Which responses became "identical"? It is not clear to me....Yes but then again i amended that spec for this kind of viewpoint and stated that the first order could be said to have a virtual Q of 0.25 not 0.5, but then i amended it a second time (perhaps not as clear) as having a Q of zero because in the limit the response becomes IDENTICAL from w=0 to w=infinity. I'll double check this though.
Please, can you tell me why we should even try to define a Q value for a 1st-order function?I guess the main theme i am seeing from all these tests and thoughts is that although saying the Q should be 0.5 may not be the best idea, it can be said that the first order filter has an equivalent "Lowest possible Q" maybe without assigning a number to it, or Q=0.
Is there any sense or advantage or even a necessity?
I understand what you mean - and, in general, I agree with you.Please keep in mind that the pole position idea came from the distant past. From that point of view, this is the future. The future always holds changes sometimes big changes sometimes small changes. When we seek to understand things we cant always rely on a mechanical application of theory sometimes we have to amend or it may be good to amend. Along the way i have found many things overlooked in theory even though most if it works just fine.
However, in this specific case, I think we can and should stick to the existing definitions. As mentioned before, I see no advantage or even necessity for a redefinition of the quality factor for lowpass functions.