Equivalent One-Port Models & Topology Choice

A one-port is a black box with one terminal pair and one terminal voltage-current relation. Equivalence means that, for the declared inputs, frequency range, amplitudes, initial state, and operating conditions, the external network cannot distinguish the model from the device by observing that port. It does not mean the internals are the same.

Levels of one-port description #

The simplest model that predicts the required terminal behavior is usually the most identifiable.

Topology is a hypothesis #

Choosing series $R$-$L$, parallel $R$-$C$, or a larger ladder is not a neutral algebra step. It asserts how dissipation and storage combine. Different topologies can fit the same finite dataset, especially at one frequency.

For example, the same complex impedance at one $\omega$ can be represented by a series $R$-$L$ pair or a parallel $R$-$L$ pair with different values. A single operating point cannot decide which topology predicts another frequency correctly.

Identifiability checks #

Before fitting:

1. state the port and sign convention;
2. state whether the model is static, small-signal, sinusoidal, or dynamic;
3. count independent parameters versus independent excitation information;
4. enforce known constraints such as passivity and $R,L,C\ge0$ when physically required;
5. reserve operating conditions for validation rather than fitting all available data;
6. inspect residual structure, not only one aggregate error.

Mishchenko's instantaneous-power identification paper is useful precisely because its fitted negative and strongly time-varying elements expose the boundary between equation closure and physically interpretable topology.

Model order should be justified by predictive evidence. A richer topology that only lowers fit error on the same dataset may be less identifiable and less useful than a constrained lower-order model.