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Lecture Electric circuit theory - Two-port networks presents the following content: Parameters, relationships between parameters, two-port network analysis, interconnection of networks, equivalent two-port networks of magnetically coupled circuits,...
Nguyễn Công Phương Electric Circuit Theory Two-port Networks 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 Two-port Networks - sites.google.com/site/ncpdhbkhn Two-port Network Introduction Parameters Relationships between Parameters Two-port Network Analysis Interconnection of Networks T & П Networks Equivalent Two-port Networks of Magnetically Coupled Circuits Input Impedance Transfer Function Two-port Networks - sites.google.com/site/ncpdhbkhn Introduction I1 I2 + + Linear Network – I1 V2 – V1 I2 Two-port Networks - sites.google.com/site/ncpdhbkhn Two-port Network Introduction Parameters a) b) c) d) e) f) Impedance z Admittance y Hybrid h Inverse Hybrid g Transmission T Inverse Transmission t Relationships between Parameters Two-port Network Analysis Interconnection of Networks T & П Networks Equivalent Two-port Networks of Magnetically Coupled Circuits Input Impedance Transfer Function Two-port Networks - sites.google.com/site/ncpdhbkhn Impedance Parameters (1) I1 I2 + + Linear Network V1 – I1 V2 – V1 = z11I1 + z12I V2 = z 21I1 + z 22I I2 V1 z11 z12 I1 I1 = [z ] V = z 21 z 22 I I2 Two-port Networks - sites.google.com/site/ncpdhbkhn Impedance Parameters (2) I1 I2 – I1 I2 I1 I2 = Linear Network I Two-port Networks - sites.google.com/site/ncpdhbkhn V2 – V1 – I2 =0 I2 = – V2 I1 V2 + V1 I1 Linear Network V1 + z11 = V1 = z11I1 → → V2 = z 21I1 z = 21 + + V1 = z11I1 + z12I V2 = z 21I1 + z 22I I2 = Impedance Parameters (3) I1 I2 Linear Network V2 – V1 – I1 I2 I1 = I2 + Linear Network – Two-port Networks - sites.google.com/site/ncpdhbkhn V2 I2 – V1 + V1 z12 = I I =0 V1 = z12I → → V2 = z 22I z = V2 22 I I1 =0 + + V1 = z11I1 + z12I V2 = z 21I1 + z 22I I1 = Impedance Parameters (4) I1 I2 I2 =0 V2 I1 I2 =0 I1 =0 V2 z 22 = I I =0 – V1 I1 Linear Network V1 I1 V2 – z11 = z = 21 + + V1 = z11I1 + z12I V2 = z 21I1 + z 22I I2 V1 z12 = I2 Two-port Networks - sites.google.com/site/ncpdhbkhn Impedance Parameters (5) Ex Find [z]? I1 10Ω I2 = 30Ω 20Ω + 30Ω V2 20Ω I1 + + [z] V1 V2 – V1 z11 = I1 I2 I =0 V1 = (10 + 20)I1 = 30I1 30I1 → z11 = = 30 Ω I1 – 10Ω – + – V1 I1 I2 V1 = z11I1 + z12 I2 V2 = z 21I1 + z 22I2 Two-port Networks - sites.google.com/site/ncpdhbkhn 10 Input Impedance (5) ( Z + Z a ) Zc + Zb Z + Z a + Zc E – Method Z eq = V1 V2 I1 I2 Z + Z2 = Z*eq + What Z2 will absorb maximum power from the circuit? I2 + Z = 15 + j 25 Ω I1 – E = 220 V 30 20 z= ; 20 50 – Ex Z a = 10 Ω Z c = 20 Ω Z Z b = 30 Ω → Z eq = Za Z2 Zb Zc (15 + j 25 + 10)20 + 30 = 43.21 + j 3.77 Ω → Z = 43.21 − j 3.77 Ω 15 + j 25 + 10 + 20 Two-port Networks - sites.google.com/site/ncpdhbkhn 79 Input Impedance (6) – I2 I1 I2 V1 – I1 Linear Network Two-port Networks - sites.google.com/site/ncpdhbkhn V2 – Z2 + → Z 2in −DZ1 − B = CZ1 + A I1 + V2 DV1 − BI1 Z 2in = = − I2 −CV1 + AI1 V1 = − Z1I1 Z2 V2 – → Z1in Linear Network V1 AZ − B = CZ − D I2 + V1 AV2 − BI2 = I1 CV2 − DI2 V2 = Z2I Z1in = I1 + V1 = AV2 − BI I1 = CV2 − DI I2 80 Input Impedance (7) Z1in AZ − B = CZ − D → Z1sc Z2 = (short-circuit) AZ − B Z1in = CZ2 − D Z → ∞ (open-circuit) Z 2in = −DZ1 − B CZ1 + A B = D → Z1oc = A C → Z 2sc Z1 = (short-circuit) −DZ1 − B Z 2in = CZ1 + A Z1 → ∞(open-circuit) −B = A → Z2oc −D = C Two-port Networks - sites.google.com/site/ncpdhbkhn 81 Input Impedance (8) Z1sc B = D Z1oc A = C Z 2sc = Z 2oc −B A −D = C Z1sc Z1oc A = Z 2sc ( Z1oc − Z1sc ) B = − AZ sc → A C = Z 1oc B D = − Z 1sc Two-port Networks - sites.google.com/site/ncpdhbkhn 82 Input Impedance (9) Z1 Ex Find T? V1 A= V2 a Z3 d Z7 e Z4 Z6 Z2 I =0 b Z1sc Z1oc Z2sc ( Z1oc − Z1sc ) A= c Z8 Z5 b Z1sc = ? B = − AZ2 sc C= A Z1oc D=− Z1sc = Zab = {[(Z7//Z6//Z5)+Z3]//Z4//Z2}+Z1 B Z1sc Two-port Networks - sites.google.com/site/ncpdhbkhn 83 Input Impedance (10) Z1 Ex Find T? a c Z3 d Z7 e Z4 Z6 Z2 b Z1sc Z1oc Z2sc ( Z1oc − Z1sc ) A= Z8 Z5 b Z1oc = ? B = − AZ2 sc C= A Z1oc D=− Z1oc = Zab = [{[(Z7+Z8)//Z6//Z5]+Z3}//Z4//Z2]+Z1 B Z1sc Two-port Networks - sites.google.com/site/ncpdhbkhn 84 Input Impedance (11) Z1 Ex Find T? a c Z3 d Z7 e Z4 Z6 Z2 b Z1sc Z1oc Z2sc ( Z1oc − Z1sc ) A= Z8 Z5 b Z2sc = ? B = − AZ2 sc C= A Z1oc D=− Z2sc = Zeb = [{[(Z1//Z2//Z4)+Z3]//Z5//Z6}+Z7]//Z8 B Z1sc Two-port Networks - sites.google.com/site/ncpdhbkhn 85 Input Impedance (12) Z1 Ex Find T? a c Z3 d Z7 e Z4 Z6 Z2 Z1sc Z1oc Z2sc Z1sc Z1oc A = Z 2sc ( Z1oc − Z1sc ) B = − AZ sc → A C = Z1oc B D = − Z1sc b Z8 Z5 Two-port Networks - sites.google.com/site/ncpdhbkhn b 86 Two-port Network Introduction Parameters Relationships between Parameters Two-port Network Analysis Interconnection of Networks T & П Networks Equivalent Two-port Networks of Magnetically Coupled Circuits Input Impedance Transfer Function Two-port Networks - sites.google.com/site/ncpdhbkhn 87 Transfer Function (1) • Voltage transfer function: V2 Kv = V1 • Current transfer function: I2 Ki = I1 • Voltage – current transfer function: V2 K vi = I1 Two-port Networks - sites.google.com/site/ncpdhbkhn 88 Transfer Function (2) I2 + E [z] V2 ZL – V1 = z11I1 + z12 I V2 = z 21I1 + z 22 I V1 = E V2 = − Z L I I1 + 30 20 E = 220 V z= ; 20 50 Z L = 15 + j 25 Ω Find Kv, Ki, Kvi? – Ex I1 I2 z 22 + Z L I1 = z z − z z + z Z E 11 22 12 21 11 L E = z11I1 + z12 I → → − z 21 I = − Z L I = z 21I1 + z 22 I E z11z 22 − z12 z 21 + z11Z L Two-port Networks - sites.google.com/site/ncpdhbkhn 89 Transfer Function (3) V2 = − Z L I E [z] V2 ZL – − z 21 I2 = E z11z 22 − z12 z 21 + z11Z L I2 + z 22 + Z L I1 = E z11z 22 − z12 z 21 + z11Z L I1 + 30 20 E = 220 V z= ; 20 50 Z L = 15 + j 25 Ω Find Kv, Ki, Kvi? – Ex I1 I2 z 21Z L → V2 = E z11z 22 − z12 z 21 + z11Z L z 21Z L V2 → Kv = = = 0.28 + j 0.19 V1 z11z 22 − z12z 21 + z11Z L Two-port Networks - sites.google.com/site/ncpdhbkhn 90 Transfer Function (4) I2 + E [z] V2 ZL – z 22 + Z L I1 = E z11z 22 − z12 z 21 + z11Z L I1 + 30 20 E = 220 V z= ; 20 50 Z L = 15 + j 25 Ω Find Kv, Ki, Kvi? – Ex I1 I2 − z 21 I2 = E → K = − z 21 = −0.27 + j 0.10 i z11z 22 − z12 z 21 + z11Z L Z22 + Z L I2 Ki = I1 Two-port Networks - sites.google.com/site/ncpdhbkhn 91 Transfer Function (5) I2 + E [z] V2 ZL – z 22 + Z L I1 = E z11z 22 − z12 z 21 + z11Z L I1 + 30 20 E = 220 V z= ; 20 50 Z L = 15 + j 25 Ω Find Kv, Ki, Kvi? – Ex I1 I2 z 21Z L V2 = E → K = z 21Z L vi z11z 22 − z12 z 21 + z11Z L z 22 + Z L V2 = 6.60 + j 5.15 Ω K vi = I1 Two-port Networks - sites.google.com/site/ncpdhbkhn 92 Transfer Function (6) Ex I1 I2 + E = 380 V; Z L = 15 + j 25 Ω; K v = 0.28 + j 0.19; Find V2? + E [z] V2 ZL – – I1 V2 Kv = V1 V1 = E I2 → V2 = K v E = (0.28 + j 0.19) × 380 = 107.7 + j 70.5 V → V2 = 128.7 V Two-port Networks - sites.google.com/site/ncpdhbkhn 93 ... XI Three-phase Circuits XII Magnetically Coupled Circuits XIII.Frequency Response XIV.The Laplace Transform XV Two-port Networks Two-port Networks - sites.google.com/site/ncpdhbkhn Two-port Network... Parameters Two-port Network Analysis Interconnection of Networks T & П Networks Equivalent Two-port Networks of Magnetically Coupled Circuits Input Impedance Transfer Function Two-port Networks - sites.google.com/site/ncpdhbkhn... Parameters Two-port Network Analysis Interconnection of Networks T & П Networks Equivalent Two-port Networks of Magnetically Coupled Circuits Input Impedance Transfer Function Two-port Networks - sites.google.com/site/ncpdhbkhn