Lecture 18+19_v2

Lecture 18+19_v2 - Spring 2011 ECE 2100 Cornell U A Molnar...

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Unformatted text preview: Spring, 2011 ECE 2100, Cornell U. A. Molnar 1 Lectures 18+19 Sinusoidal steady state: basic definitions Simple analysis Spring, 2011 ECE 2100, Cornell U. A. Molnar 2 Basic Sinusoid terms • I(t)=mcos( ω t+ φ ) • m: amplitude –Peak = m –Peak-to-peak =2m –RMS=[mean(I(t)) 2 ] ½ = 2-½ m • ω : frequency – ω is in radians/s – ω = 2 π f, f is frequency in Hertz (Hz)=cycles/second –Period, T = 1/f = 2 π / ω • φ : phase –Usually in radians –Sometimes in degrees –Time delay = - φ / ω m T- φ / ω time Spring, 2011 ECE 2100, Cornell U. A. Molnar 3 Responses to sinusoids • responses of basic components to sinusoidal currents • In each case, assume • I(t)=mcos( ω t) ( 29 ( 29 ( 29 t m L t V t m dt d L dt dI L V L L ϖ ϖ ϖ sin ) ( cos- = = = I(t) R I(t) L I(t) C ( 29 ( 29 t m C t V dt t m C dt t I C V R C ϖ ϖ ϖ sin 1 ) ( cos 1 ) ( 1 = = = ∫ ∫ ( 29 t Rm t V IR V R R ϖ cos ) ( = = Spring, 2011 ECE 2100, Cornell U. A. Molnar 4 Responses to sinusoids add in series: • I(t)=mcos( ω t) I(t) R L ( 29 ( 29 ( 29 ( 29...
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Lecture 18+19_v2 - Spring 2011 ECE 2100 Cornell U A Molnar...

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