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Lectures 20+21 - Sinusoidal steady state basic definitions...

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Lectures 20+21 Sinusoidal steady state: basic definitions Simple analysis
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Basic Sinusoid terms I(t)=Acos( ω t+ φ ) A: amplitude –Peak = A –Peak-to-peak =2A –RMS=[mean(I(t)) 2 ] ½ = 2 ½ A 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 A T - φ / ω time
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Responses to sinusoids responses of basic components to sinusoidal currents In each case, assume • I(t)=Acos( ω t) ( 29 ( 29 ( 29 t A L t V t A 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 A C t V dt t A C dt t I C V R C ϖ ϖ ϖ sin 1 ) ( cos 1 ) ( 1 = = = ( 29 t RA t V IR V R R ϖ cos ) ( = =
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Responses to sinusoids add in series: • I(t)=Acos( ω t) I(t) R ( 29 ( 29 ( 29 ( 29 - = - = + = t R L t RA t A L t RA t V dt dI L IR V out out ϖ ϖ ϖ ϖ ϖ ϖ sin cos sin cos ) ( I(t) R ( 29 ( 29 ( 29 ( 29 + = + = + = t RC t RA t A C t RA t V Idt C IR V out out ϖ ϖ ϖ ϖ ϖ ϖ sin 1 cos sin 1 cos ) ( 1 I(t) R (
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