Circuit Theory/Phasors/proof7

From Wikibooks, open books for an open world
Jump to: navigation, search
g(t)=G_m cos(\omega t - \phi)
g(t)=G_m \operatorname{Re}(e^{j(\omega t - \phi)})
g(t)=G_m \operatorname{Re}(e^{-j*\phi}e^{j\omega t})
g(t)=\operatorname{Re}(G_m e^{-j*\phi}e^{j\omega t})
g(t)=\operatorname{Re}(\mathbb{G} e^{j\omega t})
\mathbb{G} = G_m e^{-j*\phi} = G_m(cos(-\phi) + j*sin(-\phi)) = G_m cos(\phi) - j G_m sin(\phi)