Lecture Electric circuit theory: Sinusoidal steady-state analysis - Nguyễn Công Phương

This chapter presents the following content: Sinusoidal steady-state analysis, Ohm’s law, Kirchhoff’s laws, impedance combinations, branch current method, node voltage method, mesh current method, superposition theorem, source transformation, Op Amp AC circuits.

Nguyễn Công Phương Electric Circuit Theory Sinusoidal Steady-State Analysis 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 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s Laws Impedance Combinations Branch Current Method Node Voltage Method Mesh Current Method Superposition Theorem Source Transformation Thévenin & Norton Equivalent Circuits Op Amp AC Circuits Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Sinusoidal Steady-State Analysis (1) 10sin5t V –+ 20i  20Ω di  idt  10sin 5t dt 0.02  i di d 2i i  20    50 cos 5t dt dt 0.02 i  I m sin(5t   ) 6H 0.02F 10 0o 20 –+  100 I m cos(5t   )  150 I m sin(5t   )  I  50 I m sin(5t   )  50 cos 5t 10 0o  2 I m sin(5t    135 )  sin(5t  90 ) o  2 I m   I m  0.35   o o o   135  90   45 j 30 o I 20  j 30  j 0.1 j 0.1  0.35  45o A  i  0.35sin(5t  45o ) A  i  0.35sin(5t  45o ) A Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Sinusoidal Steady-State Analysis (2) 10sin5t V –+ 20Ω i Transform to phasor domain Solve the problem using dc circuit analysis Transform the resulting phasor to the timedomain 6H 0.02F 10 0o j 30 20 –+ j 0.1 I I 10 0o 20  j 30  j 0.1  0.35  45o A  i  0.35sin(5t  45o ) A Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s Laws Impedance Combinations Branch Current Method Node Voltage Method Mesh Current Method Superposition Theorem Source Transformation Thévenin & Norton Equivalent Circuits Op Amp AC Circuits Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Ohm’s Law (1) VR  R I VR  RI VL  j L VL  j LI  I VC  I jC VC   jC I V  Z  V  ZI I Z: impedance (Ω) Admittance (S): Y  Z Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Ohm’s Law (2) V Z I VR R I  ZR  R VL  j L  Z L  j L I j VC   ZC   jC I jC C YR  R j YL   j L  L YC  jC Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Ohm’s Law (3)  0   Z L  j L j ZC  C ZL  ZC   Short circuit Open circuit ZL   ZC  Open circuit Short circuit Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Ohm’s Law (4) I + Z V – Z  R  jX R: resistance X: reactance Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 10 Ex Thévenin & Norton Equivalent Circuits (3) E  20  45o V; J  60o A; Z1 Z3 – Find the current of Z2? + Z1  12 ; Z  j10 ; Z3   j16 ; Z1 E Z3 Z2 J Zeq Zeq + Eeq I2 Z2 – Z1Z3 12( j16) Z eq    7.68  j 5.76  Z1  Z3 12  j16 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 57 Ex Thévenin & Norton Equivalent Circuits (4) E  20  45o V; J  60o A; a + Z1 E – Find the current of Z2? + Z1  12 ; Z  j10 ; Z3   j16 ; Z1 E Z3 Z2 J + Eeq – Z3 Zeq J – + Eeq – o E 20  45 J  60o Z1 12   54.38  140.4o V Eeq  Va  1 1   12  j16 Z1 Z3 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn I2 Z2 58 Ex Thévenin & Norton Equivalent Circuits (5) E  20  45o V; J  60o A; – Find the current of Z2? + Z1  12 ; Z  j10 ; Z3   j16 ; Z1 E Z3 Z2 J Z eq  7.68  j 5.76  Zeq + Eeq  54.38  140.4o V Eeq I2 Z2 – 54.38  140.4 o  I2    6.20  169.3o A Z eq  Z 7.68  j5.76  j10 Eeq Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 59 Thévenin & Norton Equivalent Circuits (6) E1  100 30o V; E4  80  45o V; J  5A; – Find the current of Z2? Z eq Z4 Z1 Z eq  Z1  E1 J Z3 + + Z1  10 Z  5; Z3  j 20 Z   j 25; Z4 Z2 Z1 E4 – Ex Z 3Z j 20(  j 25)  10   10  j100  Z3  Z j 20  j 25 Eeq  v a  v b Z3  Z1J  v a  E1  v a  E1  Z1J  137  j50 V J Z3 – E1 Z4 E4 v b  Z3I3  Z3  226  j 226 V Z3  Z4 + + Z1 a b  Eeq  E4 I  Eeq  v a  v b  363  j176 V Eeq Z eq  Z  363  j176  1.19  j 3.81A 10  j100  Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 60 – Ex Thévenin & Norton Equivalent Circuits (7) J3  E  E1  100 30o V; J  5A; J   45o A; Z1  10 Z  5; Z3  j 20 Z   j 25; Find the current of Z3? Z3 Z4 Z2 Z1 J4 Z eq Z eq  Z4  Z1 Z2 Eeq  v a  v b Z4 I3  10  Z1Z   j 25   3.33  j 25  10  Z1  Z2 Eeq Z eq  Z3  12.68  j 28.94 A a  E  J3  Eeq  Z4 Z2  1  E1  J3 Z1    va  Z1  v a  45,53  j16,67 V  Z1 Z     v b  141,  j16, V  v  J  J  Z b Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn b J4 61 Thévenin & Norton Equivalent Circuits (8) a E1  100 30 V; E4  80  45 V; J  5A; o Z ab Z4 E1 J Z3 + Find Zab? b Z1 + Z1  10 Z  5; Z3  j 20 Z   j 25; – o E4 Method Z4 Z1 Z3 Z 3Z j 20(  j 25) Zab  Z1   10   10  j100  Z3  Z j 20  j 25 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 62 – Ex Thévenin & Norton Equivalent Circuits (9) a E1  100 30 V; E4  80  45 V; J  5A; o b E1 I sc J Voc  363  j176 V va  Z4 Z3 + + I1 Z1 E4 Zab  E4 Vopen-circuit I short-circuit I sc  I1  J  1,39  j 3,77 A – – a E4 – Z3 J E1 Z4 Z3 J E1 Method + + Z1 a b  Voc  Z4 + Find Zab? b Z1 + Z1  10 Z  5; Z3  j 20 Z   j 25; – o – Ex E1 / Z1  J  E4 / Z4  150  j88 V 1/ Z1  1/ Z3  1/ Z4 I1  (E1  v a ) / Z1  6.39  j 3.77 A  Z ab  10  j100  Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 63 – & Norton Equivalent Circuits (10) a E1  100 30 V; E4  80  45 V; J  5A; o Z1 Iin Ein E1 Method +– Z4 Z3 Z4 Z3 J Z ab  + Find Zab? b Z1 + Z1  10 Z  5; Z3  j 20 Z   j 25; – o E4 Ein Iin Ein  100V 100 100 Iin    0.099  j 0.099A j 20(  j 25) ZZ 10  Z1  j 20  j 25 Z3  Z 100  Z ab   10  j100  0.099  j 0.099 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 64 – Ex Thévenin Ex Thévenin & Norton Equivalent Circuits (11) Find Zeq? Zeq  j6  Vopen-circuit +– I short-circuit (Vc  Vb )  16  j 6I  4I1  Voc  Vb  Vc 16 0o V  j8  I2 2I1 a 4 I1 Ic 30o A + b Voc –  Voc  16  j 6I  4I1 I1  30o I  I c  2I1   30o c  Voc  16  j   30o   30o  21.07  j 24.78 V Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 65 Ex Thévenin & Norton Equivalent Circuits (12) Find Zeq? Zeq  j6  Vopen-circuit +– I short-circuit I1  30o  I sc  o  I sc  30  I1  j8  I2 o  I  I1  30  2I1   3I1  I  30o 2I1 a 4 I1 b Ic o 30 A j 6I  4I1  16 0o I  I1  30o  I c  16 0o V Isc c  I1  0.67  j 0.41 A  I sc  30o  (0.67  j 0.41)  1.06  j1.41 A Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 66 Ex Thévenin & Norton Equivalent Circuits (13) j6  Find Zeq? 16 0o V +– Method  j8  2I1 a Zeq  Vopen-circuit 4 I1 b Ic 30o A c I short-circuit Voc  21.07  j 24.78 V I sc  1.06  j1.41 A  Zeq 21.07  j 24.78  1.06  j1.41  4.00  j18.00  Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 67 Ex Thévenin & Norton Equivalent Circuits (14) Find Zeq? a j6   j8  I1 Zeq 100  Iin 16 0o V +–  j8  2I1 a 2I1 Iin Ic b 100 V j 6( I r  I g )  4I r  100 I g  2I1  2I r 4 I1 +– 4 Method j6  b Ic 30o A c c  I r  1.18  j5.29 A  Iin  Zeq 100   4.00  j18.00  1.18  j5.29 Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 68 Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s Laws Impedance Combinations Branch Current Method Node Voltage Method Mesh Current Method Superposition Theorem Source Transformation Thévenin & Norton Equivalent Circuits Op Amp AC Circuits Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 69 Op Amp AC Circuits (1) Ex  j1000  Find Vo? k  Va 2000 – 0o o V + Vo  0 2000  j1000 + + 0o  Vo  j1000 Vb – 10  Vo –  j 2.5 0o  2.5 90o V Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 70 Op Amp AC Circuits (2) a – C1 C2 R1 e c – Va  Vb Vb b:  ZC R1 c : Vc  R3 R4 + + E  Va Va  Vo Va  Vb a:   ZC1 R2 ZC + b R2 Find vo? vo – Ex R3 Vo  Vb R3  R4  Vo  f (E, R1 , R2 , R3 , R4 , ZC1 , ZC ) Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 71 ... 45o A  i  0.35sin(5t  45o ) A Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s...  0  0  jC jC Z LC Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 11 Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s...  n )   I1  I   I n  Sinusoidal Steady-State Analysis - sites.google.com/site/ncpdhbkhn 14 Sinusoidal Steady-State Analysis 10 11 Sinusoidal Steady-State Analysis Ohm’s Law Kirchhoff’s