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EES512_L15_W2011_ACCircuits1_commented

EES512_L15_W2011_ACCircuits1_commented - Time Domain...

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EES 512 :: Electric Circuits Winter 2011 Lecture 15 :: AC Circuits [1] Sections: 111/121/131/141 Instructor: Dr. Matthew Kyan
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Outline previously: 1 st order circuits (RC & RL) Complete response Today: AC voltages AC waveforms
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DC vs AC So far we have considered only: Vs = constant; Is = constant
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AC: Sinusoidal Sources Sinusoidal waveform: Am = Amplitude of the Sinusoid ω = Angular Frequency (radians/sec) ωt = Argument of the Sinusoid T = Period of the Sinusoid f = Frequency of the Sinusoid Properties: t
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AC: Sinusoidal Sources Sinusoidal generation: ω = Angular Frequency (radians/sec) t
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AC: Sinusoidal Sources General Sinusoidal: t V(t) = Vm sin(ωt + )
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Phase Differences t V(t) = Vm sin(ωt + ) Sine / Cosine relationships:
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Graphical Approach
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Graphical Approach
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Example 1 5 sin (4π t - 60º)
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Phasors Definition: A phasor is a complex number that represents the amplitude and the phase of a sinusoid “simplifies circuit analysis of linear circuits excited by sinusoids”
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Unformatted text preview: Time Domain Phasor (frequency) Domain Phasors What have we done? – Temporarily dropped the “ωt” (time factor) – We want to exploit the convenience of working with vectors – A sinusoid can be represented as a complex number: z = x + jy z Re Im Complex numbers – quick review ● Rectangular Form: ● Polar Form: ● Exponential Form: Complex numbers – quick review ● Complex Number Algebra: – Addition/Subtraction: – Multiplication/Division: – Reciprocal: Complex numbers – quick review ● Complex Number Algebra: – Square Root: – Complex Conjugate: Euler's Identity e ±jθ = cosθ ± jsinθ Phasor representation for sinusoid: Phasor representation for sinusoid: graphically: Time → Phasor Domain: Systematic Approach 1. Express sinusoids in cosine form 2. Take magnitude and phase Example 2 Basic AC circuit ● Phasor form of Ohm's Law:...
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