7. Circuit transfer functions

7.1 Transfer function form

For example, suppose we wanted to calculate, for a given circuit initially at rest (without initial conditions), an output variable s(t) (current or voltage), in response to an action e(t). With S(p) and E(p) the respective Laplace transforms of s(t) and e(t), we have :

S(p) = H(p) E(p)

H(p) is the transfer function (transmittance) in p of the circuit.

Taking into account the properties mentioned in paragraph 1, it's easy to check that H(p) is a rational fraction in p with real coefficients.