Engineering domain: Signal Processing

## Background

Microstrip patch antennas are widely used in modern wireless communication due to their low profile, ease of fabrication, and compatibility with printed circuit board (PCB) technology. 

In this task, you are to design a rectangular microstrip patch antenna that satisfy the task objective and constraints stated below.

The antenna is centered at the origin with the patch facing the +z direction. The feed point lies in the x-y plane. The dielectric substrate must be selected from commercially available Rogers low-loss laminates, and the chosen material's permittivity will influence the design.

## Task Objective and Constraints

Your task is to design a rectangular microstrip patch antenna that meets the following specifications:

- Resonant Frequency: 1.537 GHz (S11 <= –10 dB)
- Bandwidth: >= 50 MHz
- Gain: >= 3 dBi
- Volume Constraint (Ground Plane Size) [ Length × Width × Height ]: <= 100 mm × 100 mm × 10 mm
- Feed Method: 50-ohm coaxial pin feed (from below substrate)
- Substrate Material: Rogers low-loss laminate (commercially available)

## Design Inputs

Determine the optimal design parameters to satisfy the task objectives:

- Length of Metallic Patch in mm: length_mm
- Width of Metallic Patch in mm: width_mm
- Substrate height in mm: height_mm
- Relative permittivity of selected Rogers material: epsilon_r
- Feed position in the x direction relative to patch center: feed_offset_x_mm
- Confidence of your design: confidence

## Design Context

- Ground Plane Size is 1.5 times max(Length, Width)
- Patch size (Length and Width) have to be smaller than ground plane size