Topic: Electronics Engineering
For the network shown in the figure $V_{i}(t)$ is the input and $i(t)$ is the output. The transfer function $\frac{I(s)}{V_{i}(s)}$ of the network is
- A. $\frac{C}{RCs^{2}+LCs+1}$
- B. $\frac{C}{LCs^{2}+RCs+1}$
- C. $\frac{Cs}{RCs^{2}+LCs+1}$
- D. $\frac{Cs}{LCs^{2}+RCs+1}$
Answer: D. $\frac{Cs}{LCs^{2}+RCs+1}$
Explanation: Apply KVL to the circuit:
$V_{i}(t)=Ri(t)+L\frac{di(t)}{dt}+\frac{1}{C}\int i(t)dt$
Taking Laplace transform:
$V_{i}(s)=RI(s)+LSI(s)+\frac{1}{CS}I(s)$
$\frac{I(s)}{V_{i}(s)}=\frac{1}{R+Ls+\frac{1}{Cs}} = \frac{Cs}{LCs^{2}+RCs+1}$