The following RC filter contains a dependent current source. Whilst it can effectively filter low frequencies depending on the choice of component values, the response of the system can drastically change for impulse and step inputs.

$1.$ Using the RC filter above, derive the transfer function by keeping the $\backslash ($ R C $\backslash )$ values as variables.

$2.$ Let Beta $\backslash (=-0\mathrm{.}0099,\backslash$mathrm$\{$C$\}=10\backslash$mathrm$\{$mF$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$R$\}=10\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash ).$ Calculate the impulse response of the system in the time domain.

$3.$ From the poles of the transfer function, comment if the system is stable or not. How is this related to the impulse response?

$4.$ Calculate the range of values of $\backslash (\backslash$beta $\backslash )$ that allows a stable system.