ECE 202 Lesson 2 - ECE 202 Circuit Theory 2 Lesson 2 Phasor...

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ECE 202 Circuit Theory 2 Lesson 2 Phasor Representation of Sinusoidal Waveforms Phasor Impedances Generating Phasor Circuits
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2 Euler’s Formula ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 cos sin cos sin cos sin jx j t j t e x j x x t e t j t Ae A t jA t ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ + + = + = + = + + + = + + +
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3 Sinusoidal Waveforms ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 cos sin cos Re sin Im j t j t j t Ae A t jA t A t Ae A t Ae ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ ϖ θ + + + = + + + + = + =
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4 Phasor ( 29 ( 29 ( 29 ( 29 cos Re Re sin Im Im The phasor carries the amplitude and phase information of a sinusoidal waveform j t j j t j t j j t j A t Ae Ae e A t Ae Ae e Ae ϖ θ θ ϖ ϖ θ θ ϖ θ ϖ θ ϖ θ + + + = = + = =
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5 Phasor Impedance of Resistor ( 29 ( 29 ( 29 ( 29 v v i j t j t j t j t t e i t e t R t e R e R ϖ ϖ ϖ ϖ = = = = = V I V I V I R + v( t ) - i( t )
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6 Phasor Impedance of Inductor
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