Thevenin, Norton and Maximum Power Transfer Theorems.

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CHAPTER 12 Thevenin, Norton and Maximum Power Transfer Theorems

Transcript of Thevenin, Norton and Maximum Power Transfer Theorems.

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CHAPTER 12Thevenin, Norton and Maximum

Power Transfer Theorems

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Thevenin’s Theorem

Why Thevenin’s Theorem is useful

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What is Thevenin’s Theorem?

Everything in the original circuit, except the load, maybe replaced by an equivalent circuit. The equivalent circuit consists of a series combination of a voltage source and a resistance.

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Steps to make a Thevenin Circuit

Write these on white board

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Calculating RTHEVENIN (RTH)

RTH = 5kΩ

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Calculating VTHEVENIN (VTH)

VTH = 10V

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Equivalent Thevenin Circuit

Now you can place any load in the circuit you want and the calculations are EASY!

=10kΩ.66mA

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Using the Thevenin Theorem

Solving for VTH

10V 5V

VTH = VA – VB = 5V

Determine VTH

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Using the Thevenin Theorem

Determine RTH

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Solving for RTH

What is the resistance from point a to b?

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10kΩ

10kΩ

9kΩ

3kΩ

A B

Turning Figure 12.15C into Figure 12.15D

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Using the Thevenin Theorem

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Final Thevenin Circuit(with load)

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One more Thevenin Circuit Problem

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Norton’s Theorem

Everything in the original circuit, except the load may be replaced by an equivalent circuit. The equivalent circuit consists of a parallel combination of a current source and a resistance.

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What a Norton Circuit Looks Like

2mA

Norton Current IN

NortonResistance

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Norton Shortcut There are a bunch of rules for how to

calculate the Norton Current and Norton Resistance. However, a shortcut is to find the Thevenin Equivalent circuit and then convert it to a Norton

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Using Norton Shortcut

2mA

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Norton Example

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Other Circuit Analysis Techniques

Besides using traditional circuit analysis using Ohm’s Law, or Superposition, Mesh Analysis, Thevenin’s Theorem, and Norton’s Theorem, there are other circuit analysis techniques. A couple include: Nodal Analysis and Millman’s Theorem

Do more hw problems from back of chap 12 (9, 10, 11, or 12) if time

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Practice Problem In the following circuit solve

for VTH, RTH, IN, RN, IL and VL

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Another Practice ProblemSolve for VL using traditional Ohm’s Law technique, Mesh Analysis, and Thevenin

Analysis

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Maximum Power Transfer

See notes

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RL (Ω)0 VT (V) I (A) PL(W) Pi (W) PT (W) Eff (%)

0 0 20 0 2000 2000 0

1 16.7 16.7 278.9 1394 1673.4 16.7

2 28.6 14.3 409 1022 1431.5 28.6

3 37.5 12.5 468.8 781.3 1250.1 37.5

4 44.4 11.1 492.8 616.1 1108.9 44.4

5 50 10 500 500 1000 50

6 54.5 9.1 496 414.1 910.05 54.5

7 58.3 8.3 483.9 344.5 828.35 58.3

8 61.6 7.7 474.3 296.5 770.75 61.6

9 64.3 7.1 465.5 252.1 717.55 64.3

10 66.7 6.7 446.9 224.5 671.35 66.7

20 80 4 320 80 400 80

30 85.7 2.9 248.5 42.05 290.55 85.7

40 88.9 2.2 195.6 24.2 219.8 88.9

50 90.9 1.9 172.7 18.05 190.75 90.9

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What load resistor would you use for the following circuit to have max power

transferred?

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What load resistor would you use for the following circuit to have max power

transferred?

?

What circuit analysis technique can we use to solve for this?

Thevenin’s Theorem. RTH = 5kΩ

5mW @ 5kOhm 4.94mW @ 4kOhm 4.96mW @ 6kOhm I’ve checked this technique using Ohm’s law and it works. See following numbers:

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What load resistor would you use for the following circuit to have max power

transferred?

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A Couple Thoughts FromChapter 13

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Resistance Varies on Length, Diameter and Material

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Stranded Wire vs. Solid Wire

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Switches

SPST SPDT DPST DPDT