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The Critical Q Sub-Woofer

A Non-Servo Sub-Woofer Design With Servo Performance

 NEW DESIGN - SIMPLER AMPLIFIER CHANGES - VARIABLE PHASE

Please Note, it is recommended that you use AA-0501 Plate Amp

 Updated July 2008 - NEW RECOMMENDED AMP: PARTSEXPRESS 300-804

  PLEASE DO NOT SEND ME EMAILS ASKING ABOUT USING OTHER  DRIVERS AND BOX SIZES - THEN YOU HAVE TO BE YOUR OWN DESIGNER 

This Page Contains:

  1. Introduction

  2. Oh What A Curve

  3. Flatter Response Than You Think

  4. What! No Servo?

  5. Why Servo Is Not Needed 

  6. A Little Bit of Simple Mathematics 

  7. Oh What A Driver!

  8. The Box Is The Simple Part

  9. The Right Amplifier Please 

  10. New - Sub-Amplifier Components Changes

  11. This Is An Audiophile Sub

  12. Two Are Better Than One

Construction and Technical Pages:

  1. Box Construction Page - Physical Dimensions Of Box Assembly

  2. New - Component Changes to AA-0501 Amp - Step by Step Instructions

  3. FAQ Page & Email Enquiries - Look Here Before Emailing

  4. Construction Pics - Photos of Box Construction

  5. Technical Page - Read This Even If Not All Is Understood

  6. Acoustic Measurements (Clio) - Using Calibrated Microphone

  7. User Setup Page - Recommended Room Placement

  8. Final Pictures - Look At The Finished Article

         For AA-0508 Amp

Copyright Notice: This design is not in the Public Domain. All rights are reserved and the Intellectual Property Rights are retained by the Designer. You may use it only for personal use and enjoyment. If there is any commercial intent of any kind, the Designer should be informed, and consent or license applied for such activity.

 

WARNING: DUE TO LIMITED OR NO EXCURSION LIMIT APPLIED TO THE PEERLESS XLS 12" DRIVER USED IN THIS APPLICATION - PEERLESS THEMSELVES HAVE DISAPPROVED OF THIS DESIGN. AGAIN IT MUST BE STRESSED THESE DESIGN(S) ARE ONLY FOR AUDIOPHILE USE AND NOT HOME THEATRE. IT IS NOT DESIGNED FOR EXTREME SPL LEVELS BUT FOR REALISTIC LEVELS AND SUPERB EXTENSION AND FIDELITY.

Introduction

Is it possible to get a Sub-Woofer that uses NO servo - and yet attains the performance of a Servo-Controlled Sub-Woofer? No doubt the best Subs have some kind of Servo. It makes for better performance, and high cost. It also virtually puts it outside the scope of DIY. Yet there is a way to achieve this high performance without the use of any Servo. This leads to far lesser complexity, easy for the DIY constructor, and a huge saving in outlay. The project described here will compete with Servo-Controlled Subs costing up to five times the cost, and do it easily. It does so by using a Sealed Box tuned to a Critical Q of 0.5 at its Box Resonance. Are you interested?

This project is based on an idea that has permeated in the back of my head for some years. It was partly inspired by a friend's 15 inch Tannoys that were installed in a sealed box some 90 Litres - quite small for such a large driver.

I had measured the T-S Parameters, which had very low Qt and Fs, but being 15 inch the Vas was, if memory serves me right, over 500 Litres. You would not have expected this to work well into what was a relatively small sealed box for such a huge 15" driver. But I found that the Fb of the box was around 50 Hertz and Qb 0.7 which is 2nd order Butterworth.

Those familiar with T-S Parameters will know that the
15" Tannoy's F3 (the minus 3dB response) would be at Fb 50 Hertz and the roll-off below that is 12 dB/Octave. Consequently at 25 Hertz the response will only be down -12dB.

These 15" Tannoy speakers, mounted in a relatively small sealed box, got me thinking as this gave rise to various possibilities that could be exploited. A driver with a particular mix of T-S Parameters should be capable of deep bass in a relatively small box. The Sub-Woofer presented here are partly a result of this thinking process.

Oh What A Curve?

This is where things get a little interesting: The Collom's Curve* as shown here below gives us a +5dB room boost (this is an average rather than a strict figure) at 25 Hz. This may not be easily understood, but speaker responses are known as 2Pi responses, as forward radiating devices. Yet at lower frequencies the speaker becomes spherical or omni-directional - literally a pulsating sphere, which is 4Pi response. Since our room has boundaries which will contain this energy, then at some low frequency we will have a 4Pi response boost.


This means a +10dB boost, but at what frequency is difficult to predict. But it is certain that this room boost does exist. The Cullom's Curve give us an average guide. As Subs usually sits close to the first boundary (the floor), expect the curve to start rising at a higher frequency than shown here. Notice too that the centre of the boost is approximately +5dB/Octave. We'll come back to that.

* The Collom's Curve is named by me after Martin Colloms, its creator.

Flatter Response Than You Think!

Returning to our above example, we now realise that rather than being -12dB at 25 Hertz, we're closer to being -6dB, much more respectable. Indeed we can conclude that speakers that are flat down to sub 30 Hertz will have in room peaks and that the correct response should be a gradual roll-off and thereby compliment room boost. Not surprisingly sealed boxes do this almost naturally whereas vented alignments can have huge problems unless very carefully designed with a gradual roll-off, Bessel-like alignments are preferred.

But for low frequencies using a relatively compact box, we must think sealed, a driver with low Fs, low (but not too low) Qt, and large surface area and long linear excursion. It is apparent that we must have a very large displacement capability, and basic calculations showed that a 12 inch driver to be nearly ideal and the Tannoy example indicated that this should be possible with a relatively compact size box. Much smaller than 90 Litres.

What! No Servo?

Most of the better Subs on the market uses some kind of servo-control or motional feedback. This is supposed to give tight control over excursion and equalization (EQ). But, as we know,  naturally they tend to be much more expensive as a result of increased complexity.

Why Servo Is Not Needed?

This is where my idea comes in. It has been known for some time that where-ever there is a resonance, if the Q is kept down to or below 0.5 it can be described as critically damped, so hence the title, a Critical Q Sub, short for Critically Damped Q Sub-Woofer. This Sub will have superb transient response with virtually no over-hang and will start and stop on a dime. This means we can have the same level of performance as servo-controlled subs but at substantially less complexity and cost. The only thing we may need to pay attention to is the EQ'ing of the amplitude. It also would be desirable if this EQ'ing could be reduced to a minimum.

Many who dabble with speaker design and crossovers, knows that Linkwitz-Riley 2nd and 4th order crossovers have a specified Q of 0.49 - this is no coincidence as the crossover will be critically damped, so this principle, as with many other principles, works both in the electrical and mechanical domain. It was Neville Thiele (of Thiele-Small fame) who first recognised this, and loud-speaker design has never been the same again. I can happily say that Neville is still living here in our wonderful city, Sydney - Australia.

A Little Bit of Simple Mathematics

At this point I want to point to a particular ratio that applies to all sealed box alignments. As Fs of a driver gets pushed up by the volume (actually a mechanical spring) to become the Fb of the box, the same ratio applies to the Qt of the driver. Let's look at an example:

 

 

 

Fs

Qt

=

=

20 Hz

0.25

x2

x2

Fb

Qb

=

=

40 Hz

0.5

Notice that both Fb/Fs = 2 and Qb/Qt = 2. Both our Fs and Qt are x2 or doubled. This rule or ratio is universal with all sealed alignments. Whatever the rate that Fs goes up to Fb, the Qt get pushed up proportionally by the same amount. A very interesting rule to remember. It is not coincidence that I picked the above exact set of parameters, as they are what we need to implement our idea.

Now if we could find a driver that has very close to those T-S Parameters, then we can start cooking.

Oh What A Driver!

It came down to finding the right driver. I found such a driver, the superb hi-performance Thick Nomex Cone  Peerless 12 inch XLS - Model 830500.

While not inexpensive, it does supply the performance and quality required. To get a good idea of the construction, click on this link: XLS Construction

Available from various suppliers, in United states by Madisound USD 144.00

He Sure Is A Big Fellow!

 

Fs

Qt

Vas

Xmax

 

=

=

=

=

 

18 Hz

0.23

124 Litres

12.5mm (Max Linear Excursion 28.75mm)

 

These are measured Parameters, not the Manufacturer, but reasonably close.

I adjusted the Volume to give me a Qb of 0.5 and hence Fb close to 39Hz
 

 

 

 

 

Fb

Qb

Vb

Ratio

=

=

=

=

39 Hz

0.5

42 Litres

x2.17      (Fb/Fs & Qb/Qt)


So we need to construct a sealed box with 42 Litres volume. Let's do some basic maths, we know that Q = 0.5 means our 2Pi response is -6dB at Fb 39 Hz. A brief calculation shows that to be -14dB at 20 Hz. Consulting our Collom's Curve shows +7dB room boost, hence we will be -7dB in room.

This figure is not difficult to accommodate by EQ'ing - which we will cover later.
 

The Box Is The Simple Part

All the drawings supplied here (see Box Construction Page makes the box relatively easy to make, you can either do it yourself or get a professional to do it, based on the drawings even though the joints might be different, just maintain the 25mm MDF construction and all critical measurements. You will be able to download all drawings from this site, see below.

Warning: The Cut-Outs shown in those drawings should be double checked after buying the suitable 'Plate' Sub Amplifier.

The Right Amplifier Please

Now we come to the question of the amplifier recommended, previously there were two,  but now recommend only one. But beware, the one available in Australia from Jaycar Electronics and the other one from Parts Express in the USA, both look the same but are not. The two are visually the same but internally they are set up differently.

Both need some mods applied to them, but the Parts Express version is set up a bit better, but can be improved.

The Jaycar version is severely compromised and changes must be made.

Jaycar Electronics, Australia:

 

 

 

350W Subwoofer Amp w/Remote Cat No AA-0501 AUD 369.00 (Used by me)

http://www.jaycar.com.au & Search for AA-0501

In the United States, from Parts Express:

 

 

 

250W Subwoofer Amp w/Remote Part Number:
300-794
USD 128.00

www.partsexpress.com/pe/pshowdetl.cfm?&PartNumber=300-794&DID=7

Earlier Sub Plate Amplifiers are no longer available. But PartsExpress makes what looks like a suitable amplifier, part number 300-804. According to the PDF file, the stock unit without any changes will give you good all round performance being -1.5dB @ 20 Hertz. But if you limit the subwoofer for only audiophile use, change R35 from 24K to 15K and R36 from 150K to 470K.

The box cut-out for the amplifier now need to be 216mm by 216mm.

Sub-Amplifier Components Changes

A number of component values are changed, but not as many as before. If you are not suitably qualified, then please get someone to do it for you, otherwise you may come to grief.

There may be other Sub Amplifiers out there that would also work, but the box cut-outs would have to be changed and the component table below would not exactly apply. But those with the necessary ability can explore alternatives.

These Component Changes Tables are available at these pages:

                Amp Components Change Table

See Box Construction Page for detailed Drawings, Cutting Sheet and other Box Diagrams

See Technical Page for in depth discussion of EQ approach used.

See User Setup Page for Operating Instructions.

This Is An Audiophile Sub

I want to make this clear: This is primarily Audiophile - not A-V (Audio-Visual) nor Home Theatre Sub-Woofer project.

The primary function is to augment the existing response of the Main Speakers in your System.

In no way should the High-Pass function of the Sub-Plate amplifiers be used.

This is not to say that you cannot use it for watching your favourite and spectacular Movies. In fact, you may find it very good for that purpose, less impressive initially but more satisfying and realistic in the long run. It might be a good idea to look at the cone excursion if watching movies and if more than 30-35 mm then damage may occur.

Two Are Better Than One

I strongly suggest you build two Subs - I will deal with this in more detail in the User Setup Page. But essentially two Subs will act as a Line Source at Low Frequencies, if set up correctly. Also there will be an improved efficiency caused by the mutual coupling of the Radiating Impedance of two Subs. These features result in better dynamics, greater Headroom and max potential SPL.

The 'Cutting Sheet' using 25mm MDF - 2400mm (L) by 1200mm (W) allows for two Subs. You could make one Sub with the option of making a second later, as you then would already have the cut MDF when needed.

Now it's time to view the other Construction Pages - you will find a great deal of detail to study, view  and use. Have fun with your Sub Project, you will not be disappointed , unless you actually love inferior Subs. Yikes!

Joe Rasmussen

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Send mail to joeras@vacuumstate.com with questions or comments about this web site.
Copyright 2003-10 Joe Rasmussen & JLTi
Last modified: Sunday January 05, 2014

Just had a terrible thought. If "intelligent design" is unscientific, then who will design our audio equipment?