There is no optimum length. If the patch is properly matched to the cable then the length of the cable is irrelevant, except for any loss it has.

If the length of the cable affects the resonant frequency then the cable is not matched, at both ends, or the feed is not balanced/unbalanced correctly, so that there is current down the outside of the coaxial cable.

It does not matter as HFSS see the voltage at the feeding point. I do use 10 mm long. If the length of cable effect, then there must be some kind of mismatch. It should not affect the performance of the antenna. Due to that reason, in practice, the length of cable must be accounted during calibration.

Thanks Malcolm White and Sudipta Maity for your comments. i overlooked this aspect when designing, surely it will help improve my designs, i will try these suggestions.

Malcolm White can you elaborate a little about your comment,"or the feed is not balanced/unbalanced correctly."

I think you are talking about the coaxial cable being unbalanced line so must be balanced

Dipoles require a balanced feed and if fed directly from coax which is unbalanced then current ends up on the outside of the coax, which is not terminated and causes resonances depending on the coax length. A balun is used to stop this. If you are feeding your patch with the wrong kind of line, that might result in currents on the outer and resonances. It would be surprising because a patch over ground requires an unbalanced feed, but if the ground wasn't big enough then you would get currents on the outside of the cable.

The point of the feed cable is that it should be matched to its characteristic impedance at both ends. Patches have transforming sections or slots or stubs to do this if it is needed. Most generators are designed to be matched to the cable impedance usually used, which is 50 or 75 ohms depending on the application.

Matching using a long cable with a strange impedance and mismatches at both ends could be done but will be very narrow band and liable to de-tuning with temperature and cable movement.

Thanks Malcolm White my case is similar to what you described, the patch has small ground plane

For the small values of the inner and outer radius of coaxial cable, you can take its length between 5 and 6.5mm for cable impedance equal to 50ohm.

Thank you Raja Mchaalia , I usually take radius 1.04mm for inner conductor and 3.54mm for outer. As Malcolm and Sudipta said the shouldn’t matter, what matters is the impedance at each end of coax. But I would definitely try what u said, can u also mention the radius u are talking about or tell the range for my values mentioned above.

I took 0.8mm for inner radius and 2.7mm for outer radius and 5.5mm for cable length.

Good luck

Thank you once again Raja Mchaalia

I think to determine the inner and outer conductor diameters one should use the equation for co-axial cable for desired characteristics impedance.

Yes Krunal Patel but you can use SMA connector which has the impedance value what you need and also frequency range

Hey Krunal Patel the values that I have taken, I have simulated and checked the impedance in HFSS, and it is almost 50Ohms. I agree with both of you Krunal Patel and Raja Mchaalia

It is always better to choose the dimensions of the coaxial probe as available in the local market. Otherwise, it will cost you huge. I was not able to publish one journal paper just because of coaxial probe (which cost rs. 20,000/- per items). We do have 0.65mm and 2.1mm rad of inner and outer conductor, er =2.2 Teflon. I do prefer to use that one only as it is available in our local market easily

Thanks Sudipta Maity , you are absolutely correct about the market availability. This is good info, i have also faced similar situations to procure PCBs based on few substrates.

Thats why, choose your coaxial probe first, then use it in your antenna, then modify the ground plane or other items.

First, see the market availability of your cables then try to simulate with those dimensions. Also, the longer length has not any effective change in the results at the simulation so this is not a serious thing.

Thanks

thanks for sharing Harshavardhan Singh

The length of the probe will not affect the results if you have made the calibration procedure at the tip of the cable