Thevenin, Norton and Maximum Power Transfer Theorems

 Why Thevenin’s Theorem is useful

 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.

Write these on white board

R TH = 5k Ω

V TH = 10V

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

.66mA

=10k Ω

Determine V TH Solving for V TH

10V 5V

V

TH

= V

A

– V

B

= 5V

Determine R TH

What is the resistance from point a to b?

 http://www.youtube.com/watch?v=SWWt9I C7mGs&NR=1&feature=fvwp  https://www.facebook.com/photo.php?v=133 641650156241

 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.

Norton Current I N

2mA

Norton Resistance

 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

2mA

 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



In the following circuit solve for V

TH

, R

TH

, I

N

, R

N

, I

L

and V

L

Solve for V L using traditional Ohm’s Law technique, Mesh Analysis, and Thevenin Analysis

 See notes

R L (Ω)0

0 1 2 3 4 5 6 7 8 9 10 20 30 40 50

V T (V)

0 16.7

28.6

37.5

44.4

50 54.5

58.3

61.6

64.3

66.7

80 85.7

88.9

90.9

I (A)

20 16.7

14.3

12.5

11.1

10 9.1

8.3

7.7

7.1

6.7

4 2.9

2.2

1.9

P L (W)

0 278.9

409 468.8

492.8

500 496 483.9

474.3

465.5

446.9

320 248.5

195.6

172.7

P i (W)

2000 1394 1022 781.3

616.1

500 414.1

344.5

296.5

252.1

224.5

80 42.05

24.2

18.05

P T (W)

2000 1673.4

1431.5

1250.1

1108.9

1000 910.05

828.35

770.75

717.55

671.35

400 290.55

219.8

190.75

Eff (%)

0 16.7

28.6

37.5

44.4

50 54.5

58.3

61.6

64.3

66.7

80 85.7

88.9

90.9

?

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

Thevenin’s Theorem.

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

SPST SPDT DPST DPDT