I have been trying to find the transfer function of this circuit but I am not getting the right result. it is solved in the textbook but so many steps are skipped. here is the circuit.

enter image description here

here are the equations. enter image description here

using the cramer's rule we can obtain TF=I2(s)/(Vs) enter image description here


1 Answer 1


If you distribute the denominator you have $$ \left(R1+Ls\right)\left(R2+Ls+\frac{1}{Cs}\right)-L^2s^2 = R1R2+R1Ls+\frac{R1}{Cs}+R2Ls+L^2s^2+\frac{Ls}{Cs}-L^2s^2 = R1R2+R1Ls+\frac{R1}{Cs}+R2Ls+\frac{L}{C} $$ mutiplying by Cs we have $$ R1R2Cs+R1LCs^2+R1+R2LCs^2+Ls $$ Rearranging $$ R1LCs^2+R2LCs^2+R1R2Cs+Ls+R1 $$ Combining terms $$ \left(R1+R2\right)LCs^2+\left(R1R2C+L\right)s+R1 $$


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