Quality factor of a short circuited transimission line A resonant freqency...

Hi

From Pozar, I know that Q=beta/(2*alpha) = pi/(4*alpha*length); ---valid for short circuited transmision lines

and from resonant theory (parallel resoant circuit) Q= slope(imag) * fo /(2R).

I am using ADS, I use 2 port simulation to extract alpha and beta..and find Q? or use one port simualtion to extract Q?

Which one is valid?

Thanks
Venu

None! I guess you have to do experiment in order to find the Q.

So, there's no qualitative treatment for estimating thequality factor of a short circuited tx line?

Yes, there are. If you want to simulate, you have to get all the parameters right, such as metal loss, dielectric loss, radiation loss, etc, and also assuming the software you use was correctly programmed regarding estimating quality factors. It's much easier to do the experiment and measure the quality factor. You may also use empirical formula (either by someone else or by yourself) for your estimation.

So, in oder to be empirically, there's are 2 techniques which i understood..

Using a simulator Q=im(Zin)/real(Zin)...

But i wanted to find the Q for a resonator @ at the frequency of resonance..

So, I used a short circuit transmission line resonator ..

In pozar they have stated that Q = beta / (2*alpha); and
in a paper i came across Q is proportional to change in imaginary part (d(Xc)/df)

The one thing which i am unable understand which one is right..? are both valid ...

The deduction from
Q= w/(2*R) * dX/Dw@wres
to
Q=beta/(2*alpha)
is shown in this paper (in the Appendix)
Lee et al. - "Lumped-element planar strip array (LPSA) for parallel MRI"
Magnetic Resonance in Medicine 2004 Jan;51(1):172-83.
There are some assumptions as long as I can see.