1. ECE 1270: Introduction to Electric Circuits
Lecture 17:
1) Sinusoidal Source
2) Complex Numbers
Chapter 9: Sinusoidal Steady-State Analysis
Section 9.1 & Appendix B

2. Chapter 9
Sinusoidal Source

3. Sinusoidal Voltage
Frequency, Angular Frequency, Amplitude, Phase (deg and radians), Period

4. Sinusoidal Voltage: Phase Angle ϕ
Positive phase change: shift to the left
Negative phase change: shift to the right
Example of Phase Change in Matlab

5. Sinusoidal Voltage: RMS Value
Vrms
RMS=Root Mean Squared
Important for Power Calculations and Noisy Waveforms

6. RMS of Noisy Signal
Vrms

7. Wall Outlet Signal in RMS
1) Wall outlet (voltage delievered from power plant) has
120 Vrms at 60 Hz
2) Actual voltage peak =169.7 V

8. P9.7: Find the RMS value

9. Appendix B
Complex Numbers

10. Representation of Complex Numbers
Rectangular Form (real and imaginary)
Polar Form (magnitude and phase)
Exponential Form

11. What are Complex Numbers?
-Complex numbers are used to represent reactive
components such as inductor and capacitor
-Think in terms of phase change (voltage and current in reactive components)
-Multisim Examples of Inductor and Capacitor

12. Examples

13. B.3 (p725): Complex Arithmatic
Tips
1) When adding or subtracting, use rectangular form
2) When multiplying or dividing or finding power, use polar or exponential form
3) Complex number x Complex Conjugate = amplitude2
Examples