TransmissionLine

class pmrf.models.components.lines.uniform.TransmissionLine(*, name: str | None = None, metadata: Any = None)

Bases: Model

Abstract base class for all uniform transmission line models.

Provides the fundamental equations to construct S-parameters based on frequency-dependent characteristic impedance (\(Z_c\)) and total complex electrical length (\(\gamma L\)). Derived classes must implement the zc_gammaL method.

Mathematical Formulation

For a single-ended 2-port transmission line, the traveling wave S-parameters with respect to \(Z_c\) are:

\[S_{11} = S_{22} = 0\]

\[S_{21} = S_{12} = e^{-\gamma L}\]

This model computes these S-parameters and then re-normalized them into \(Z_0\) and the power-wave definition using pmrf.rf.renormalize_s().

abstractmethod zc_and_gammaL(frequency: Frequency) → tuple[Array, Array]

Calculates characteristic impedance (\(Z_c\)) and complex electrical length (\(\gamma L\)).

Parameters:

frequency (Frequency) – The frequency axis.

Returns:

Array of characteristic impedance (\(Z_c\)) and complex electrical length (\(\gamma L\)).

Return type:

tuple[jnp.ndarray, jnp.ndarray]