An embodiment of a module (e.g., an amplifier module) includes a substrate, a transmission line, and a ground plane height variation structure. The substrate is formed from a plurality of dielectric material layers, and has a mounting surface and a second surface opposite the mounting surface. A plurality of non-overlapping zones is defined at the mounting surface. The transmission line is coupled to the substrate and is located within a first zone of the plurality of non-overlapping zones. The ground plane height variation structure extends from the second surface into the substrate within the first zone. The ground plane height variation structure underlies the transmission line, a portion of the substrate is present between the upper boundary and the transmission line, and the ground plane height variation structure includes a conductive path between an upper boundary of the ground plane height variation structure and the second surface.