbers (2) 34jr ? Imaginary axes j rxy22 rab2234 22 5 y 11oy 4 yr sin  tan tan 53.1 y x 3   tan1 x 1 o 345j 53.1 0 xr cos x Real axes Ex. 2 10 60o xjy ? x 10cos60o 5 y 10sin 60o 8.66 10 60o  5j 8.66 Mạch xoay chiều - sites.google.com/site/ncpdhbkhn 6 Complex Numbers (3) zxjyz; 11  x  jyr 11  12222; zxjyr  2 zz12 ()() xx 12jy 1  y 2 zz12 ()() xx 12jy 1  y 2 zz12 rr 12 12 zr11  12 zr22 11   zr zr  /2 zxjyr*    re j Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 7 Ex. 3 Complex Numbers (4) 3456jj(3 5)jj (4  6) 8 2 34(56)jj(3 5)jj [4  ( 6)] 2 10 oo 345j 30o 34[(5cos30)(5sin30)]34(4.332.50)jjjj      1.33 j 6.50 (3jj 4)(5 6) 35jjjj 453  6  4  6 15jj 20  18  ( 1)24 39j 2 o o oo  5 53.1 7.81  50.2  (5 7.81) 53.1 50.2  39.1 2.9o Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 8 Ex. 4 Complex Numbers (5) 34 j 3456jj35 jjjj 453 6 4 6 15 jj 20 18 24   56 j 5656jj 5(6)22 j 25 ( 1)36 938 j 938j   0.15 j 0.62 61 61 61 5 53.1o 5   53.1oo ( 50.2 )  0.64 103.3o 7.81  50.2o 7.81 Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 9 Ex. 5 Complex Numbers (6) o 345j 30o 7.33 j 6.50 7.33 j 6.50 9.80 41.6    o (4jj 5)(6 7)* (4jj 5)(6 7)* 59.00 100.7o 59.00 100.7  0.17  51.1o 5 30oo (5cos30 )jj (5sin 30 o )  4.33 2.50 o 345j 30o  (3jj 4)  (4.33  2.50)  7.33  j 6.50  0.41  25.6 (4j 5)(6jjj 7)* (4 5)(6 7) 45j 4522  tan1 (5/ 4) 6.40 51.3o 67j 6722  tan1 (6 / 7) 9.22 49.4o o o o (4jj 5)(6 7) 6.40 51.3 9.22 49.4  59.00 100.7 7.33j 6.50 7.3322  6.50 tan1 (6.50 / 7.33) 9.80 41.6o Mạch xoay chiều - sites.google.com/site/ncpdhbkhn 10 Sinusoid & Phasors 1. Sinusoids 2. Complex Numbers 3. Phasors 4. Phasor Relationships for Circuit Elements Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 11 Phasors (1) 2sint + 4sin(t+30o) xt() 2sin t X 2 0o 4sin(t+30o) yt() 4sin( t 30)o Y 4 30o 2sint xt() yt () XY 0 X  2 02o  Y  4 30o  3.46j 2 XY2 (3.46 jj 2)  5.46  2  5.82 20o xt( ) yt ( ) 5.82sin( t  20o ) xt() Xmm sin( t ) X X  Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 12 Phasors (2) Ex. 4sin(20t  40o ) 4 40o 6sin(314t  120o ) 6 120o 5cos(100t 20o ) 5sin(100t  110o ) 5 110o o 12 30o 12sin(t  30 ) o 24 60o 24sin(t 60 ) 34 j  5 53.1o 5sin(t  53.1o ) Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 13 Phasor Relationships for Circuit Elements (1) i R I R + v – + V – iIsin( t ) m vRIsin( t  ) vRi m V RIm  v(t) VIR I  Im  V Im 0 i(t)  ωt I  Re Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn0 14 Phasor Relationships for Circuit Elements (2) i L I jωL + v – + V – iIm sin( t ) o di vLItm sin(  90 ) VIjL vL dt i(t) v(t) Im V 0 φ ωt I Re 900  0 Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 15 Phasor Relationships for Circuit Elements (3) 1 i C I jC + v – + V – vVm sin( t ) o dv iCVtm sin(   90 ) IVjC iC dt 1 900 VI v(t) jC i(t) Im ωt I φ 0 V  Re Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn0 16 Phasor Relationships for Circuit Elements (4) i L C i R di i 1 vRi vL vidt dt C  + v – + v – + v – 1 I R I jωL i jC 1 VI R VI jL VI + V – + – jC V + v – V Im Im Im V I V I I  Re  Re  Re 0 0 0 Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 17 Phasor Relationships for Circuit Elements (5) Ex. 1 10sin5t V20Ω 6H 0.02F 20 20 – + 6H jL  jj56  30 1110 j10 0.02 F jC j50.02 j 10 0o 1 20 j30 o j0.1 10sin5t 10 0 – + + – + – Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 18 Phasor Relationships for Circuit Elements (6) Ex. 2 L + + R R e = 10sin10t V; j = 4sin(10t + 30o) A; 1 2 – 1 – e = 6sin(10t + 60o)V; L = 1 H; R = 1 Ω; 2 1 C e1 j e2 R2 = 5 Ω; C = 0.01 F. Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 19