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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
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)\By KVL in the right-hand- mesh

\\{ V }_{ o }(s) =R_{ 2 }I(s)+\frac { 1 }{ sC } I(s)\The transfer function from the above two equations is given by,