Hello! First of all sorry for my poor English.
I would like to put here my recent experience about Q factor concept and definition. Yes, there is a little bit of confusion about the Q factor, especially on the web. But my focus is to understand the definition of Q inside the Generic Equaliser in EQ module of REW.
My experience was this:
I was running the REW (v5) EQ module defining a Generic Equaliser because I don't have none of the predefined equalisers in REW (TMREQ, Behringer DSP1124P, …).
I have a 1/3 oct equliser by Samson, the model D2500. So, I was interested to put the right information on the panel "EQ filters" in order to have the possibility to run the REW EQ procedure to have some suggestion about the equalisation correction for my room (considering measurement made previously).
The first little pboblem is that the Generic Equaliser has 20 filters to be defined and the D2500 (as other 1/3 oct equalisers) has 31 filters. But this was not a big issue because by defining only the first 20 filters I covered the fraquency range from 20 Hz to 1.6kHz. That was enough for me, because the most important 'issues' on my acoustic responce was in the lower range (I have a small room).
The 'challage' was to put the right Q value in the REW Generic equaliser panel! So the question was, what's the Q value of my D2500 filters? I foud a lot of articles about this argument and honestly speaking I found a lot of bad information. So I made some measurement on the D2500 and some filter simulation in REW EQ panel. As alway the best approach is to measure and to understand!!
In the "EQ filters" panel for my 'generic equaliser' I wrote some Q value as defined in many sites on the web (-3dB BW / central frequency or the number that is given by conversion tables so 1/3 oct BW --> Q=4.32 or as the ratio between the resonat frequency and the damping factor in the second order filter…).
But all these definitions was wrong fot the Q to put in the REW EQ Generic equaliser to simulate my D2500 equaliser.
Infact, making a verification, always I found the Q value I wrote in the text box was not corresponding to the real frequency response of my D2500. In order to verify if the Q I selected was right or not, I made the REW measuremt of the frequency responce of my D2500 for a given frequncy (only one filter with a given gain). Of course for this measurement was not used speakers and mic, but was made directly by electrical way (REW outs in the D2500 and D2500 outs in REW). After this, I compared the measured curve of the D2500 filter at that given freqency with the shape displayed in the EQ panel activating the "filter" checkbox under the graph panel. Also I de-selected "invert filter response" in the "Graph contol" options (gear icon in the up-right of the graph window).
In this way you have the measured D2500 filter frequency response curve overlapped to the curve that REW EQ is considering as Generic Equaliser response, i.e. the resulting filter curve after I defined freq, gain and Q in the Generic Equaliser panel.
So, the result is this: the value for Q that fits the real frequency response of my D2500 is 3.0.
For all frequency/filter. Also, this number is constant and it is not depending by the gain of the filter. So, this is the measurement resut. But, which is the Q definition that is matching with this measured number?
This number, 3.0, correspond to the definition of Q as the ratio between central freqency of the filter and the BW at the half value of the peak of the dB magnitude filter frequency response. It must not be confused with the -3dB response! They are very different definitions (infact, as JohnM says "...for filters that have less than 3 dB of gain/cut " the -3dB definition has not sense … "where is the -3 dB point for a 2 dB filter?")
The final check was to set a random curve on my D2500.
I measured that frequency response with REW.
Then I set the same gain values of D2500 in the generic equaliser in the EQ panel (of course with Q=3.0).
I found that the measured curve (the real D2500 response) and the response curve calculated by REW (the "filters" curve in the graph of EQ module) are perfectly overlapped (see figure below).
I don't know, if Q=3.0 is a common number for all the 1/3 oct eqauliser, for sure by inputting Q=3.0 in REW EQ Generic Equaliser you will have the right simulation of the the Samson D2500 by REW EQ module sotware.
Despite my terrible english, I hope you understand something! ;-) By the way if you have some question I will try to answer you (depending of my english capability!!).