Transfer Function of Electrical Circuit

Procedure for finding the transfer functions of electric networks:
1. First draw the given electrical network in the s domain with each inductance L replaced by sL and each capacitance replaced by 1/sC.
2. Replace all sources and time variables with their Laplace transforms so that v(t) is replaced by V(s) and i(t) by I(s) respectively.
3. Use KVL,KCL , mesh analysis, node analysis to write the network equations
4. Solve the equations simultaneously for getting the output.
5. Form the transfer function
Example:
Determine the transfer function of the phase lag network shown in the figure,

Solution: Figure shows the network in s-domain

By KVL in the left hand- mesh,

$\\{ V }_{ i }(s) = { R }_{ 1 }I(s)+R_{ 2 }I(s)+\frac { 1 }{ sC } I(s)\$