1. Dr. Cynthia Furse University of Utah
Introduction to Electrical & Computer Engineering Thevenin & Norton Equivalent Circuits
Dr. Cynthia Furse
University of Utah

2. Thevenin & Norton Equivalent Circuits
How to Analyze SYSTEMS? Simplify your circuit!
Voltage Loading and Rin & Rout
Thevenin Equivalent Circuit
Vth Rth (3 methods)
Norton Equivalent Circuit
Maximum Power Transfer
Updated ECE Circuit Analysis Toolbox

3. 10 Ω
100 Ω
Today’s systems are complex. We use a block diagram approach to represent circuit sections.
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4. Voltage Loading
10 Ω
100 Ω
Rtotal = 10Ω + 100Ω || 100Ω = 10 Ω + 50Ω = 60 Ω
I = 100V / Rtotal = 1.83 A
What is the voltage across the fan & lamp? (measured by DVM)
Voltage Divider:
Vfan = Vlamp = 110 V [50 Ω / (10 Ω + 50 Ω ) ] = 92 V
This is significantly less than Vs (110V)! Eek!
Voltage LOADING occurred.
Where did the voltage go? Across Rs.
By permission of © 2013 National Technology and Science Press

5. Input & Output Resistance
10 Ω
100 Ω
Rin = 2 MΩ
If Rout << Rin No voltage loading Circuits DEcoupled
Otherwise Voltage Loading occurs Circuits Coupled
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6. Thevenin Equivalent Circuit
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7. Find Vth: Open Circuit Method
Vth = Voc
How?
Measure
Calculate
Simulate
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8. Find Rth: #1 Equivalent Resistance Method
No dependent sources
All independent sources deactivated
Short
Circuit
Open
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9. Example 3-11: #1 Equivalent Resistance
(Circuit has no dependent sources)
Replace with SC
Replace with OC
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
By permission of © 2013 National Technology and Science Press

10. Find Rth: #2 Open/Short Circuit Method
Works for all circuits
How?
Measure
Calculate
Simulate
By permission of © 2013 National Technology and Science Press

11. Example 3-10: #2 OC/SC Method
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
By permission of © 2013 National Technology and Science Press

12. Find Rth: #3 External Source Method
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By permission of © 2013 National Technology and Science Press

13. Example
Example
4Ix
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By permission of © 2013 National Technology and Science Press

14. Calculate Rth: #3 External Source
Example (continued)
Calculate Rth: #3 External Source
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15. By permission of © 2013 National Technology and Science Press
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
By permission of © 2013 National Technology and Science Press

16. In many situations, we want to maximize power transfer to the load
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Power Transfer
In many situations, we want to maximize power transfer to the load
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
By permission of © 2013 National Technology and Science Press

17. ECE Circuit Analysis Toolbox
Va-Vb=IR= VΔ
Node Voltages
Vnode, VΔ
Va,Vb
Vother node VΔ
Vnode, I R
Va Vb
KVL
ΣVΔ (loop) =0
Difference Voltages
Vs,I,R VΔ
Vs,Is,R I
Kirchoffs Laws
KCL
ΣI in = ΣI out
Branch Currents
I in or out
I out or in
Node Voltage Method
Vs,Is,R
Vnodes
Resistors in Series & Parallel
Many R
Simple R
Ohm’s Law
VΔ=IR
Voltage Differences
VΔ,I
VΔ,R
I,R R I VΔ
Power
P=IV P
VΔ,R
I,R
VΔ,I
Voltage Divider
Vs, R VΔ
Thevenin/Norton
Complex Ckt
Simple Ckt
Superposition Σ
Many Sources
ΣV, VΔ,I
Current
Divider
Is, G (=1/R) I

18. Thevenin & Norton Equivalent Circuits
How to Analyze SYSTEMS? Simplify your circuit!
Voltage Loading and Rin & Rout
Thevenin Equivalent Circuit
Vth Rth (3 methods)
Norton Equivalent Circuit
Maximum Power Transfer
Updated ECE Circuit Analysis Toolbox

19. Snow crystals and juniper near Mercur, Utah