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

Chapter 9 Sinusoidal Source

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

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

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

RMS of Noisy Signal Vrms

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

P9.7: Find the RMS value

Appendix B Complex Numbers

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

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

Examples

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