Coupling Coefficents for square open loop resonators ?

when u compute coupling coefficents from em simulation the formula Kij =±(f2b-f2a)/(f2b+f2a) is only valid for narrow BW as derived from lumped element approximation. How to compute Coupling coefficents for wider BW ?

Thanks

further detail :
i had been designing cross coupled filters for narrow BW using this technique (up to 10%). now i need a miniaturized filter design so i will go for Aperture coupled open loop resonators (double sided, back to back) bt i need BW of 16%. i know it prior that theory wouldnt work because it was derived for narrow BW approximation.
Can any one help me out on this ?

Thanks

How did you know that the formula is valid for 10% bandwidth while not valid for 16% bandwidth? I designed filter as wide as 50% (non-cross coupled), and didn't see any big problem with it.

As for the cross coupled filter, you cannot make wide bandwidth only because you cannot make strong enough cross coupling, which may not have anything to do with the formula itself.

I believe this equation still works for wider BW. Only difference is the Kij you calculated is biger than your narrow band.

You can use the exact same way, get fb and fa from eigen mode and do the calcualtion.

I did a 15% BW filter before.

ya i agree, for some 50 % BW i can not make strong enough cross coupling but for low BW (say 20 %) it is quite possible to achieve such couplings. Thicker board (50 mil or higher) would made the job easy and low dielectric if size is not a constraint.

But the thing is when i design CQ filters for some 20 % BW , return loss is not satisfactory not optimum. it is barely -10 dB.
i want sharp cut off (thats why inserting transmission zeroes ) , BW approx 20 % and good return loss. can u help me out ? and plz suggest me some good topoligies for wide BW filters say 40 % .
Thanks

---------- Post added at 18:23 ---------- Previous post was at 18:15 ----------

Thanks for answer buddy :) bt this procedure is for low BW only. i refer to ieee paper " coupling of microstrip square open loop resonators for cross coupled planar microwave filters " by j s hong.
the formula was derived from lumped element approx which is only valid for small BW near resonance.

i would appreciate ur comments :) and wat was ur design procedure for 15 % BW . which em simulator u used and what was the return loss ?