Since the early 2000s, High Electron Mobility Transistors (HEMTs) have been the preferred choice for the first-stage amplification of qubit readout resonators at cryogenic temperatures. However, Josephson Parametric Amplifiers (JPAs) have recently emerged as a more attractive alternative due to their quantum-level noise performance. Despite their advantages, JPAs face significant challenges such as narrow bandwidths, low dynamic ranges, and limited gains, which hinder their widespread adoption. By presenting an optimized JPA chip design with a Kerr coefficient of 1000 Hz and a Kappa value of 100 MHz that operates in the 4-8 GHz range, this thesis seeks to address these issues. The design methodology involves an iterative process using Comsol and Microwave Office softwares to refine the design and the resulting Kappa and Kerr coefficients at each phase of development. This approach results in a JPA design that overcomes the traditional limitations, making it a viable candidate for broader applications in quantum technology.