Equivalent Circuits: Voltage R eq Thevenin Theorem Thevenin - PowerPoint PPT Presentation

2/19/20 Overview • Review concepts of Equivalent Circuits: • Voltage • R eq Thevenin Theorem • Thevenin Equivalent Circuit • Equivalent V s -with-series-R • “Equivalent” V-I-R behavior to an actual power supply or ‘driving’ circuit. EGR 220, Chapter 4.5 - 4.11 (not section 4.9) February 20, 2020 2 1 2 Equivalent Resistance • Equivalent circuits concept • Equivalent resistance and voltage are terminal- a) Indistinguishable from each other, dependent • Ohm’s Law tells us that V = I*R so… b) …In terms of the V – I – R eq characteristics, • R = V / 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 4 3 3 4 1

2/19/20 Source Transformation & Equivalents Source Transformation Voltage V ab and R eq can be measured across any • nodes of any device or circuit. We are interested in this measured orcalculated • V – I – R behavior I sc v s = i s R !!!!!!!!!!!!! ⇔ !!!!!!!!!!!!! i s = v s R R eq • 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 = ∞𝐵 à Your computer will melt Find V oc and I sc • V = 0𝑊 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 V oc and I sc 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 R Th : ⏚ 2) Find V Th : 15 16 15 16 4

2/19/20 Thevenin Equivalent – Process Thevenin Equivalent – Process 1) Find R Th : 1) Find R Th : 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 V Th : 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 V Th , R Th • 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, R Th , and a voltage source, V Th 19 20 19 20 5

2/19/20 Thevenin: Find V Th , R Th Thevenin: Find V Th , R Th 21 22 21 22 Thevenin: Find V Th , R Th Thevenin: Find V Th , R Th 23 24 23 24 6

2/19/20 Thevenin: Find V Th , R Th Thevenin: Find V Th , R Th • 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 V Th , R Th Thevenin: Find V Th , R Th 27 28 27 28 7

2/19/20 Thevenin: Find V Th , R Th Thevenin: Find V Th , R Th 29 30 29 30 * Maximum Power Transfer * Concept Question • Are equivalent circuits all the same? • How would we find the P max delivered to R L ? • Discuss V Th , R Th at a-b and b-c • Do not solve – discuss strategy (chapter example) • What is R L for maximum power transfer, and how do you find the amount of power transferred? 31 32 31 32 8

2/19/20 Thevenin Self-Review Concept Question • Are equivalent circuits all the same? • What is a Thevenin Equivalent Circuit? • Discuss V Th , R Th at a-b and b-c • Draw a generic Thevenin equivalent circuit • What is R L for maximum power transfer, and how do you • Discuss and write down 3 good uses for a Thevenin equivalent circuit, or for the Thevenin theorem find the amount of power transferred? • 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 = V v • Equivalency Th oc • Equivalent resistance • Voltage – Current – R eq behavior = I i • Thevenin equivalent circuit N sc • V-source & series resistor v • Uses for Thevenin equivalent circuits = = = R R R oc • Only need to know the Norton equivalent exists. We will Th N in focus on Thevenin i sc 35 36 35 36 9

2/19/20 Questions? 37 10