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Lecture Electric circuit theory: Circuit theorems presents the following content: Source transformation, linearity and superposition, Thévenin Equivalent Subcircuits, Norton Equivalent Subcircuits, maximum power transfer.
Nguyễn Công Phương Electric Circuit Theory Circuit Theorems 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 Sinusoidal Steady State Analysis X AC Power Analysis XI Three-phase Circuits XII Magnetically Coupled Circuits XIII.Frequency Response XIV.The Laplace Transform XV Two-port Networks Circuit Theorems - sites.google.com/site/ncpdhbkhn Circuit Theorems Source Transformation Linearity and Superposition Thévenin Equivalent Subcircuits Norton Equivalent Subcircuits Maximum Power Transfer Circuit Theorems - sites.google.com/site/ncpdhbkhn Source Transformation (1) R + R J – E E J= R E = RJ E = Ri + v E v i= − R R Circuit Theorems - sites.google.com/site/ncpdhbkhn Source Transformation (2) Ex a J = A; R1 = Ω; R2 = Ω; find i2? i2 R1 J E = R1 J = × = V R2 b E i2 = = = 0.8 A R1 + R2 + a + + J E R – R E J= R R1 E E = RJ Circuit Theorems - sites.google.com/site/ncpdhbkhn i2 R2 b – Source Transformation (3) R1 Ex R3 a Find the current i3 b i3 R2 + – E1 R4 J + – E2 c Circuit Theorems - sites.google.com/site/ncpdhbkhn Circuit Theorems Source Transformation Linearity and Superposition Thévenin Equivalent Subcircuits Norton Equivalent Subcircuits Maximum Power Transfer Circuit Theorems - sites.google.com/site/ncpdhbkhn Linearity and Superposition (1) E i –+ + R2 i R2 – R1 J E R1 –+ R1J i= R1 J + E R1 J E = + R1 + R2 R1 + R2 R1 + R2 = i E =0 E i E =0 J R1 R2 – + R1 Circuit Theorems - sites.google.com/site/ncpdhbkhn + i J =0 i J =0 R2 Linearity and Superposition (2) y = a1 x1 + a2 x2 + + an xn = y1 + y2 + + yn yi = y x = , k ≠ i k Circuit Theorems - sites.google.com/site/ncpdhbkhn Linear and Superposition (3) + + deactivated v=0 – – i=0 deactivated Circuit Theorems - sites.google.com/site/ncpdhbkhn 10 Norton Equivalent Subcircuits (1) i i + v + RL Jeq Req – v RL – Jeq : the short-circuit through the terminals Req : the input or equivalent resistance at the terminals when the independent sources are deactivated Circuit Theorems - sites.google.com/site/ncpdhbkhn 38 Norton Equivalent Subcircuits (2) Jeq : the short-circuit through the terminals + R1 – R2 E J eq = iR = R2 E R2 R3 Req R3 E 30 = R1 10 = 3A Req : the input or equivalent resistance at the terminals when the independent sources are deactivated R1 R1 + R1 = 10Ω, R2 = 20Ω, R3 = 30Ω, E = 30V Find the current of R3? – Ex Jeq 1 + v = J eq Req Req R3 → v = 13.36 V = 6.67Ω v → i3 = = 0.55 A R3 Circuit Theorems - sites.google.com/site/ncpdhbkhn 39 R1 × R2 = R1 + R2 Norton Equivalent Subcircuits (3) Ex a E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find the Norton equivalent subcircuit? b R1 + E R2 R3 J – c Jeq : the short-circuit through the terminals b a b R1 + E Jeq R2 J R3 Jeq Req c c Circuit Theorems - sites.google.com/site/ncpdhbkhn 40 – Norton Equivalent Subcircuits (4) Ex J eq = i2 E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find the Norton equivalent subcircuit? 1 E + va = + J R1 R1 R2 Jeq : the short-circuit through the terminals 16 1 1 → + va = + 4 6 i2 a b R1 + E → va = 14.40 V R2 J R3 Jeq c → i2 = va 14.40 = = 2.40 A R2 → J eq = 2.40 A Circuit Theorems - sites.google.com/site/ncpdhbkhn 41 – Norton Equivalent Subcircuits (5) Ex a E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find the Norton equivalent subcircuit? b R1 + E R2 R3 J – c Req : the input or equivalent resistance at the terminals when the independent sources are deactivated a R1 b b R2 R3 Jeq Req Req c c Circuit Theorems - sites.google.com/site/ncpdhbkhn 42 Norton Equivalent Subcircuits (6) Ex E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find the Norton equivalent subcircuit? Req = ( R1 + R2 ) // R3 R1 + R2 ) R3 ( = R1 + R2 + R3 Req : the input or equivalent resistance at the terminals when the independent sources are deactivated a R1 b R2 R3 Req (4 + 6)8 = 4+ 6+8 = 4.44 Ω c Circuit Theorems - sites.google.com/site/ncpdhbkhn 43 b R1 + E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find the Norton equivalent subcircuit? a – Ex Norton Equivalent Subcircuits (7) E R2 R3 J c b J eq = 2.40 A Req = 4.44 Ω Jeq Req c Circuit Theorems - sites.google.com/site/ncpdhbkhn 44 Norton Equivalent Subcircuits (8) Ex b a + – E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; RL = Ω; find i2? R1 E R2 J i2 RL R3 c a R1 Req b i2 RL R3 c a i2 Jeq Req = ( R3 // RL ) + R1 R3 RL 8×5 = + R1 = + = 7.08 Ω R3 + RL 8+5 Circuit Theorems - sites.google.com/site/ncpdhbkhn Req R2 b 45 b a + E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; RL = Ω; find i2? – Ex Norton Equivalent Subcircuits (9) R1 E R2 J i2 RL R3 c b a + i1 R1 E Jeq J RL R3 a i2 – c J eq = i1 + J Jeq Req R2 1 1 E + + v = + J → va = 10.43V b a R1 R1 R3 RL E − va → i1 = = 1.39 A → J eq = 1.39 + = 3.39 A R1 Circuit Theorems - sites.google.com/site/ncpdhbkhn 46 Norton Equivalent Subcircuits (10) Ex b a R1 + E – E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; RL = Ω; find i2? R2 J i2 RL R3 c J eq = 3.39 A Req = 7.08Ω – = 24 V + Eeq = Req J eq a a Req Eeq i2 i2 R2 Jeq b Req R2 b Eeq 24 i2 = = = 1.84 A Req + R2 7.08 + Circuit Theorems - sites.google.com/site/ncpdhbkhn 47 Thévenin & Norton Equivalent Subcircuits (1) i + v RL – Req i i Eeq = Req Jeq + + – Eeq v – RL + Jeq Req = Eeq J eq Req v RL – vopen-circuit Eeq = vopen-circuit → Req = i short-circuit Jeq = ishort-circuit Circuit Theorems - sites.google.com/site/ncpdhbkhn 48 Thévenin & Norton Equivalent Subcircuits (2) a Ex R1 ishort-circuit = – Req = + E = 16 V; J = A; R1 = Ω; R2 = Ω; R3 = Ω; Rt = Ω; find Req? vopen-circuit b E R2 J R3 c Eeq J eq Eeq = 10.67 V → Req 10.67 = = 4.44 Ω 2.40 J eq = 2.40 A Circuit Theorems - sites.google.com/site/ncpdhbkhn 49 Circuit Theorems Source Transformation Linearity and Superposition Thévenin Equivalent Subcircuits Norton Equivalent Subcircuits Maximum Power Transfer Circuit Theorems - sites.google.com/site/ncpdhbkhn 50 Maximum Power Transfer (1) Req i + Eeq – Eeq → pL = R Req + RL L dpL =0 dRL + pL = i RL Eeq iL = Req + RL L v RL – ( R + R ) − RL ( Req + RL ) dpL eq L → = Eeq dRL ( Req + RL ) Req + RL − RL Req − RL 2 = Eeq = Eeq =0 3 ( Req + RL ) ( Req + RL ) RL = Req Circuit Theorems - sites.google.com/site/ncpdhbkhn 51 Maximum Power Transfer (2) Ex E = 16 V; R1 = Ω; R2 = Ω; R3 = Ω; R4 = 10 Ω; Find the value of RL for maximum power transfer? R1 E +– RL = Req R4 4.6 2.10 = + + + 10 = 4, 07 Ω Req Eeq – Req R1 R2 RR + R1 + R2 R3 + R4 R4 + R3 R2 RL R3 Req = R1 E R2 i + v RL – → RL = 4.07 Ω Circuit Theorems - sites.google.com/site/ncpdhbkhn 52 ... 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... Three-phase Circuits XII Magnetically Coupled Circuits XIII.Frequency Response XIV.The Laplace Transform XV Two-port Networks Circuit Theorems - sites.google.com/site/ncpdhbkhn Circuit Theorems. .. Transfer Circuit Theorems - sites.google.com/site/ncpdhbkhn 20 Thévenin Equivalent Subcircuits (1) Req + – Eeq Circuit Theorems - sites.google.com/site/ncpdhbkhn 21 Thévenin Equivalent Subcircuits