PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION C H A P T E R 3 Resistive Network Analysis Mc. Graw-Hill 1 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 2 Use of KCL in nodal analysis By KCL : i 1 – i 2 – i 3 = 0. In the node voltage method, we express KCL by va – v b vb – vc – R 1 R 2 va R 1 – v b R 3 vb i 1 – vd R 3 i 2 =0 vd i 3 R 2 vc Mc. Graw-Hill 2 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 3 Illustration of nodal analysis Node a R 2 i. S Node b R 1 R 3 Node c va i. S i 1 R 2 vb i 2 i 3 R 3 vc = 0 Mc. Graw-Hill 3 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 5 Node 1 R 3 R 2 R 1 R 4 I 2 I 1 R 3 Node 2 R 2 I 1 Mc. Graw-Hill R 1 R 4 I 2 4 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 8 Nodal analysis with voltage sources va + _ Mc. Graw-Hill R 1 v. S vb vc R 3 R 2 5 GIORGIO RIZZONI R 4 i. S © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 12 A two-mesh circuit R 1 v. S Mc. Graw-Hill +_ i 1 R 3 R 2 6 GIORGIO RIZZONI i 2 R 4 © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 13 Assignment of currents and voltages around mesh 1 Mesh 1: KVL requires that v S – v 1 – v 2 = 0, where v 1 = i 1 R 1 , v 2 = ( i 1 – i 2 ) R 1. R 3 R 1 + v. S +_ v 1 – + i 1 v 2 R 2 i 2 R 4 – Mc. Graw-Hill 7 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 14 Assignment of currents and voltages around mesh 3 Mesh 2: KVL requires that v 2 + v 3 + v 4 =0 where v 2 = ( i 2 – i 1 ) R 2, v 3 = i 2 R 3 , v 4 = i 2 R 4 R 1 R + v. S Mc. Graw-Hill + _ i 1 R 2 3 v 3 – v 2 + 8 GIORGIO RIZZONI i 2 – R 4 + v 4 – © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 18 Mesh analysis with current sources 5 + _ Mc. Graw-Hill 2 + 10 V i 1 vx – 2 A 4 i 2 9 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 26 The principle of superposition +_ v. B 2 + _ v. B 1 i R = v. B 1 + _ i. B 1 R + v. B 2 _+ i. B 2 R The net current through R is the sum of the individual source currents: i = i. B 1 +i. B 2. Mc. Graw-Hill 10 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 27 Zeroing voltage and current sources 1. In order to set a voltage source equal to zero, we replace it with a short circuit. R 1 v. S _+ R 1 i. S R 2 A circuit i. S The same circuit with R 2 v. S = 0 2. In order to set a current source equal to zero, we replace it with an open circuit. R 1 v. S _+ i. S A circuit Mc. Graw-Hill R 2 v S +_ The same circuit with 11 GIORGIO RIZZONI R 2 i. S = 0 © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 28 One-port network i + Linear v network – i Mc. Graw-Hill 12 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 29 Illustration of equivalent-circuit concept i + v. S + _ v R 1 R 2 R 3 – Source Mc. Graw-Hill Load 13 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 31 Illustration of Thevenin theorum i Source Mc. Graw-Hill + v – i RT Load v. T + _ 14 GIORGIO RIZZONI + v – Load © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 32 Illustration of Norton theorum i i Source Mc. Graw-Hill + v – – Load i. N 15 GIORGIO RIZZONI RN + v – Load © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 34 Equivalent resistance seen by the load R 3 R 1 a R 2 b R 3 a R 1 || R 2 RT b Mc. Graw-Hill 16 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 35 An alternative method of determining the Thevenin resistance What is the total resistance the current i S will encounter in flowing around the circuit? R 3 a + R 1 R 2 vx i. S – b R 3 R 1 R 2 i. S R T = R 1 || R 2 + R 3 Mc. Graw-Hill 17 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 46 R 1 R 3 i. L v. S Mc. Graw-Hill + _ R 2 18 GIORGIO RIZZONI RL © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 47 R 3 R 1 + v. S + _ R 2 v OC – Mc. Graw-Hill 19 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 48 R 1 R 3 + v. S + _ R 2 i Mc. Graw-Hill + v OC – 20 GIORGIO RIZZONI 0 V – + v OC – © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 49 A circuit and its Thevenin equivalent R 1 R 3+R 1||R 2 i. L v. S + _ R 2 A circuit Mc. Graw-Hill RL i. L v. S R 2 + _ R 1+R 2 RL Its Thévenin equivalent 21 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 57 Illustration of Norton equivalent circuit One-port network i. N Mc. Graw-Hill i SC RT = R N 22 GIORGIO RIZZONI i SC © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 58 Computation of Norton current Short circuit replacing the load R 1 v. S Mc. Graw-Hill + _ i v R 3 R 2 1 23 GIORGIO RIZZONI i i S C 2 © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 63 Equivalence of Thevenin and Norton representations RT One-port network v. T + _ Thévenin equivalent Mc. Graw-Hill 24 GIORGIO RIZZONI i. N RT Norton equivalent © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 64 Effect of source transformation R 1 v. S R 3 + _ R 2 i SC R 3 v. S R 1 Mc. Graw-Hill R 1 R 2 i SC 25 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 65 Subcircuits amenable to source transformation Node a a R or + _ v. S i. S or i S R R v. S _+ b b b Node b The venin é subcircuits Mc. Graw-Hill Norton subcircuits 26 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 71 Measurement of open-circuit voltage and short-circuit current a Unknown network Load An unknown network connected to a load Unknown network b a A “ i SC ” b Network connected for measurement of short-circuit current a + Unknown “ v. O C ” network rm V rm – b Network connected for measurement of open-circuit voltage Mc. Graw-Hill 27 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 73 Power transfer between source and load Practical source Load RT v. T + _ RL RL i. L Source equivalent Given v. T and RT , what value of R L will allow for maximum power transfer? Mc. Graw-Hill 28 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 74 Source loading effects vint + – RT v. T + _ RL i Source Load i i. N + int RT v RL – Source Mc. Graw-Hill 29 GIORGIO RIZZONI Load © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figeure 3. 77 Representation of nonlinear element in a linear circuit Nonlinear element as a load. We wish to solve for v x and i x. RT ix + v. T + _ vx Nonlinear element – Mc. Graw-Hill 30 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 78 Load line i. X v. T RT Load-line equation: ix = – v. T 1 vx + RT RT – 1 RT v. T Mc. Graw-Hill 31 GIORGIO RIZZONI vx © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 79 Graphical solution equations 3. 48 and 3. 49 ix v. T RT i-v curve of “exponential resistor ” i = I o e v, v > 0 Solution v. T 1 Load-line equation: i x = v + RT x RT v. T Mc. Graw-Hill vx 32 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 3. 80 Transformation of nonlinear circuit of Thevenin equivalent + Linear network v RT ix Nonlinear load x + v. T + _ – Mc. Graw-Hill ix Nonlinear x load v – 33 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000