The effect of the biasing network (BN), formed by coplanar transmission lines (CPWs) built into the ground plane itself, on the dispersion characteristics of a tunable unit cell (UC) is investigated. The UC consists of an elliptical patch and multiple vias placed inside a parallel plate waveguide. One of the vias attached to a patch positioned on the top surface of a dielectric substrate connects the patch to the ground plane. Another via, symmetrically positioned with respect to the patch center, can be connected to the same ground plane or let to float depending on the state of a diode positioned at its base. The effect of the different components of the BN is analyzed step by step. For each intermediate configuration, the corresponding dispersion diagram (DD) is computed, allowing extraction of fundamental information on the influence of each part of the CPW circuit on the band-gap characteristics. The orientation of the BN is also discussed. The presented results can guide the dispersion engineering process when a tunable electromagnetic band-gap (EBG) structure is designed for a specific guided-wave application.