Hi perado and rezaee
I did a bit of reading about different definitions of Q and I have to say I am quite confused, there are a lot of references to Q being defined as
Im(Z)/Re(Z)
at 'resonance' but...
...this definition usually provides a different result for Q than the other common definition that holds for second order systems with complex conjugate poles/zeros
1+1/Q (s/w0) + (s/w0)^2
I am under the impression that the two are related but do not coincide even in the case of high Q (the first definition seems to be a factor of 2 larger than the second)
Given that the system you guys are looking at has second order behavior at resonance (the admittance pole R/L is much smaller than w0), I would stick with the second definition, in that case you can easily calculate (see #41)
Q = 1/(2*zeta) ~ w0 (LG+RC) ~ w0/LG =sqrt(C/L)/G ~sqrt(gm2/gm1) sqrt(Cgs1/Cgs2)
a possible way to get Q in ADS (beware I have never even seen the tool) would be to find the value of Y at resonance as the minimum of Y(iw), the value should be in linear scale
ymin = sqrt(C/L)/Q
not a direct measure but still...
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This
link should cast some light on the different definitions: according to it, both definitions are used as figure of merit for resonant circuits and at high Q the two Q's are proportional but not the same
I guess in your case all that matters is consistency between what you calculate for the active inductor from small-signal parameters and what you simulate in ADS; in one case (second order Q parameter) the hand calculation result is simpler, in the other (ratio of imag/real at resonance) the simulation is easier to perform but hand calculation results are harder to get and the result more cumbersome