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The recurring discussion of  "fast bass" has led me to suggest that differences in group delay can account for this perceived phenomenon.   Below is my recent post followed by comments from David and Dan.  At the bottom of the page is a screen shot showing comparisons of the frequency response and group delay for three closed boxes which differ only in their low end bandwidth.   Finally, I offer a way to extend the bass of closed boxes using a "Linkwitz Transform" line level equalizer.


Here is how the recent discussion went:

Bassers,

David Hyre wrote:

<< The topic of "fast drivers" came up 1-2 weeks ago and it took me a while
to find relevant data. Here is a table I posted a long time ago. The basic
risetime data was posted by George Li, so I asked him to send me the
high-end rolloff points of the drivers as well, to prove a point I and
others were trying to make at the time. I argued that the "speed" of a
driver is nothing more than its bandwidth and can be approximated by op-amp
theory. >>

Thanks to David for pointing out that "fast" (fast rise time) is just another way of looking at system (driver) bandwidth. I'd agree with Dave that the high frequency bandwidth of our woofers is probably not the parameter that relates to perceived "fast bass". It must be something else.

I think that when audio enthusiasts talk about "fast bass" it is the subjective effect of group delay that they are hearing. What we really crave is bass that is "on time". That is, not lagging behind the rest of the frequency components of broad spectrum (10 octaves!) audio. This delay that changes with frequency is also what can muck up the shape of a square wave as it passes through a filter. In order to reproduce a square wave all frequencies must arrive at the same time.

A well known characteristic of high pass filters is the fact that the signal experiences frequency dependent delay. All the frequency components of the signal might go into the filter (loudspeaker) synchronized in time but they emerge with the lows tending to be delayed more than the highs. This results in what I call "time smear". The only way to really reduce it is to extend the low frequency cutoff of the system ever lower.

Consider two of our most common enclosure types: a closed and a vented box. If we do a quick model of each type of system where the cutoff frequency of each system is about 32 Hz then we see that the closed box experiences a group delay of about 7 milliseconds at the 32 Hz corner frequency while the vented box experiences about twice that delay at the same frequency. This makes sense when you consider that a 4th order high pass filter can be modeled as two 2nd order filters in cascade. My intention here is not to compare closed and vented boxes but to point out that ALL our speakers have this characteristic of "time smearing" in the bass region. I suggest that to the extent that we reduce the group delay we will achieve "fast" (i.e. not late) bass.

OK, so to me it would appear that we want our highs "fast" (implying bandwidth) . . . but we just want our bass to be "on time"! ;-)

Regards,
John Murphy
True Audio
https://www.trueaudio.com 


Date: Mon, 2 Mar 1998 15:22:36 -0800
From: "Daniel C. Wiggins" DanWiggins@avatar.cnchost.com
To: "'Bass List'" bass@mcfeeley.cc.utexas.edu
Subject: RE: Real data on "fast" drivers

John,

I always understood group delay to be the negative derivative of phase
versus frequency. If this is so, then a system with a LOWER cutoff
frequency will ALWAYS exhibit larger group delay! That is, whichever
system has a lower -10 dB point will have higher group delay - but in this
case, bass extension (and the accompanying group delay) is a good thing!
So, I don't think that group delay can really be used as an indicator of
bass "speed"; however, it is indicative of extension and phase linearity.

Dan

+--------------------+--------------------+-------------------------------+
| Daniel C. Wiggins | PO Box 85891 | DanWiggins@avatar.cnchost.com |
| President | Seattle, WA 98107 | avatar@avatar.cnchost.com |
| Avatar Audio, Inc. | (206)789-6340 | http://www.avatar.cnchost.com |
+--------------------+--------------------+-------------------------------+


Subj: Re: Real data on "fast" drivers
Date: 3/2/98 8:16:16 PM Pacific Standard Time
From: DavidHyre@Avatar.cnchost.com (David E. Hyre, PhD)
To: DanWiggins@Avatar.cnchost.com (DanWiggins@avatar.cnchost.com), bass@mcfeeley.cc.utexas.edu ('Bass List'), JonMurphy@AOL.COM

John Murphy wrote:

>>All the frequency components of the signal might go into the filter
>>(loudspeaker) synchronized in time but they emerge with the lows
>>tending to be delayed more than the highs. This results in what I
>>call "time smear". The only way to really reduce it is to extend
>>the low frequency cutoff of the system ever lower.

Dan Wiggins replied:

>I always understood group delay to be the negative derivative of phase
>versus frequency. If this is so, then a system with a LOWER cutoff
>frequency will ALWAYS exhibit larger group delay! That is, whichever
>system has a lower -10 dB point will have higher group delay - but in
>this case, bass extension (and the accompanying group delay) is a good
>thing!

But doesn't group delay settle down towards zero above tuning? If so,
pushing the system cutoff down lower (e.g. from 20 Hz to 10 Hz) will reduce
the group delay of the remaining frequencies above the previous tuning point
(e.g. 20 Hz), right? The magnitude of the group delay *at the tuning point*
(e.g. 10 Hz) will be twice as large, as Dan states, but it will be centered
twice as low, too. So as Dan says, it's a good thing!

-David

+--------------------+-------------------+-------------------------------+
| David E. Hyre, PhD | PO Box 85891 | DavidHyre@Avatar.cnchost.com |
| Vice President | Seattle, WA 98107 | Avatar@Avatar.cnchost.com |
| Avatar Audio, Inc. | (206)789-6340 | http://www.avatar.cnchost.com |
+--------------------+-------------------+-------------------------------+



Yes, as Dan notes, the group delay that a closed box loudspeaker exhibits at its corner frequency does increase as the corner frequency is lowered. But, as David notes, the entire curve is being shifted down in frequency also. It is not obvious from the discussion so far that group delay is "improved" as the corner frequency is lowered. But, it is true. The lower the cutoff frequency of the system , the lower the group delay in the pass band.

Below are three simulated frequency response curves along with their corresponding group delay responses.

group delay comparison

The rightmost curve has a 3 dB corner at about 30 Hz and experiences about 8 msec of group delay at 30 Hz.

The middle curve is a simulation of  a similar system (Qtc = .707 for all three cases) but with a corner frequency of 15 Hz.  This system has a group delay of 15 msec at its corner frequency but has only 4 msec of delay at 30 Hz.

The third (leftmost curve) system has a corner frequency of 7.5 Hz and while it experiences a full 30 msec of delay at its corner frequency it only has   about 2 msec of delay at 30 Hz.

System Corner Frequency Delay at Corner Frequency Group Delay at 30 Hz
30 Hz 8 msec 8 msec
15 Hz 15 msec 4 msec
7.5 Hz 30 msec 2 msec

From the table you can see that lowering the corner frequency reduces the group delay of the system at a given pass band frequency (30 Hz in this example).  I suggest that the 7.5 Hz system would have what many would perceive as "faster" bass than the 30 Hz system.  But it is not a fast rise time that we need for "fast" bass.  As David has pointed out, the systems rise time only relates to the high frequency bandwidth of the driver.  Rather, I suggest that the physical variable that corresponds to perceived "fast bass" is  group delay in the bass range.  The less delay the better.  Ideally the low frequency components of the program signal would experience NO DELAY compared to the mids and highs.

One way to experiment with very low corner frequencies in closed boxes that does not require the "brute force" of a huge enclosure is to apply a line level "Linkwitz Transform" to the system.  This is a simple one op-amp stage that neutralizes the existing 2nd order high pass response and then imposes a new (lower corner frequency and new Qtc) high pass response.  Think of it as surgically precise equalization.  You can read the details about this circuit in Speaker Builder issue 4/1980.  Here's the circuit to show you the idea:

Linkwitz Transform Circuit

Say your existing closed box is is characterized as: Fsc =  40 Hz and  Qtc = .95. 

You can use the above circuit to change the response to Fsc = 20 Hz with Qtc = .5

...or to any other Fsc and Qtc.

I have created an Excel spreadsheet that calculates the values for the above "Linkwitz Transform" circuit.  You can download it here: Linkwitz Transform Spreadsheet

Also, see my new Tech Topic: Designing a Linkwitz Transform Circuit

Enjoy these new bass response possibilities!

John
john.murphy@trueaudio.com

 


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