I'm having a little trouble with the derivation. In my electromagnetics book it states:
V(t) = \(Vocos(wt + \phi)\)
and to convert between real time and phasor notation use:
V(t) = Re {Ve\(^{jwt}\)}
But in every example (and by every example I mean the only 2 in the book ) the \(e^{jwt}\) is omitted from the answer. Is this because you assume the \(jw\) or \(\theta\) is constant somehow? I was just confused because it seems like you "lose" information about the signal if you don't explicitly tag on the \(e^{jwt}\) on every signal you put into the phasor domain.
Maybe it'll make more sense if someone can explain how to represent the following signals as phasors:
a) \(cos(wt)\) (= \(e^{jwt}\) ? since \(\phi\) is zero? )
b) \(3cos((120\pi t) - \pi /2)\) ( = \(6e^{-j\pi / 2}e^{j120\pi t} \)or just\( 6e^{-j\pi / 2} \)?)
V(t) = \(Vocos(wt + \phi)\)
and to convert between real time and phasor notation use:
V(t) = Re {Ve\(^{jwt}\)}
But in every example (and by every example I mean the only 2 in the book ) the \(e^{jwt}\) is omitted from the answer. Is this because you assume the \(jw\) or \(\theta\) is constant somehow? I was just confused because it seems like you "lose" information about the signal if you don't explicitly tag on the \(e^{jwt}\) on every signal you put into the phasor domain.
Maybe it'll make more sense if someone can explain how to represent the following signals as phasors:
a) \(cos(wt)\) (= \(e^{jwt}\) ? since \(\phi\) is zero? )
b) \(3cos((120\pi t) - \pi /2)\) ( = \(6e^{-j\pi / 2}e^{j120\pi t} \)or just\( 6e^{-j\pi / 2} \)?)