How to obtain unloaded quality factor using group delay?

[tucheng]

Hi everyone
The equation below shows how to obtain unloaded quality factor using group delay(f0 is resonant frequency. IL is insertion loss at f0. td is group delay). But I do not know how this equation is obtained. Can anyone give me some clues? Thanks.
Qu = pi*f0*td*( 10^(IL/20) )/( 10^(IL/20) - 1 )

 

[Luism]

That equation is derived in Matthaei's book in section 6.15 pag. 343. The equation number is 6.15-4.

I'm also looking for a similar, but more general, derivation. If you find one please let me know.

Reference: Microwave filters, impedance-matching networks, and coupling structures. Matthaei, Young, and Jones.