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Src Transformation & Thevenin 2/19/20 Overview • Review concepts of • Voltage Equivalent Circuits: • Req Thevenin Theorem • Thevenin Equivalent Circuit • Equivalent Vs-with-series-R • “Equivalent” V-I-R Behavior to an actual power supply or EGR 220, Chapter 4.5 - 4.11 ‘driving’ circuit. (not section 4.9) February 20, 2020 2 1 2 Equivalent Resistance •Equivalent circuits concept • Equivalent resistance and voltage are terminal- dependent a) IndistinguishaBle from each other, • Ohm’s Law tells us that V = I*R so… b) …In terms of the V – I – Req characteristics, V • R = /I c) …At the specified terminals (nodes) • Electrical resistance is the ratio of: • The (open circuit) voltage across a pair of nodes to • The (short circuit) through the pair of nodes 3 4 3 4 1 2/19/20 Source Transformation & Equivalents Source Transformation • Voltage Vab and Req can Be measured across any nodes of any device or circuit. • We are interested in this measured orcalculated V – I – R behavior Isc v v = i R!!!!!!!!!!!!! ⇔ !!!!!!!!!!!!!i = s s s s R Req • Caution: maintain polarity of sources (“sc” = short circuit; “oc” = open circuit) 5 6 Your Mission Will your computer melt/do nothing? • Find two circuits with equivalent behavior with 1) 1 current source + 1 resistor 2) 1 voltage source + 1 resistor • If you design a power source with output of • I = ∞� à Your computer will melt Find Voc and Isc • V = 0� à Your computer will Be a paper weight 7 8 7 8 2 2/19/20 Will your computer melt/do nothing? Later: Can these be equivalent? Find Voc and Isc 9 10 9 10 Later: Can these be equivalent? Later: Can these be equivalent? 11 12 11 12 3 2/19/20 • Find i in the circuit below Source Transformation • Find i in the circuit below 13 14 Thevenin Equivalent Thevenin Equivalent – Process 1) Find RTh: ⏚ 2) Find VTh: 15 16 15 16 4 2/19/20 Thevenin Equivalent – Process Thevenin Equivalent – Process 1) Find RTh: 1) Find RTh: a) Remove the load resistor (if there is one) a) Remove the load resistor (if there is one) b) Set all (independent) sources equal to zero. b) Set all (independent) sources equal to zero. • V-source = 0V ð < open / short > • V-source = 0V ð < open / short > • I-source = 0A ð < open / short > • I-source = 0A ð < open / short > c) Find the equivalent resistance from the specified nodes c) Find the equivalent resistance from the specified nodes 2) Find VTh: a) Return to the original circuit, remove the load again, But keep all sources, and b) Find the open-circuit voltage across the specified nodes 17 18 17 18 Thevenin Equivalent Thevenin: Find VTh, RTh • A Thevenin equivalent circuit is • An equivalent version of a different circuit • …In terms of the V-I characteristic, at the specified nodes • Defined in terms of specified terminals/nodes • Consists of a single resistor, RTh, and a voltage source, VTh 19 20 19 20 5 2/19/20 Thevenin: Find VTh, RTh Thevenin: Find VTh, RTh 21 22 21 22 Thevenin: Find VTh, RTh Thevenin: Find VTh, RTh 23 24 23 24 6 2/19/20 Thevenin: Find VTh, RTh Thevenin: Find VTh, RTh • Try setting up a solution method for all our analysis techniques and think aBout pros and cons of the different approaches 25 26 25 26 Thevenin: Find VTh, RTh Thevenin: Find VTh, RTh 27 28 27 28 7 2/19/20 Thevenin: Find VTh, RTh Thevenin: Find VTh, RTh 29 30 29 30 * Maximum Power Transfer * Concept Question • Are equivalent circuits all the same? • How would we find the Pmax delivered to RL? • • Do not solve – discuss strategy (chapter example) Discuss VTh, RTh at a-b and b-c • What is RL for maximum power transfer, and how do you find the amount of power transferred? 31 32 31 32 8 2/19/20 Concept Question Thevenin Self-Review • Are equivalent circuits all the same? • What is a Thevenin Equivalent Circuit? • Discuss VTh, RTh at a-b and b-c • Draw a generic Thevenin equivalent circuit • What is RL for maximum power transfer, and how do you • Discuss and write down 3 good uses for a Thevenin find the amount of power transferred? equivalent circuit, or for the Thevenin theorem • How might you find the maximum power that can Be delivered to any load from any circuit? • Why is this an important question? 33 34 33 34 Norton Equivalent Circuit Summary • Source transformation • Equivalency VTh = voc • Equivalent resistance • Voltage – Current – Req behavior I N = isc • Thevenin equivalent circuit • V-source & series resistor v • Uses for Thevenin equivalent circuits oc • Only need to know the Norton equivalent exists. We will RTh = RN = Rin = focus on Thevenin isc 35 36 35 36 9 2/19/20 Questions? 37 10.
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