Square Patch Antenna and Rectangular Patch Antenna Calculations

Please can anyone help me with the difference between the calculations for square patch antenna and rectangular patch antenna calculations since there is only one dimension to be calculated for a square. What dimension decides the resonant frequency of a square patch ?

Please help thanks in advance :)

Some time ago I found many formulas on patch antenna calculation. There are many authors discuss this formulas in different ways. You may try to find them too in google. Don't forget to add "filytype:pdf" to your search query (without quotes).
Resonant frequency of patch antenna is mostly dependent on patch length, input impedance is dependent on patch width. Assuming feeding line is at the bottom.
Although in reality everything affects everything. Now-days patch antennas often designed this way:
1) get initial patch size using formulas
2) use EM simulator, and do sweep through patch width, length, inset length, etc.. around initial values
or even manufacturing and measuring prototypes with stepped sizes. 3 widths (+-0.5m), 3 lengths, 3 insets, 3x3x3= only 27 prototypes of single patch.

Thanks for the answer :) If I want to make it a square with only one dimension (width or length) which formula do I use since the formulae on the web are for length and width, should I use their length equation or width equation (given below on this page)

https://www.everythingrf.com/rf-calc...nna-calculator

Georgy gave the answer: "Resonant frequency of patch antenna is mostly dependent on patch length"

You can start with simpler formula:
L ≈ 0.45 * λ₂₀,
0.45 - empirical coefficient mainly for open end effect
λ₂₀ - wavelength for 20 ohm microstrip line (wavelength in wide patch seems to be similar to wide low-impedance microstrip line)
Then use L for both patch width and patch height.

For example:
F=10.525 GHz
Er=4.3
t=1[mm]

20 ohm microstrip line will have λ₂₀≈14.4

Then L ≈ 0.45*14.4 = 6.48 [mm]

Patch height = patch width = 6.48 [mm]

Remaining part is to obtain patch input impedance Z_in by some formula or by simulation.
some more formulas here: http://www.antenna-theory.com/antenn...hes/patch3.php

update: I used different formulas to calculate Z_in, found in different papers. Results was very different, around 100 to 300 Ohm for the same patch W/H , Er, substrate thickness. So do not rely on those formulas for too much.

To add to the discussion, an antenna being square or rectangle have no effect on it. Important parameters are Gain, Return Loss, Directivity etc.
After your calculations it may end up being a square, but its not an important topic. As Georgy already explained in detail, you can use width and length in resistance and resonance calculations.

ktr, patch antenna being square or rectangular does have effect: if you want to maximize gain; for determining location of feed point.

You may have specs in your hand to determine the characteristics of an antenna. After your calculations, it may end up being square or rectangle, but I have never seen an antenna engineer to put focus on antenna being square to maximize gain. Determining feed point is related to impedance of antenna, not with its geometrical shape. Being square or rectangle is just an arbitrary thing in the scheme of antenna design.

"... I have never seen an antenna engineer to put focus on antenna being square to maximize gain..."
now you see one. If you understand how patch radiates it is obvious that antenna width effects both it's gain and impedance.

Yes, exactly. Important parameters are gain and impedance not the actual width itself, hence being square is just arbitrary depending on the specs on hand.

Width effects gain and impedance but I give no importance to "width" and "length" of antenna being "equal" when designing an antenna: because its arbitrary.