Question

Circuits

\text { The input voltage in the circuit is } v_{g}=30 e^{-|t|} \mathrm{V} \text {. }

Use the Fourier transform method to find v, (t) in the circuit. (15pts)

V_{o}(\omega)=\frac{21}{(j \omega+1)(j \omega+0.5)(-j \omega+1)}

V_{e}(\omega)=\frac{-21}{j \omega+1}+\frac{32}{j \omega+0.5}+\frac{8}{-j \omega+1}

\text { Calculate the } 1 \Omega \text { energy content of } v_{g} .(5 \mathrm{pts})

\text { Calculate the } 1 \Omega \text { energy content of } v_{o} .(5 \mathrm{pts})

What percentage of the 1 ohms energy content of v, lies in the frequency range0 < lw| <2 rad/s? (10pts)

What percentage of the 1 ohms energy content of v, lies in the frequency range0 < lw| <2 rad/s? (15pts)