5: Thévenin and Norton Equivalents • Equivalent Networks • Thévenin Equivalent • Thévenin Properties • Determining Thévenin • Complicated Circuits • Norton Equivalent • Power Transfer • Source Transformation • Source Rearrangement • Series Rearrangement 5: Thévenin and Norton • Summary Equivalents E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 1 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent • Thévenin Properties • Determining Thévenin • Complicated Circuits • Norton Equivalent • Power Transfer • Source Transformation • Source Rearrangement • Series Rearrangement • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement • Series Rearrangement • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement Eliminating X gives: V = 3I + 6. • Series Rearrangement • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement Eliminating X gives: V = 3I + 6. • Series Rearrangement a b • Summary There are infinitely many networks with the same values of and : E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement Eliminating X gives: V = 3I + 6. • Series Rearrangement a b • Summary There are infinitely many networks with the same values of and : E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement Eliminating X gives: V = 3I + 6. • Series Rearrangement a b • Summary There are infinitely many networks with the same values of and : These four shaded networks are equivalent because the relationship between V and I is exactly the same in each case. E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Equivalent Networks 5: Thévenin and Norton V aI b Equivalents From linearity theorem: = + . • Equivalent Networks • Thévenin Equivalent Use nodal analysis: • Thévenin Properties X − X−V • Determining Thévenin KCL@X: 1 6 + 2 = 0 • Complicated Circuits − • Norton Equivalent KCL@V: V X − I = 0 • Power Transfer 2 • Source Transformation • Source Rearrangement Eliminating X gives: V = 3I + 6. • Series Rearrangement a b • Summary There are infinitely many networks with the same values of and : These four shaded networks are equivalent because the relationship between V and I is exactly the same in each case. The last two are particularly simple and are respectively called the Norton and Thévenin equivalent networks. E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 2 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer • Source Transformation • Source Rearrangement • Series Rearrangement • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer We can replace the shaded part of the • Source Transformation circuit with its Thévenin equivalent • Source Rearrangement • Series Rearrangement network. • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer We can replace the shaded part of the • Source Transformation circuit with its Thévenin equivalent • Source Rearrangement • Series Rearrangement network. • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer We can replace the shaded part of the • Source Transformation circuit with its Thévenin equivalent • Source Rearrangement • Series Rearrangement network. • Summary The voltages and currents in the unshaded part of the circuit will be identical in both circuits. E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer We can replace the shaded part of the • Source Transformation circuit with its Thévenin equivalent • Source Rearrangement • Series Rearrangement network. • Summary The voltages and currents in the unshaded part of the circuit will be identical in both circuits. The new components are called the Thévenin equivalent resistance, RTh, and the Thévenin equivalent voltage, VTh, of the original network. E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Equivalent 5: Thévenin and Norton Equivalents Thévenin Theorem: Any two-terminal network consisting of resistors, fixed • Equivalent Networks voltage/current sources and linear dependent sources is externally • Thévenin Equivalent • Thévenin Properties equivalent to a circuit consisting of a resistor in series with a fixed voltage • Determining Thévenin source. • Complicated Circuits • Norton Equivalent • Power Transfer We can replace the shaded part of the • Source Transformation circuit with its Thévenin equivalent • Source Rearrangement • Series Rearrangement network. • Summary The voltages and currents in the unshaded part of the circuit will be identical in both circuits. The new components are called the Thévenin equivalent resistance, RTh, and the Thévenin equivalent voltage, VTh, of the original network. This is often a useful way to simplify a complicated circuit (provided that you do not want to know the voltages and currents in the shaded part). E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 3 / 12 Thévenin Circuit Properties 5: Thévenin and Norton Equivalents A Thévenin equivalent circuit has • Equivalent Networks a straight line characteristic with • Thévenin Equivalent • Thévenin Properties the equation: • Determining Thévenin V R I V • Complicated Circuits = Th + Th • Norton Equivalent • Power Transfer • Source Transformation • Source Rearrangement • Series Rearrangement • Summary E1.1 Analysis of Circuits (2017-10110) Thevenin and Norton: 5 – 4 / 12 Thévenin Circuit Properties 5: Thévenin and Norton 1 Equivalents A Thévenin equivalent circuit has • Equivalent Networks a straight line characteristic with 0 • Thévenin Equivalent • Thévenin