Q-Factor vs. Bandwith - Page 2 - Home Theater Forum and Systems - HomeTheaterShack.com

Old 03-20-15, 03:50 AM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

Here below you can find the results if we take another definition for Q.

I calculated Q, as in the previous case, as the ratio between center frequency and the bandwidth, Q= fo/BW, but now condidereing BW= fb - fa, where fa and fb are the frequences where the curve value is the half of the peak value.
The results are these:

Gain= +12 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= +11 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= +10 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= + 9 dB, fa=21.0 Hz, fb=29.2 Hz ---> BW= fb-fa= 8.2 Hz ---> Q= 25 / 8.2 = 3.0
Gain= + 8 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= + 7 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= + 6 dB, fa=21.5 Hz, fb=29.7 Hz ---> BW= fb-fa= 8.2 Hz ---> Q= 25 / 8.2 = 3.0
Gain= + 5 dB, fa=21.5 Hz, fb=29.7 Hz ---> BW= fb-fa= 8.2 Hz ---> Q= 25 / 8.2 = 3.0
Gain= + 4 dB, fa=21.0 Hz, fb=29.2 Hz ---> BW= fb-fa= 8.2 Hz ---> Q= 25 / 8.2 = 3.0
Gain= + 3 dB, fa=21.2 Hz, fb=29.5 Hz ---> BW= fb-fa= 8.3 Hz ---> Q= 25 / 8.3 = 3.0
Gain= + 2 dB, fa=21.2 Hz, fb=29.4 Hz ---> BW= fb-fa= 8.2 Hz ---> Q= 25 / 8.2 = 3.1
Gain= + 1 dB, fa=21.4 Hz, fb=29.3 Hz ---> BW= fb-fa= 7.9 Hz ---> Q= 25 / 7.9 = 3.2

Here below you can see the graph for the case +12dB:

As you can see the result is always Q=3.

Last edited by Confocal; 03-20-15 at 08:46 AM.
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Old 03-20-15, 07:51 AM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

I uploaded some images in my previous post. In this way I hope it is more clear...
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Old 03-20-15, 10:22 AM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

As a side effect of my measurements on Samson D2500 to understand how to simulate it in REW, there is an important discovery: the Samson D2500 is not a true GRAPHIC equalizer. It means that the D2500 NOT truly delivers the "graphic" representation of the equalization curve with the front panel sliders. This type of 'error' is caused by the NOT constant Q filter (where Q is defined as the BW at -3dB from peak). See my previous post, where the Q defined by -3dB BW goes from 5.7 to 1.8 changing the gain from +12 dB to +4dB.

This is an interesting article from Rane: http://www.rane.com/note101.html

The 'side effect' conclusion is: when I look the sliders curve on the front panel of my D2500 equalizer, this 'curve ' is not the true equalization curve that the device is performing. If you want to know the true equalization delivered by the D2500, you need to measure it with REW or to 'simulate' it with the EQ module of REW (use Generic equalizer with Q=3.0).

An example of what I am saying is the measurement I made on the D2500 response when it shows this slider positions:

The resulting measure is this one:

It is clear that at 20 Hz I'm not having -12dB as cursor says, but about -17 dB! This is because at 20Hz there is also the 'side' effect of 'some other gain' performed by the adjacent 25Hz filter.

This kind of error is more evident for low values of gain.

An other example is for this set-up:

The red curve is the position of the cursors on the front panel of Samson D2500
The yellow curve is the REW measure of the equalization curve

The errors, in dB, between two curves are:

f=20 Hz, cursor at -12dB, Measured value = -16.1 dB, error -4.1 dB,
f=25 Hz, cursor at -12dB, Measured value = -18.3 dB, error -6.3 dB
f=31.5 Hz, cursor at -12dB, Measured value = -12 dB, error 0 dB
f=40 Hz, cursor at +12dB, Measured value = +10.2 dB, error -1.8 dB
f=50 Hz, cursor at +12dB, Measured value = +13.7 dB, error +1.7 dB
f=63 Hz, cursor at 0 dB, Measured value = +4.8 dB, error +4.8 dB
f=80 Hz, cursor at 0 dB, Measured value = +1.8 dB, error +1.8 dB
f=100Hz, cursor at 0 dB, Measured value = +1.1 dB, error +1.1 dB
f=125Hz, cursor at 0 dB, Measured value = +1 dB, error +1 dB
f=160Hz, cursor at 0 dB, Measured value = +1.9 dB, error +1.9 dB
f=200Hz, cursor at +2 dB, Measured value = +4.6 dB, error +2.6 dB
f=250Hz, cursor at +5 dB, Measured value = +7.7 dB, error +2.7 dB
f=315Hz, cursor at +5 dB, Measured value = +7.7 dB, error +2.7 dB
f=400Hz, cursor at +2 dB, Measured value = +4.3 dB, error +2.3 dB
f=500Hz, cursor at +2 dB, Measured value = +1.5 dB, error -0.5 dB
f=630Hz, cursor at -5 dB, Measured value = -4.7 dB, error +0.3 dB
f=800Hz, cursor at -3 dB, Measured value = -4.0 dB, error -1.0 dB
f=1000Hz, cursor at 0 dB, Measured value = -1.3 dB, error -1.3 dB
f=1250Hz, cursor at 0 dB, Measured value = -0.4 dB, error -0.4 dB

The error may be of several dB of of the same quantity of the dB desired correction!!

Last edited by Confocal; 03-20-15 at 12:13 PM.
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Old 03-20-15, 05:00 PM
Shackster

Join Date: Oct 2013
Location: EU-FIN
Posts: 40
Re: Q-Factor vs. Bandwith

Quote:
Confocal wrote: View Post
...
The resulting measure is this one:

It is clear that at 20 Hz I'm not having -12dB as cursor says, but about -17 dB! This is because at 20Hz there is also the 'side' effect of 'some other gain' performed by the adjacent 25Hz filter.

This kind of error is more evident for low values of gain.

...
You should study little how the graphic equalizer works ... try find some graphic or parametric equalizing software with plot feature (standalone or plugin (for plug-in you'd need some host software)) to see how peaking filter (this is the common filter type used in graphic EQ's) acts (google is a good friend in this but, I could suggest my own fPEQ for this which is kind of dummy parametric EQ used for to write filter commands into a file to be used with EqualizerAPO).
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Old 03-28-15, 10:12 AM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

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Old 03-28-15, 04:42 PM
HTS Senior Moderator

Join Date: Apr 2006
Location: Katy, Texas
Posts: 8,809
Re: Q-Factor vs. Bandwith

Interesting study, Confocal.

Quote:
Confocal wrote: View Post
Here below you can find the measurement results on my Samson D2500 equaliser (1/3 oct equaliser).

The first measure was the 0 gain curve, the other 12 measures was about the 12 positive gain positions of the cursor at 25Hz with 1dB step (I made only the measurements with the positive gain, i.e. the cursor on D2500 is moved up). See image below:

As you have discovered, the Samson D2500 is an example of a variable Q equalizer, where the filter Q changes with the amount of gain applied. See below the graph below of a constant Q equalizer, the Yamaha YDP2006 digital parametric. Notice that the filter shape stays fairly constant no matter what the gain setting.

Not that variable Q equalizers are necessarily bad, they certainly have their place. They aren’t a good choice for room correction, but they are good as “tone controls,” where a change in audible sound of the speaker or instrument at a certain frequency is desired. The point is, the equalizer type needs to be chosen for desired the task.

Quote:
Confocal wrote: View Post
As a side effect of my measurements on Samson D2500 to understand how to simulate it in REW, there is an important discovery: the Samson D2500 is not a true GRAPHIC equalizer. It means that the D2500 NOT truly delivers the "graphic" representation of the equalization curve with the front panel sliders.
Sure, it is a graphic equalizer. It’s merely a generic term to describe the type, which gives an idea of response changes when the settings are moved, as opposed to a parametric EQ or a 1/3-octave EQ like the White Instruments 4400. No one who knows how filters behave expects the sliders to give a laboratory-accurate presentation of response, and people familiar with equalizers in general know that the sliders with a good constant Q design will give a better representation of actual response changes than a variable Q.

Quote:
It is clear that at 20 Hz I'm not having -12dB as cursor says, but about -17 dB! This is because at 20Hz there is also the 'side' effect of 'some other gain' performed by the adjacent 25Hz filter.

Yes, you’re seeing the effect of “stacking” filters. This will happen with probably any equalizer.

To be fair to the Samson, you might be expecting too much from a \$200 equalizer. Take another look at your graph below, and notice how the D2500 shifts the frequency center back and forth with different gain settings. The 10 dB trace (blue-green, fourth from the top) is a bit below the 24.98 Hz center line, as is the 4 dB trace (purple, fourth from the bottom). Conversely, the 5 and 6 dB traces (red and blue) are centered above the 24.98 reference.

Perhaps you can see why top-grade models cost 4-5+ times more than the Samson.

Quote:
If you want to know the true equalization delivered by the D2500, you need to measure it with REW
Well said. This is true of any equalizer, no matter the make, model or cost.

Regards,
Wayne

Wayne A. Pflughaupt is offline
Old 03-30-15, 04:28 PM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

Quote:
Wayne A. Pflughaupt wrote: View Post

To be fair to the Samson, you might be expecting too much from a \$200 equalizer.
Maybe I was not so clear because my poor English…. I know I have a 200\$ equalizer and I know which results I can expect from this device! I write some notes about the 'true' frequency response vs the graphic curve of the front panel sliders, because I think a lot of people don't know this important issue! They spend a lot of time to adjust + or -0.5 dB on the sliders and they don't know that they are making errors of several dBs compared with the sliders curve! Do you agree?!

I agree perfectly with you that this type of equalizer (graphic equalizer) is not the best to make room correction. Graphic eq are not so useful for room equalization…the best are parametric eq as you are saying (I'm looking for something…). In the while, I have this Samson graphic equalizer, so I am trying to do the best with this device.

It's very interesting to use the EQ module in REW to have some suggestions about an equalization curve to correct 'the defects' of my room. After some diffusers, some absorbers and bass traps…now it's the moment for me to try to adjust a little bit the final frequency response with an equalizer. I have a very small room for audio production and there are a lot of interesting challenges in the frequency range under 400Hz!!
So, the main target of my post was to tell everybody that, with some measurement, I discover the right Q number to put in the 'Generic EQ' in REW EQ module if you want to 'simulate' a Samson D2500. This value is Q=3.0. And this value matches with the 'half peak value' bandwidth definition (that is not the -3dB bandwidth).

Of course when you perform measurement, you discover always something else of interesting…but, I repeat it, the main target for me was to understand which is the best value to put in the Q 'text box' of EQ REW module to have the best modeling in REW of my Samson D2500.

Thank you again for the interesting post about the constant Q eq and the other notes!

Regards!

PS: I recently bought a Behringer DSP 1124P from an important online store. When I received it, I was very surprised about the poor quality of this device !! Ok, it's another cheap device…but the quality of the assembly and manufacture was very very poor. Inside there was a ferrite free to move because the glue that fix it, was broken. The PCB's inside was very poor, the internal wiring was fixed with other detached glue, one important cable connector was partially inserted and partially off from the PCB socket, the packaging was poor, …. at the end I returned the equalizer!!! The store apologize with me and they sent another unit. The 'new' one has the same kind of problems! I returned also that unit! Now I am looking for a parametric equalizer, but my budget is small I am looking for an used Yamaha YDP2006…any suggestion for a cheap but 'honest' device?
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Old 03-30-15, 04:38 PM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

Quote:
Wayne A. Pflughaupt wrote: View Post
Interesting study, Confocal.

...

Yes, you’re seeing the effect of “stacking” filters. This will happen with probably any equalizer.
Yes, you are in right, it is the effect of the side band of the near filters, that add 'other' gain or cut to the selected filter. But I think in the equalizers with constant Q factor this 'issue' is not so big.

For example here there is a interesting article from Rane: http://www.rane.com/note101.html
Confocal is offline
Old 03-30-15, 06:20 PM
HTS Senior Moderator

Join Date: Apr 2006
Location: Katy, Texas
Posts: 8,809
Re: Q-Factor vs. Bandwith

Quote:
Confocal wrote: View Post
Maybe I was not so clear because my poor English…. I know I have a 200\$ equalizer and I know which results I can expect from this device! I write some notes about the 'true' frequency response vs the graphic curve of the front panel sliders, because I think a lot of people don't know this important issue! They spend a lot of time to adjust + or -0.5 dB on the sliders and they don't know that they are making errors of several dBs compared with the sliders curve! Do you agree?!
Depends on the equalizer. For variable Q equalizers I’d tend to agree. A boost or cut of say 3-4 dB results in a boost of at least 1 dB or more change at the adjacent slider, even if it hasn’t been moved. (It’s not uncommon for people knowledgeable about equalizers like this to slightly adjust the adjacent sliders to counteract the variable Q effect – they even have a term for it, “equalizing the equalizer!")

However, I would expect most decent constant-Q graphic EQs to give a reasonably good visual of the change in response introduced by the sliders, at least until severe boost or cut amounts are applied (say, more than 5-6 dB).

Quote:
So, the main target of my post was to tell everybody that, with some measurement, I discover the right Q number to put in the 'Generic EQ' in REW EQ module if you want to 'simulate' a Samson D2500. This value is Q=3.0. And this value matches with the 'half peak value' bandwidth definition (that is not the -3dB bandwidth).
Hopefully people with that equalizer will find your hard work to their benefit.

Quote:
PS: I recently bought a Behringer DSP 1124P from an important online store. When I received it, I was very surprised about the poor quality of this device !! Ok, it's another cheap device…but the quality of the assembly and manufacture was very very poor. Inside there was a ferrite free to move because the glue that fix it, was broken. The PCB's inside was very poor, the internal wiring was fixed with other detached glue, one important cable connector was partially inserted and partially off from the PCB socket, the packaging was poor, …. at the end I returned the equalizer!!! The store apologize with me and they sent another unit. The 'new' one has the same kind of problems! I returned also that unit!
Sad to hear this. In recent years Behringers has noted on their website that they had quality-control problems for years with the Chinese factories they contracted with, so they ultimately decided to build their own factory in China to have complete control on quality. Sounds like it’s not working out.

Quote:
Now I am looking for a parametric equalizer, but my budget is small I am looking for an used Yamaha YDP2006…any suggestion for a cheap but 'honest' device?
As you said, the YDP2006. It’s as good as it gets. Lots of satisfied users here and at other Forums. I’m proud to say that I was the one who discovered this baby and introduced it to home theater enthusiasts. Just check my review for tips on how to make sure you get a good one, not one that’s been beat to death. You can find it in my signature.

Speaking of, would you mind if I use your variable Q graph in the review? I’m currently using one from Rane, but yours is much better! I’d give you credit as the source, naturally.

Quote:
Confocal wrote: View Post
Yes, you are in right, it is the effect of the side band of the near filters, that add 'other' gain or cut to the selected filter. But I think in the equalizers with constant Q factor this 'issue' is not so big.
Correct.

Quote:
For example here there is a interesting article from Rane: http://www.rane.com/note101.html
Yes I’ve seen it, and the other Rane articles on equalization too. All good stuff.

Regards,
Wayne

Wayne A. Pflughaupt is offline
Old 04-01-15, 03:55 PM
Shackster

Join Date: Feb 2013
Posts: 12
Re: Q-Factor vs. Bandwith

Quote:
Wayne A. Pflughaupt wrote: View Post
Speaking of, would you mind if I use your variable Q graph in the review? I’m currently using one from Rane, but yours is much better! I’d give you credit as the source, naturally.

Of course! You can use my measured curves as you prefer! Do you need some other measurements on my D2500? Do you want the same set of curves but centered in the 'usual' 1kHz frequency? Let me know!

Bye!
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