Thevenin and Norton Equivalent Circuits

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Presentation transcript:

Thevenin and Norton Equivalent Circuits Read: pages 120 – 133 Problems: 4.53 and 4.68 (Due 10/29/01) Consider any circuit divided into separate circuits, where the two parts are connected at two points A and B as shown. Any Circuit Circuit A (Linear) Circuit B A B + VAB - IAB Fall 2001 ENGR-201 Thevenin's Theorem

ENGR-201 Thevenin's Theorem Everything inside the linear circuit (A) can be replaced by an equivalent circuit that consists of two components, an ideal voltage source in series with a resistor. Circuit A (Linear) Circuit B A B + VAB - IAB Circuit B A B + VAB - IAB VTH RTH Two circuits are equivalent if they produce the same load voltage and current (VAB and IAB) for every possible load condition. Fall 2001 ENGR-201 Thevenin's Theorem

ENGR-201 Thevenin's Theorem Norton’s Theorem Everything inside the linear circuit (A) can be replaced by an equivalent circuit that consists of two components, an ideal current source in parallel with a resistor. Circuit A (Linear) Circuit B A B + VAB - IAB Circuit B A B + VAB - IAB IN RN The trick is to find the values of VTH and RTH (IN and RN). Fall 2001 ENGR-201 Thevenin's Theorem

ENGR-201 Thevenin's Theorem Finding VTH and RTH Two circuits are equivalent if they produce the same load voltage and current (VAB and IAB) for every possible load condition. Consider one extreme load condition: open circuit where IAB = 0 A. Circuit A (Linear) A B + VAB = VOC - IAB = 0 A A B + VAB = VTH - IAB = 0 A VTH RTH If the two circuits are equivalent, then VTH = Voc. Fall 2001 ENGR-201 Thevenin's Theorem

ENGR-201 Thevenin's Theorem Finding VTH and RTH Consider the other extreme load condition: short circuit where VAB = 0 A. Circuit A (Linear) A B + VAB = 0 V - IAB = ISC A B + VAB = 0 - VTH RTH ISC If the two circuits are equivalent, then ISC = VTH/RTH  RTH = VTH/ ISC Fall 2001 ENGR-201 Thevenin's Theorem

Summary: Finding VTH and RTH In summary, VTH and RTH can be found by performing two tests on a linear circuit: Circuit A (Linear) A B + VAB - IAB A B + VAB - VTH RTH IAB = Open Circuit Test: VTH = VOC Short Circuit Test: RTH = VTH/ ISC Circuit A (Linear) A B + VAB = VOC - IAB = 0 A Circuit A (Linear) A B + VAB = 0 V - IAB = ISC Q: How practical are these two tests? Fall 2001 ENGR-201 Thevenin's Theorem

Norton’s Theorem: Finding IN and RN Using arguments similar to the ones for finding RTH an VTH, it can be shown that : IN = ISC and RN = RTH = VOC/ISC Circuit A (Linear) Circuit B A B + VAB - IAB Circuit B A B + VAB - IAB IN RN Fall 2001 ENGR-201 Thevenin's Theorem