side coupled ring-resonator, Q-value equations etc?

Hi

I have a microstrip line side coupled to a microstip ring-resonator, that is the ring is placed beside a normal microstrip line.

The measured and simulated values gives only an S21 of about -0.35dB at resonance? Compared to the value of about -0.25dB of the pure microstrip line at the same frequency.
My microstrip and ring width is 206 um, substrate thickness 80um, er=3.05, tand=0.024, ring diam=16mm, gap=30um between ring and microstrip line, microstrip line length of the coupled line is 15mm.

How to calculate the Qu value and also the loss Eeff from this circuit and where to find the defined equations for this case? Since my resonance point is not so low I can't define and use the normal -3dB bandwidth as normally used for the end coupled resonators.

I have only found equations,papers for the end coupled ring resonator which normally gives a distinct resonnance with S21-30dB or similar for a low coupling.

But in this case the coupling gives only a resonance of aboyt S21-0.35dB, that is very low. Is this normal? WHat is the advantage of using a side coupled resonator instead of a end coupled when e.g. performing material characterization of eeff and tand of a unknown material?
Pleas if any one have papers about the two port side coupled ring-resonator please email me or upload them for me. I haven't been able to find any closed form equations for the side coupled ring resonator in the litterature useful for determing the eeff and tand at the resonant point.
Thank you

For characterization of material the arrangement that you have shown is not prefered.
If you can design a ring & place feed or say coupling line bellow the ring then you can get good results.
this structure is also movable so you can adjuct the coupling.
The S21 you have got is low.
Have you tried varing coupling between ring & microstrip line?
For what purpose do you need this structure?
If you can specify then it is possible to find perticular paper.
Which software have you used for simulation?

The intention is to use this structure to measure the materials tand and eeff from the resonance peak.

The gap is small between the line and the resonator,which are made on the same layer, gap=30um
This should generate an sufficient coupling but the resonance is still very low. A larger gap gives even a lower value of the resonance (less peak).
The simulation is made in HFSS but I have also simulated the same response with ADS layout (Momentum).

I have no title of any paper since I haven't found any reference or paper describing the exact Q-value and derivation of the tand from the measured S21 resonance peak for this set up. I dont know how to do this with this structure.

There are equations for the end coupled case and should also excist for the side coupled resonator. But I haven't found any why I need help.

Thank you