help understanding balanis definitions of total qulity factor

[yefj]

Hello,there is a balanis definition of quality factor shown below where we use VSWR f0 and VSWR.
but what the exact definition of fractional bandwdth they use ?
the delta_f,where its written in the book?
Thanks.

 

[JonathanC]

Not sure if I understand your question correctly. Delta F is the frequency operation bandwidth. The meaning of this equation is basically telling you that you can increase your operation bandwidth by reducing the Q factor.

 

[volker@muehlhaus]

delta_f,where its written in the book?

I don't know where it is written in your Balanis book, but bandwidth used in this resonator Q equation is half power bandwidth (-3dB)

If you have access to Pozar "Microwave Engineering", you can find detailed derivations for series and parallel resonstors.