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

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

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

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

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

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

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

8. 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 1 2 3 4 5 6 7

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

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

11. Circuit Analysis Substitute the currents into fundamental cut-set equation. v 2, and v 6 must be expressed in terms of branch voltages using fundamental circuit equations.

12. Circuit Analysis 1 2 3 4 5 6 7

13. 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 = v 3 a b c d 1 2 3 4 5 6 7

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

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

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

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

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

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

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

24. Chord Currents Method Using Eqns.(1) and (2), i 2 and i 4 can be calculated as

25. Chord Currents Method Consider the following circuit. Find v 0.