Calculating microstrip ring resonator frequency using formula.

Fcenter=C/(2*Pi*R*Sqrt(Ereff))

The microstrip ring will resonate at fundamental fo when the circumference 2*Pi*R = λg, where λg is the guided wavelength.
A ring resonator has multiple resonant frequencies which correspond to a condition where the parameter of the ring is an integer multiple of the guided wavelength (f = n*fo, where n=2,3,4...)

Information about guide wavelength you can get from here:
http://www.microwaves101.com/encyclo...eguidemath.cfm

i did calculations based on photos of ring push-push oscillators from few papers, where Er is given and microstrip lenghts can be calculated relative to active device photos. After checking photo scale in mm/pixel we able to convert photos to 1:1 true layouts with all sizes in millimeters. Problem is ring resonator radius on layouts always differs from my calculations radius by huge amount of about 2mm, wich is very big difference in frequency. There are few ring resonator oscillator papers available in internet, and i always get such result. At first i thought that maybe photo provided in paper is some prototype with other frequency, but after checking another paper with another photo i get the same difference. I used simple formula with effective dielectric constant to to obtain radius.