CHAPTER 12Thevenin, Norton and Maximum

Power Transfer Theorems

Thevenin’s Theorem

Why Thevenin’s Theorem is useful

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.

Steps to make a Thevenin Circuit

Write these on white board

Calculating RTHEVENIN (RTH)

RTH = 5kΩ

Calculating VTHEVENIN (VTH)

VTH = 10V

Equivalent Thevenin Circuit

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

=10kΩ.66mA

Using the Thevenin Theorem

Solving for VTH

10V 5V

VTH = VA – VB = 5V

Determine VTH

Using the Thevenin Theorem

Determine RTH

Solving for RTH

What is the resistance from point a to b?

10kΩ

10kΩ

9kΩ

3kΩ

A B

Turning Figure 12.15C into Figure 12.15D

Using the Thevenin Theorem

Final Thevenin Circuit(with load)

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.

What a Norton Circuit Looks Like

2mA

Norton Current IN

NortonResistance

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

Using Norton Shortcut

2mA

Norton Example

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

Practice Problem In the following circuit solve

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

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

Analysis

Maximum Power Transfer

See notes

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

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

transferred?

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:

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

transferred?

A Couple Thoughts FromChapter 13

Resistance Varies on Length, Diameter and Material

Stranded Wire vs. Solid Wire

Switches

SPST SPDT DPST DPDT