Mathematical Modeling and Analysis of Cylindrically Curved Partially Reflective Surface (PRS)
Budget: $8 – $15 USD
I am working on a high-frequency antenna project involving cylindrically curved Partially Reflective Surfaces (PRS) integrated with Fabry-Pérot Cavity (FPC) antennas for potential mmWave applications (e.g., 28 GHz band). The focus is on:
-Analyzing phase angle compensation, effective path length ΔL, and reflection-based geometric series on a curved PRS.
-Understanding how the cylindrical curvature impacts phase, gain, and bandwidth.
-Modeling multiple internal reflections using geometric series under cylindrical geometry.
-Computing field strength magnitudes and power patterns under infinite reflection approximations.
-Verifying and simplifying complex equations such as the attatched papers
-Producing plots, parametric sweeps (R, h, theta), and simulation-ready models.
Key Requirements:
1-Review the current cylindrical PRS mathematical models provided.
2- Explain and refine the phase, effective length(L1,L2..etc), and reflection series models under curvature.
3- Develop clean, reusable Python/MATLAB scripts to compute and visualize: ΔL vsθ,R,h
4-Phase (Epsi) vs frequency/angle
5-Power patterns and absolute Electric Field
-Suggest simplifications for infinite series under practical antenna parameters.
-(Optional) Provide simulation-ready model suggestions for validation.
Ideal Skills and Experience:
- Check Advanced Electromagnetics (antenna theory, Fabry-Pérot resonators, PRS concepts). attatched 1956 paper is the most needed in term of EM.
- Mathematical Modeling (phase analysis, geometric series, infinite sum simplifications).
- A brief background in Microwave Engineering and mmWave design
If you have a passion for mathematics and a knack for problem-solving, I would love to see your approach to this challenge.
-Analyzing phase angle compensation, effective path length ΔL, and reflection-based geometric series on a curved PRS.
-Understanding how the cylindrical curvature impacts phase, gain, and bandwidth.
-Modeling multiple internal reflections using geometric series under cylindrical geometry.
-Computing field strength magnitudes and power patterns under infinite reflection approximations.
-Verifying and simplifying complex equations such as the attatched papers
-Producing plots, parametric sweeps (R, h, theta), and simulation-ready models.
Key Requirements:
1-Review the current cylindrical PRS mathematical models provided.
2- Explain and refine the phase, effective length(L1,L2..etc), and reflection series models under curvature.
3- Develop clean, reusable Python/MATLAB scripts to compute and visualize: ΔL vsθ,R,h
4-Phase (Epsi) vs frequency/angle
5-Power patterns and absolute Electric Field
-Suggest simplifications for infinite series under practical antenna parameters.
-(Optional) Provide simulation-ready model suggestions for validation.
Ideal Skills and Experience:
- Check Advanced Electromagnetics (antenna theory, Fabry-Pérot resonators, PRS concepts). attatched 1956 paper is the most needed in term of EM.
- Mathematical Modeling (phase analysis, geometric series, infinite sum simplifications).
- A brief background in Microwave Engineering and mmWave design
If you have a passion for mathematics and a knack for problem-solving, I would love to see your approach to this challenge.