Q$.$For the given RC low$-$pass filter:

$(1)$ Derive the transfer function $V_o\frac{s}{V_i}(s).$

$(2)$ Use it to determine the cutoff frequency.

$(3)$ Design a low$-$pass filter with a cutoff frequency of $50$kra$\frac{d}{s}$ using a $500$ nF capacitor."

Answer:

$5.H(s)=\frac{\frac{1}{R}C}{s+\frac{1}{R}C}$

$C=500nF,R=40Q$