Calculale R, L, C of a spiral resonator

[nvt088]

Hi everyone.
I want to make an equivalent circuit and calculate R, L and C value of a spiral resonator, which is printed on a substrate as I show in the picture.

Can you help me how to do it? What is the best way?
Is there any good book or paper talking about this issue? Many thanks.

 

[zhul3]

I am not a planar guy but the basics are always the same.

The structure looks to me like a T network, two series inductors and a shunt capacitor between them.

Spiral inductor, you can find equations everywhere online to calculate an approximate L
Capacitor, you can use the parallel-plate equation, get the metal areas, gap length, to calcate the approximate C

Then do some optimization based on the initial L, C, to meet the simulated center freqeucy = 1/sqrt(LC)

regarding R, just find the simulated Loss and do the curve fitting to achieve the R

 

[D.A.(Tony)Stewart]

These can be printed on certain papers and found in high end stores using RFID's.

Some designs here for 13.56 MHz
https://ww1.microchip.com/downloads/en/AppNotes/00710c.pdf