You dont "HAVE TO" have Q in your equations, its just another look
at a networks behaviour. That being said a 2 pole filter can exhibit
"peaking" which is where Q is often used as an indicator or the level
of peaking. Example in a LPF :
As poles approach y axis Q rises because energy dissipated in real R drops :
So Q here is meaningful about this peaking effect but is NOT NECESSARY in a T(jw) expression.
Pole Zero locations and effects (exponential growth/decay) on a signal "
Practice makes perfect as the expression goes. You write node and loop
equations, those are fairly simple, and solve for T(jw) or T(s) = Vout / Vin.
Straightforward algebraic manipulation. Note however as the number
pole zeroes rises > 2 that becomes very tedious. Thats why things like
signal flow graphs reduce the pain and tendency to want to jump off a
bridge trying to solve. As was done in post #6.
Regards, Dana.