Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE 1105 : Introduction to EE Freshman Seminar Lecture 5: Thevenin Equivalent, Norton Equivalent,

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Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE 1105 : Introduction to EE Freshman Seminar Lecture 5: Thevenin Equivalent, Norton Equivalent, Delta-Wye, Wye-Delta Conversion

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Th é venin’s Theorem A linear circuit can be represented at its output terminals as an equivalent circuit consisting of a voltage source Vth in series with a resistor Rth. Vth is determined when no load is applied on the output. Rth is determined by deactivating all independent sources in circuit. Network 1 Network 2 A B Application: Coupled networks.

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Example – Note, this does not work with dependent sources Place a voltmeter across terminals A-B and read the voltage. We call this the open-circuit voltage. No matter how complicated Network 1 is, we read one voltage. We call this voltage V AB =V THEVENIN = V TH Deactivate independent sources Place an ohmmeter across A-B and read the resistance. We call this the Thevenin equivalent Resistance R TH

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Alternate Method: Shortcircuit

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Example: Voltage Divider

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Norton Equivalent

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Wye/Delta Conversion (1/2) WyeDelta

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Wye/Delta Conversion (2/2)

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Delta/Wye Conversion

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Effects of  -Y & Y-  Conversions  -Y Conversion eliminates a loop but adds a node. Y-  Conversion eliminates a node but adds a loop.

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Resistive Wye Circuit Eqn 1

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Resistive Wye Circuit Eqn 2

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Resistive Delta Circuit Eqn 3

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Resistive Delta Circuit Eqn 4

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Delta-Wye Derivation Use Eqn 4 to solve for delta voltages: Simplifying: Eqn 5 Eqn 6

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Delta-Wye Derivation Equating the row 1, column 2 term of eqn 2 to the row 1, column 2 term of eqn 6:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Delta-Wye Derivation Equating the row 1, column 1 term of eqn 2 to the row 1, column 1 term of eqn 6: Removing R 3 :

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Delta-Wye Derivation Similarly, it can be shown that:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Wye-Delta Derivation Use Eqn 2 to solve for wye currents: Simplifying: Eqn 15 Eqn 16

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Wye-Delta Derivation Equating the row 1, column 2 term of eqn 4 to the row 1, column 2 term of eqn 16: Then Equating the row 1, column 1 term of eqn 4 to the row 1, column 1 term of eqn 16:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Wye-Delta Derivation Removing R 3 : Similarly, it can be shown that:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Y-  Conversion Example Find R ab Several Methods: We choose to eliminate node c, then simplify.

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Y-  Conversion Calculations

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 New Circuit

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Further Simplifications

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Acknowledgements: Dr. Bill Dillon Homework 5 due next class Next Time: Exam – Midterm 1, closed book, no calculator, multiple choice. 26