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Lecture Chapter 4C Thevenin Equivalent Circuits

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Problem 1Problem 1 Two measurements are made on the same "linear mystery circuit" as shown. What would be the measured current Im if the 50-ohm resistor is replaced by a short circuit? ( 96 Amps)

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Thevenin: simple model for complex circuit To find Thevenin Equivalent at a terminal a-b: 1.Find V open circuit 2.Find I short circuit 3.Vth = Voc 4.Rth = Voc/Isc Vth = Voc = 30V; Rth = 120Ω

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"Lookback" resistance Another way to find Rth – Turn off all sources Replace Voltage source with short Replace Current source with open Calculate Rab, equivalent resistance

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Find Thevenin Eq at a-b note how R4 does not affect Voc! [Vth=__Rth=8]

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Problem 3Problem 3 Find the Thèvenin equivalent circuit at the terminals A-B. Rt = 25Ω;Vt = 160V

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Norton Equivalent Norton vs Thevenin Equivalents – same at a-b

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Thevenin and Norton Equivalents would be indistinguishable at a-b To find Norton Equivalent, find Thevenin, set In = Vth/Rth, and Rn = Rth this is the basis of the "source transform" method, which can help simplify circuits

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Given Thevenin Equivalent, What is the Norton Equivalent?

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Find Thevenin by "Source Transform"

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Another Way to Look at Thevenin Equivalents All our circuit elements and laws are linear – Vs = 9V, Is = 10A, V=IR, sum of v= 0, sum of i=0 We can model the V-I curve of any linear circuit – define equation of line: slope and a y-offset Rth and Vth

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Do Handouts Problem 1/2

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More Thevenin Equivalents Dependent Sources – Find Voc the same (use NV, MC, Source Xform, etc) – For Rth: You can always find Isc, then Rth = Voc/Isc OR Turn off Independent sources, – hook up a “Test Voltage Source” Vt (not Vth!!) – Find current produced by test source It, » Then Rth = Vt/It

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Find Thevenin at a-b (Vth=8, Rth=1) Option 1) Find Voc, Isc 24

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Option 2, Rth by Test Source 24

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Problem 2Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V. (Rt = 9.74) Circuits with only dependent sources are resistive. MUST hook up external test source

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One More (if time permits)

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Do Handout problems 3 and 4

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Max Power Transfer Q: What is the most power we can deliver to RL?

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RL gets Max Power when RL = Rth Thevenin Eq of circuit in previous slide:

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Example: Max power RL can get?

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Find io by Superposition Fundamental theorem in physics, – applies to ccts too.

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Superposition continued Activate each source separately, add results

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Handouts

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1) (ans: 48V, 16 Ohms)

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2) Find Thevenin Equivalent to left of 8 ohm R This can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

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3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H. (Vth=12, Rth=34)Problem 1

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4) Problem 14) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

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Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

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Problem 2Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)

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Find Thevenin at a-b (Vth=8, Rth=1) Option 1) Find Voc, Isc 24

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Option 2, Rth by Test Source 24

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Problem 2Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V. (Rt = 9.74) Circuits with only dependent sources are resistive. MUST hook up external test source

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One More (if time permits)

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Do Handout problems 3 and 4

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Max Power Transfer Q: What is the most power we can deliver to RL?

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RL gets Max Power when RL = Rth Thevenin Eq of circuit in previous slide:

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Example: Max power RL can get?

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Find io by Superposition Fundamental theorem in physics, – applies to ccts too.

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Superposition continued Activate each source separately, add results

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Handouts

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1) (ans: 48V, 16 Ohms)

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2) Find Thevenin Equivalent to left of 8 ohm R This can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

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3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H. (Vth=12, Rth=34)Problem 1

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4) Problem 14) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

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Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

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Problem 2Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)

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Thevenin’s Theorem Statement: Thevenin’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources.

Thevenin’s Theorem Statement: Thevenin’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources.

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