As discussed in the previous session, transfer functions are used to characterize the input-output relationships of components or systems that can be described by linear, time-invariant, differential equations. For any type of linear time invariant dynamic system, such as electrical mechanical, thermal. biological etc., we can derive its transfer function by following the steps described in the previous session. In this session, we are going to study how to find the transfer functions of electrical and mechanical systems.
If we assume zero initial conditions, we will get the Laplace transform of the above relationships as,
We now combine these components into circuits, decide on the input and the output and find the transfer function. As you have studied in your Principles of Electricity course, the basic laws governing linear electrical circuits are, Kirchoff’s current law and voltage law. Using the above basic elements and the Kirchoff’s laws, we can obtain the differential equations which describe the circuit. Then, we take the Laplace transforms of the differential equations and fmally solve the transfer function.