**2. The design of the 3DMAs geometries**

The reference Flat Microstrip Antenna (FMA), shown in **Figure 1**(**a**), consists of a square copper patch, *L*p in side length. The dielectric substrate has a thickness of *h* and the relative permittivity is denoted by *ε*r. The patch is rotated by 45 with respect to the substrate layer.

Two types of 3DMAs are considered in this Chapter. The first is bent downward D3DMA shown in **Figure 1**(**b**), the cross-sectional view of which is shown in **Figure 1**(**c**). The second is the bent upward U3DMAs depicted in **Figure 2**(**a**). The D3DMA is shown in **Figure 2**(**b**). The side lengths of the ground plane and substrate are denoted by *L*g *× L*g and *L*s *× L*s, respectively, where *L*g = *L*s. The D3DMA has a square flat top with a side length of *L*f*,* and the drooped angle with respect to the flat top side is denoted by *ϕ*. The length, *L*p of the square patch is chosen to

**Figure 1.** *(a) Reference FMA, (b) the D3DMA, (c) The resonant cavity.*

**Figure 2.** *(a) The U3DMAs, (b) The resonant cavity.*

achieve the desired resonant frequency and bandwidth of the GPS L1 carrier and varies according to *ϕ*, *h*, and *ε*r. A 50 Ω coaxial probe is used to feed all antennas presented in this Chapter, the inner conductor terminates on the patch.
