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This paper models transmission lines (TLs) fabricated over a printed circuit board substrate made of woven fiber fabric that causes resonances in the insertion and return loss. The modeling relies on the fact that these lines can be analyzed as periodically loaded TLs. Here, a method to determine the associated equivalent propagation constant and characteristic impedance is proposed. This allows to accurately reproduce the S-parameters for a TL of arbitrary length and for any periodicity of the fiber weave pattern along the line requiring neither multi-staged equivalent circuits, nor full-wave simulations.