S-parameters Explanation

Hello to everyone.I have designed a multiband antenna(microstrip rectangular) based on metamaterials(SRR). My resonant frequency is 2.5GHz, but my antenna is also multiband at frequencies 2.6, 5, 7.6, 8.9, 11.8. I have not discrete ports, I have a waveguide port. Can you please explain me from where do derive these frequencies in S-parameters? Why is there a frequency at 7.6 and not at 6 or 8 or anywhere else? My main question is in which theory do the S-parameters based on, so I can realise why I have these results(frequencies).

Thanks in advance

when you excite your structure with waveguide port then all possible modes are excited the structure which can exist in your structure which you can see with Eigen solver. You can force your structure to have a particular set of modes by imposing boundary conditions which will eliminate a set of modes. So it is the design of your structure and boundary condition which will define the modes/ frequencies which can be excited in the structure. Now coming to the second half of the problem for any driven model you define the solution frequency in your solution setup and HFSS/CST solves model on that particular frequency and calculates S matrix now if your structure is not tuned for that solution frequency you will get max reflection very bad transmission and no isolation and in some cases nothing may be coupled at all.

I understand this,but I need to prove that the design is responsible for these specific s-parameters.In other words it is like I want to know the algorithm or the equations that may CST use to get these S parameters.

thanks for your answer

i think cheking the current distribuation on antenna helps you.

It is not that simple to understand how CST/HFSS solve Maxwell equations to get the results as both are based on FEM Finite Element method. If you are really interested then you can start with some basic book of FEM.

I know about FEM that is a method to calculate the dimensions,but my main question is why do i get these results for S-parameters and not something else? Is it all about dimensions? And if it is,how can I prove this? How can I explain the fact that my S-parameters are at 2, 5, 7, 8GHz and not at (for example) 3,4,6,10GHz? Are there any equations that combine S-parameters, dimensions, or anything else? thanks a lot for your answers.

I know about FEM, but my main question is why do i get these frequencies for S-parameters? Are there any equations that combine the s parameters with dimensions? and if there are i wanted to know them.
thanks a lot!

The frequencies what you are seeing is roughly nfo. The designed antenna may also be resonant at all these frequencies. If you see the current distribution at far fields these frequencies may exhibit the maximum current distribution.