moebius_transform

pysmithchart.utils.moebius_transform(z, norm=1)[source]

Apply Möbius transformation to impedance values.

Maps impedance space to reflection coefficient space.

Formula: S = 1 - 2*norm / (z + norm)

Parameters:

z (complex or array) – Complex impedance value(s)
norm (float) – Normalization constant - Use 1 for normalized impedance - Use Z0 (e.g., 50) for absolute impedance

Returns:

complex or array – Complex reflection coefficient value(s)

Examples

>>> # Normalized impedance to S-parameter
>>> z_norm = 1 + 0.5j
>>> s = moebius_transform(z_norm, norm=1)

>>> # Absolute impedance to S-parameter
>>> Z_abs = 50 + 25j
>>> s = moebius_transform(Z_abs, norm=50)