thevenin, norton and maximum power transfer theorems
TRANSCRIPT
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
Random Video of the Day
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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