EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 17: 1) Sinusoidal Source 2) Complex Numbers Chapter 9: Sinusoidal Steady- State Analysis Section 9.1 & Appendix B

EE 1270 Introduction to Electric Circuits Suketu Naik 1 Chapter 9 Sinusoidal Source

EE 1270 Introduction to Electric Circuits Suketu Naik 2 Sinusoidal Voltage Frequency, Angular Frequency, Amplitude, Phase (deg and radians), Period

EE 1270 Introduction to Electric Circuits Suketu Naik 3 Sinusoidal Voltage: Phase Angle ϕ Example in Matlab

EE 1270 Introduction to Electric Circuits Suketu Naik 4 Sinusoidal Voltage: RMS Value RMS=Root Mean Squared Important for Power Calculations V rms

EE 1270 Introduction to Electric Circuits Suketu Naik 5 RMS Noise V rms

EE 1270 Introduction to Electric Circuits Suketu Naik 6 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

EE 1270 Introduction to Electric Circuits Suketu Naik 7 P9.7: Find the RMS value

EE 1270 Introduction to Electric Circuits Suketu Naik 8 Appendix B Complex Numbers

EE 1270 Introduction to Electric Circuits Suketu Naik 9 Representation of Complex Numbers Rectangular Form (real and imaginary) Polar Form (magnitude and phase) Exponential Form

EE 1270 Introduction to Electric Circuits Suketu Naik 10 What are Complex Numbers? Complex numbers are used to represent active components

EE 1270 Introduction to Electric Circuits Suketu Naik 11 Examples

EE 1270 Introduction to Electric Circuits Suketu Naik 12 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 = amplitude 2 Examples