Skip to content

Linear One-Ports#

Definition: Strictly Linear One-Port

A linear one-port is strictly linear if its V-I characteristic can be written as

\[ aU + bI = 0 \]

Theorem: Equivalent Definition

A one-port is strictly linear if and only if its V-I characteristic \(\mathcal{F}\) simultaneously has the following properties:

  • If \((U, I)\) is in \(\mathcal{F}\), then so is \((\lambda U, \lambda I)\) for all \(\lambda \in \mathbb{R}\).
  • If \((U_1, I_1)\) and \((U_2, I_2)\) are in \(\mathcal{F}\), then so is \((U_1 + U_2, I_1 + I_2)\).
Proof

TODO

Graphically, the V-I characteristic of a strictly linear one-port is a straight line passing through the origin \((0, 0)\):

V-I of Strictly Linear One-Ports

Theorem: Polarity of Strictly Linear One-Ports

All strictly linear one-ports are unpolarized.

Proof

TODO