Switches#

Definition: Switch

A switch is a one-port which can behave either as an open circuit or a short circuit.

Notation

When a switch behaves like an open circuit, it is denoted by

Open Switch Symbol

When it behaves like a short circuit, it is denoted by

Closed Switch Symbol

We often model switches using a function \(S(t)\) defined in the following way:

\[ S(t) \overset{\text{def}}{=} \begin{cases} 1 \qquad \text{when the switch is closed} \\ 0 \qquad \text{when the switch is open}\end{cases} \]

Theorem: Duality of Switches

The dual of a switch \(S\) is the switch \(S_d\) which is open when \(S\) is closed and is closed when \(S\) is open:

\[ S_d(t) = 1 - S(t) \]

Proof

TODO