Introduction to Electrical & Computer Engineering
Equivalent Circuits
Dr. Cynthia Furse
University of Utah
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Equivalent Circuits
• Equivalent V and I
• Series & Parallel
– Resistance & Conductance
– Voltage & Current Sources
• Voltage & Current Dividers
• Equivalent Sources
2
Equivalent Circuits
• If the current and voltage characteristics at nodes are identical, the circuits are considered “equivalent”
• Identifying equivalent circuits simplifies analysis
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS
Press, Used with Permission by the Publisher
Series: Same Current
Parallel: Same Voltage
VΩ com A
All rights reserved. Do not reproduce or distribute.
© 2013 National Technology and Science Press
Resistors in Series Add
Req
Req =
R1 + R2 + R3 + R4
Voltage Divider
Voltage divided over resistors (voltage divider)
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS
Press, Used with Permission by the Publisher
Voltage Divider
V1
VDC
V2
R1
R2
V1
V2
Voltages In Series ADD
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
Used with Permission by the Publisher
Currents In Series Have to be the SAME or ….
Unrealizable
Circuit
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
Used with Permission by the Publisher
Resistors in Parallel
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
Used with Permission by the Publisher
Another Way to Think of This (commonly used in electromagnetics)
• Conductance (G) = 1 / Resistance (R )
• Conductances in Parallel Add
G1
G2
G3
G1 = 1 G2= 1 G3= 1
R1
R2
R3
Geq=G1+G2+G3
Req = 1 / Geq
11
Current Divider (or Adder)
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
12
Used with Permission by the Publisher
Current Divider (or Adder)
I1
I DC
I2
I1
R1
I DC
I2
R2
Voltages in Parallel Have to be the SAME or ….
Unrealizable
Circuit
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
Used with Permission by the Publisher
Source Transformation
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press,
Used with Permission by the Publisher
All rights reserved. Do not reproduce or
distribute.
© 2013 National Technology and Science Press
Example 2‐10: Source Transformation
Equivalent Circuits
• Equivalent V and I
• Series & Parallel
– Resistance & Conductance
– Voltage & Current Sources
• Voltage & Current Dividers
• Equivalent Sources
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Rim of Snow Canyon
Saint George, Utah
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