The Transfer Function

The transfer function ($H(s)$) connects inputs and outputs in the s domain.

\[X(s)H(s) = Y(s)\]

Finding the Transfer Function

Finding the transfer function is normally a simple process outside of some laborious algebra.

1. Convert the given circuit to the s domain.
2. Relate the input and output using any circuit analysis method. The node voltage method works well—create the equations.
3. Solve for the transfer function by dividing the output by the input in the s domain.

Properties of the Transfer Function

• The transfer function will be different depending on the input and output.
• The transfer function is also not reversible in the sense that

\[X(s)H(s) \neq Y(s)H(s)\]

• You can find the transfer function signal by inputting a delta signal and measuring the output which will be the transfer function signal. This is because the delta will simply evaluate to one in the s domain

\[\delta(t) = 1 \Rightarrow Y(s) = 1\cdot H(s) = H(s) \Rightarrow h(t)\]