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EE 529 Circuit and Systems Analysis

EE 529 Circuit and Systems Analysis. Lecture 5. c. a. 1. 2. d. b. Mathematical Model of a Dependent Source. A. Voltage Controlled Voltage Source. c. a. 1. 2. d. b. Mathematical Model of a Dependent Source. B. Current Controlled Voltage Source. c. a. 1. 2. d. b.

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EE 529 Circuit and Systems Analysis

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  1. EE 529 Circuit and Systems Analysis Lecture 5 EASTERN MEDITERRANEAN UNIVERSITY

  2. c a 1 2 d b Mathematical Model of a Dependent Source A. Voltage Controlled Voltage Source

  3. c a 1 2 d b Mathematical Model of a Dependent Source B. Current Controlled Voltage Source

  4. c a 1 2 d b Mathematical Model of a Dependent Source A. Voltage Controlled Current Source

  5. c a 1 2 d b Mathematical Model of a Dependent Source A. Current Controlled Current Source

  6. Circuit Analysis A-Branch Voltages Method: Consider the following circuit. Find v and i

  7. 5 6 4 3 7 2 1 Circuit Analysis • Draw the circuit graph

  8. 5 6 4 3 7 2 1 Circuit Analysis • Select a proper tree: (n-1=4 branches) • Place voltage sources in tree • Place the voltages controlling the dependent sources in tree • Place current sources in co-tree • Complete the tree from the resistors

  9. 5 6 4 3 7 2 1 Circuit Analysis • Write the fundamental cut-set equations for the tree branches which do not correspond to voltage sources.

  10. 5 6 4 3 7 2 1 Circuit Analysis • Write the currents in terms of voltages using terminal equations.

  11. Circuit Analysis • Substitute the currents into fundamental cut-set equation. • v2, and v6 must be expressed in terms of branch voltages using fundamental circuit equations.

  12. 5 6 4 3 7 2 1 Circuit Analysis

  13. Circuit Analysis • Therefore and

  14. Circuit Analysis • Subst. Eq. (2) into (1) yields

  15. Chord Currents Method • Consider the circuit. Find v using chord currents method.

  16. Chord Currents Method • Draw the circuit graph. • v = v3 a 5 4 3 c b 6 2 7 1 d

  17. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Select a proper tree

  18. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Write the fundamental circuit equations for the chords which are not current sources.

  19. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Write all resistor voltages in terms of terminal currents using terminal equations.

  20. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Substitute the terminal equations to fundamental circuit equations

  21. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Write fundamental cut-set equations for i3 and i6.

  22. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Substitute the fundamental cut-set equations to fundamental circuit equations

  23. a 5 4 3 c b 6 2 7 1 d Chord Currents Method • Substitute the fundamental cut-set equations to fundamental circuit equations

  24. Chord Currents Method • Using Eqns.(1) and (2), i2 and i4 can be calculated as

  25. Chord Currents Method • Consider the following circuit. Find v0.

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