Calculating Q of slot resonators

Hi all,

I want to calculate the Q of a resonator. The resonator is basically a slot in the ground plane of a microstrip line. I want to calculate the uloaded Q. I mean I want to decouple the effect of microstrip - slot coupling.

-svarun

Hi!

What comes in my mind...
The Q will be dominantly given by radiation Q (I think we can ommit dielectric losses - the slot is filled by air and conductor losses).
Thus, what about to calculate the full structure in IE3D (using magnetic currents) and calculate the radiated power using ONLY selected cells (actually the cells forming the slot only)?
From radiated power and input power you can be able to calculate the desired Q, am I right?

You can find Q_loaded and Q_unloaded using S11 curve

Q_unloaded = (2+b^2+sqrt(4+b^4))/2b

Q_loaded = (1+b+b^2+(1+b)sqrt(1+b^2))/b

where b = S11 or 1/S11 at F_res - coupling coefficient (overcoupled or undercoupled cases)

Hi navuho,

Can you please give me the reference where these formulas are derived ? Else if you derived on your own, let me know some crucial steps.

-svarun