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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
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Chapter 9 Sinusoidal Source
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Sinusoidal Voltage Frequency, Angular Frequency, Amplitude, Phase (deg and radians), Period
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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
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Sinusoidal Voltage: RMS Value
Vrms RMS=Root Mean Squared Important for Power Calculations and Noisy Waveforms
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RMS of Noisy Signal Vrms
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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
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P9.7: Find the RMS value
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Appendix B Complex Numbers
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Representation of Complex Numbers
Rectangular Form (real and imaginary) Polar Form (magnitude and phase) Exponential Form
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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
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Examples
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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
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