### Design equations of Rectangular Microstrip Patch Antenna

Following design equation can be used to calculate the width and length of rectangular microstrip patch antenna and simulation of 2.4 GHz inset-feed rectangular patch antenna can be found in follwing video.

 Microstrip antenna with inset-feed line                          Part-1 Design step for the calculation of W and L Step-1: To calcualte width 'W' use follwing formula Step-2:  Calculate the effective dielectric constant using formula below. Here  'εr' is relative dielectric constant of the material. 'h' is height of the substrate and W is the width of patch calculated in first step. Step-3:  Calculate ΔL using formula below. Step-4:  Calculate length of the patch using formula below. v0  is speed of light in free space. Step-1:  Calculate the input impdedance of the patch using follwing formula. (Typically between 200 Ω to 250 Ω. You can assume 225 Ω for simplicity and proceed to step 2 and later on using simulation software the position can be optimized for the best return loss. Where G1  and G2 are conductance of slot #1 and slot #2 of the patch antenna. + sign is used for the odd resonant voltage distribution beneath the patch and between the slot and - sign is used for even resonant voltage distribution. Step-2:  Calculate y0 using formula below by assuming Rin(y=y0) as 50Ω and Rin(y=0) from the above calculation. L is the length of patch. The calculated value of y0 will be between 0 and L/2. Step-3:  Finally you can caculate the width of 50Ω feedline using formula for the microstrip line.

Source:
1. Balanis, Constantine A. Antenna theory: analysis and design. John wiley & sons, 2016.
2. Pozar, David M. Microwave engineering. John Wiley & Sons, 2009.

1. Madam, How did you considered the substrate length & width and size of radiation box? in the antenna design. The above equations are patch antenna design (matching with the simulated design)

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