Circular Microstrip Patch Antenna Calculator

Input

Frequency \(\nu \)
Substrate Relative Permittivity \(\epsilon_{r}\)
Substrate Height \(h\)


Output

Patch Physical Radius \(a \) ____
Effective Radius \(a_e \) ____
Directivity D ____ dBi


Circular Patch Antenna

The dimensions of circular patch antenna is calculated for the dominant \(TM_{110}^{z} \) mode.

Formula

\(a=\frac{F}{\left \{ 1+\frac{2h}{\pi\epsilon_rF}\left [ ln(\frac{\pi F}{2h}+1.7726 ) \right ] \right \}^\frac{1}{2}}\)

\(F= \frac{8.791e^9}{f_r\sqrt{\epsilon_r}}\)

\(a_e=a{\left \{ 1+\frac{2h}{\pi a \epsilon_r}\left [ ln(\frac{\pi a}{2h}+1.7726) \right ] \right \}^\frac{1}{2}}\)

\(D_{0}=\frac{(k_{0}a_{e})^{2}}{120G_{rad}}\)

\(G_{rad}=\frac{(k_{0}a_{e})^{2}}{480}\int_{0}^{\pi/2}\left [J_{02}^{'2}+cos^{2}\theta J_{02}^{2} \right ]sin \theta d \theta\)

\(J_{02}^{'}=J_{0} (k_{0}a_{e}sin \theta)-J_{2} (k_{0}a_{e}sin \theta)\)

Where:
\(f_r \) = Frequency
\(\epsilon_{r}\) = Substrate Relative Permittivity
\(h\) = Substrate Height
\(a \) = Physical Radius of Patch
\(a_e \) = Effective Radius
\(D_{0} \)= Directivity of Patch Antenna
\(G_{rad} \) = Conductance across the gap between the patch and the ground plane
\(J_{0}\) = Bessel function of the first kind of order 0

Reference:
- [1] Balanis, C.A. (2016). Antenna Theory: Analysis and Design. 4th ed. Hoboken, New Jersey Wiley, pp.814–823. Chapter 14.3 Circular Patch.

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