4.1.9. ExercisesΒΆ

  1. Prove that the Laplace transform of \(Ae^{st}\) equals \(A/(s+a)\).

  2. What is the transfer function \(H(s)=\frac{U_{\mbox{out}}(s)}{U_{\mbox{in}}(s)}\) for the electronic scheme shown below.

    \draw (0,1) node[anchor=east]{$u_{\mbox{in}}(t)$} (0,2) to[C, l=$10\mu F$, o-] (2,2) (2,2) to[generic, l=$8\Omega$] (2,0) (2,2) to[short, -o] (4,2) (0,0) to[short, o-o] (4,0) (4,1) node[anchor=west]{$u_{\mbox{out}}(t)$};

  3. Plot the frequency response of the filter sketched above.