**Generalised S-plane Impedance**

Impedance defined in terms of *jω* can strictly only be applied to circuits which are energised with a steady-state AC signal. The concept of impedance can be extended to a circuit energised with any arbitrary signal by using complex frequency instead of *jω*. Complex frequency is given the symbol *s* and is, in general, a complex number. Signals are expressed in terms of complex frequency by taking the Laplace transform of the time domain expression of the signal. The impedance of the basic circuit elements in this more general notation is as follows:

Element | Impedance expression |
---|---|

Resistor | |

Inductor | |

Capacitor |

For a DC circuit this simplifies to *s* = 0. For a steady-state sinusoidal AC signal *s* = *jω*.

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