1. Complex Impedances Sinusoidal Steady State Analysis ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall

2. Complex Impedances ELEC 3082  Inductance and Capacitance represented as Complex Numbers

3. Inductance ELEC 3083

4. Inductance ELEC 3084

5. Impedance  Ohm’s Law in phasor form: Phasor voltage equals impedances times the phasor current  Impedance is COMPLEX, in general Can be strictly REAL Impedance = Resistance Can be strictly IMAGINARY Impedance = Reactance Both inductances and capacitances ELEC 3085

6. Capacitance ELEC 3086

7. Capacitance ELEC 3087

8. Resistance  The phasors are related by V R = RI R ELEC 3088

9. Exercise 5.7 ELEC 3089

10. Exercise 5.8 ELEC 30810

11. Steady-State Circuit Analysis Circuit Analysis Using Phasors and Impedances 1.Replace the time descriptions of voltage and current sources with corresponding phasors. All of the sources must have the SAME frequency! 2.Replace inductances, capacitances, and resistances with their corresponding impedances. 3.Analyze the circuit using any of the techniques from Chapters 1 and 2 by performing the calculations with complex arithmetic. ELEC 30811

12. Example 5.4  Find the steady-state current for the circuit shown below. Also, find the phasor voltage across each element and construct a phasor diagram. ELEC 30812

13. Phasor Diagram ELEC 30813

14. Example 5.5  Series and Parallel Combinations of Complex Impedances  Find the voltage v c (t) in steady state. Find the phasor current through each element, and construct a phasor diagram showing the currents and source voltage. ELEC 30814

15. Phasor Diagram ELEC 30815

16. Exercise 5.9  Find i(t) in the circuit below. What is the phase relationship between v s (t) and i(t)? ELEC 30816

17. Exercise 5.9  Find i(t) in the circuit below. What is the phase relationship between v s (t) and i(t)? ELEC 30817

18. Exercise 5.10  Find the phasor voltage and current for each circuit element. ELEC 30818

19. Summary  Complex Impedances Inductance Capacitance Resistance  Sinusoidal Steady State Analysis Ohm’s Law KVL (Mesh-Current Analysis) KCL (Node-Voltage Analysis) ELEC 30819