Resonator Parameters

Click here to go to our main page on filters

Click here to go you our (extremely modest) page on resonant cavities

New for July 2021. This analysis is valuable to anyone who needs to look at unloaded resonator Q.

From Professor J.M. O'Callagan at the Commsenslab Unidad de Excelencia María de Maeztu over at the Polytechnic University of Catalonia ( 

We have put together a free, web-executable resonator parameter calculator.  It only requires uploading a Touchstone file (.s2p) with the measured S-parameters and the calculator returns resonant frequency, loaded and unloaded Q, and coupling factors.  You can check it at:

The tool is very easy to use - just upload a Touchstone file and the results display as graphs on the web page.  It's also cool that they have released it all as free and open source - you can get all the source files on github.

ABSTRACT: We describe an algorithm capable of extracting the unloaded quality factor and the resonant frequency of microwave resonators from vector S-parameters. Both symmetrical (Lorentzian) and asymmetrical (Fano) transmission responses are supported. The algorithm performs an adaptive outlier removal to discard measurement points affected by noise or distortion. It removes the effects caused by imperfections in he device (such as modes with close resonance frequencies or stray coupling between the resonator ports) or the experimental setup (such as lack of isolation or dispersion in the test-set and cables). We present an extensive assessment of the algorithm performance based on a numerical perturbation analysis and on the evaluation of S-parameter fitting results obtained from network analyzer measurements and resonator equivalent circuits. Our results suggest that uncertainty is mainly caused by factors that distort the frequency dependence of the S-parameters, such as cabling and coupling networks and is highly dependent on the device measured. Our perturbation analysis shows improved results with respect to those of previous publications. Our source code is written in Python using open source packages and is publicly available under a freeware license.

FULL PAPER: (requires login)

or - (requires login - but i was able to download the PDF)

ARPE  (Algorithm for Resonator Parameter Extraction) online calculator: ARPE (

UPC = Polytechnic University of Catalonia - Barcelona Tech 

You can watch a video about the Commsenslab:


Source : ARPE