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Updated 00-09-03

DSC00008.jpg (106825 bytes)

Mini Subwoofer

This project has been started in order to try out the principles of building an active subwoofer. As I would rather make mistakes on a small scale, I decided to build a small version first using a small 6,5 inch Peerless speaker I once bought on a sale (thinking it would come in handy one day).

The subwoofer is housed in a 10,5 l sealed cabinet of heavy MFD plates. The subwoofer uses the small 25 amplifier to power it, and a small electronic equalizer which extends the output down to 32 Hz.

This is of cause not a "THX ultra" rated subwoofer and it will not shake the foundation, but it is though suited for many purposes anyway, and is not smaller than some commercially available types, used for smaller satellite systems.

The circuits and principles shown here can readily be used for constructing a larger sub-woofer which can deliver the bass foundation of your dreams!

The Woofer

Peerless CSC Series 850116 176 WR 33 90 SD 8 ohm

Technical Specifications:

Znom

8 ohm

Sd

143 cm2

Re

6.1 ohm

Vas

28.5 l

Le

1.5 mH

BL

5.9 N/A

fs

36.7 Hz

Sensitive

85.5 db

Qts

0.59

Max Power

150 W

Mms

18.5 g

 

 

Simulation of the woofer in a 10.5 l sealed enclosure. As you can see there are usable output down to about 50 Hz which is not too bad but not good enough to be called a sub-woofer. (Simulation made with PCLoud4).

loud.gif (12585 bytes)

The parameters for the system is using filling (Rockwool or Acustilux):

Vb 10.5 liter
f3 55.8 Hz
fc 66.3 Hz
Qtc 0.88
Peak 0.57 db

The Bass Equalizers

Equalizer #1

The equalizer used here has been presented by J.E Benson and W. Marshall Leach Jr. members of AES [1] and dates back to the late 70'th.

Theoretically the overall resonance frequency of the system using a sealed enclosure and the electronic equalizer can be found by:

Using the figures found by the simulation program we get a new fc = 44.5 Hz, which is a lot better than without the equalizer. The combined system will have the of a 4. order Butterworth system (bass reflex) with a 24 db/octave roll off compared with the sealed systems 12 db/octave roll off.

You can for sure find speakers that are better suited for this kind of system, but this system is not intended as a main sub for THX system and an fc of 44.5 Hz is actually not bad at all.

There are no magic here the physical laws still exists, and the speaker still have to move a lot of air to give a high output at low frequencies. What we get is the possibility to use a smaller enclosure on the expense of having to use a larger amplifier! Today this is really not a problem, and you'll see more and more commercially system like the Sunfire True Sub and systems from Velodyne using a relative small speaker with extreme stroke capability in very small enclosures, powered by a class D amplifier of more than 1000 Watt.

Back to our system here we can see that we get an extra gain at 45 Hz of around 3 db which is really not that much and will not require a colossal amplifier, so we can still go for the use of the small 25 W amplifier posted on these pages.

The circuit is based on three opamps configured as two 2. order high pass filters and a modified differential amp.

The components are straight forward to find using the equations below:

 

 

 

 

 

 

R5 can be freely chosen i.e. 10 kohm

 

 

 

Using the figures fond by the simulation program and choosing R5 to be 10 k ohm we get the following values (closest 1% values):

R1 4k87 C1 680 nF
R2 5k62 C2 680 nF
R3 2k05 C3 680 nF
R4 14k0 C4 680 nF
R5 2k05    
R6 2k49    

The components can be calculated using this Excel file download.

A speaker in a sealed box can be simulated in PSpice together with the bass equalizer. The bass speaker in a sealed enclosure can be simulated as a second order high pass filter. I have used a Sallen Key configuration for the simulation:

Bass_sim.GIF (3407 bytes)

The components can be calculated using the following equations:

 

 

 

Using the Qts and Fc for the Peerless speaker in a 10.5 l box, and using C = 680 nF gives:

C5 680 nF
C6 680 nF
R7 6213
R8 2006

The components can be calculated using this Excel file download.

The Spice simulation of the speaker in the sealed box looks quite the same as was found by the PCLoud simulation tool:

Spice_HT.gif (5263 bytes)

-3 db is at 55,8 Hz exactly as predicted by PCLoud.

The simulation of the whole system can be seen at the figure below:

SPICE_EQ.gif (5826 bytes)

The red line is the frequency response of the equalizer and the green line is the result of the whole system (speaker in box + equalizer). -3 db is at 45 Hz as predicted.

The PSpice file for simulating Equalizer #1 can be downloaded here.

Equalizer #2

In electronics World February 2000 [2] another equalizer was presented. It only uses one op-amp but has the ability to lower the resonance frequency almost arbitrary and even when you can also decide on the Q yourself!!! This seams to be a bit of a wonder circuit.

 

bas_eq2.gif (4814 bytes)

The circuit has two break frequencies one at Fc and one at Fe. The circuit can successfully compensate for the peak at Fc caused by a high Qtc. The roll off under Fe is only of second order as is the case for the sealed box alone. For equalizer #1 the roll off is of fourth order, the same as for a bass reflex (vented) box. As the roll off is only of second order the output will still be reasonable at quite low frequencies. Don't choose the cut off frequency Fe too low, do remember that the physical laws still works, and a normal 6,5" speaker is not capable of playing 20 Hz tones at crescendo levels. If you choose a very low cut off frequency you'll not be able to play anything at a reasonable level, as the speaker will start hitting the back plate with danger of damaging the speaker and your mood (this doesn't sound good). As a rule of thumb don't choose the cut off frequency lower than stated in the table below. Of cause there are speakers which are of the "long throw" types which are capable of quite long membrane movements (often denoted as Xmax). For such speakers you can choose lower cut off frequency. No matter what, you can always try it all out, to change the cut off frequency, is just a matter of changing 9 passive components. It of cause also depends on both the number of speakers used and the purpose. For a THX system you really want the possibility of a high output but as a small sub for your computer you don't need much output at all.

Speaker diameter Lowest recommended cut off frequency Speaker diameter Lowest recommended cut off frequency
6,5" 40 Hz 12" 30Hz
8" 35 Hz 15" 25 Hz
10" 30 Hz 18" 20 Hz

Freq respons for eq2.GIF (4494 bytes)

The components for the second equalizer circuit can be calculated from the following equations. Decide on the lower 3 db point Fe (we = 2 p Fe), the overall Qe and use Ra as input (start with 10k ohm).

 

 

 

 

 

 

 

 

In practice k must be larger than zero which means

 

 

SPICE_EQ2.gif (5710 bytes)

Using standard components  the -3 db is at 32,4 Hz (we aimed at 30 Hz) and the gain of the filter at this frequency is 8,9 db (see the the figure above, the red line is the total system and the green line is the equalizer alone). At 20 Hz the gain is 12 db.

The components used in the simulation:

RA1 10k RC1 48k7
RA2 10k CA 1uF
RB1 23k7 CB1 56nF//5,6nF
RB2 23k7 CB2 56nF//5,6nF
RC1 48k7 CC 180nF

To get close to the required 62 nF for CB I've used two standard capacitors in parallel.

The components can be calculated using this Excel file download.

Choosing the equalizer

Seeing these results and looking at the versatility of this circuit, I find it hard not choose second equalizer over the first equalizer presented!

For the most "normal" speakers I would choose the second equalizer for the following reasons:

  • The 2. order roll off characteristic is more compliant to the room response. At lower frequencies the room will act as an natural amplifier. This phenomenon rolls off with 12 db/octave (second order) toward higher frequencies, so if you choose the cut off frequency of your sub to match exactly with the room, you would get a flat response down to almost 0 Hz. This is not so easy as it depends on both the room the listening position and the position of the speaker in the room.
  • The circuit only uses one active component (one opamp) which if you don't choose very expensive capacitors will make it quit cheap.
  • You can choose the cut-off frequency and Q as you like

In some cases I would choose the first equalizer. As an example take the new Peerless 10" XLS speaker. A speaker specially made for active subwoofer use in larger systems (in build a bit similar to the speakers used by Sunfire True Sub and Velodyne). The speaker has an extensive membrane movement capability (Xmax lin = 2,5 cm ~1 inch).

Put this 10" speaker in a 5 l sealed box, use the first equalizer and get a flat response down to 11 Hz. Bellow 11 Hz the response will fall with 24 db / octave (fourth order), which I would prefer over the 12 db / octave roll off the second Eq would give, a small protection for all it is worth.

By the way this speaker is more than just interesting, and I'll try it out as my next subwoofer project. But as it requires a 28 db gain at 20 Hz, it will require no less than 6300 W to get 100 db output at 20 Hz (not counting in the room effect)!!!! So a speaker like this will need a little more than my 25 W mini amp!

The circuit used for the mini sub

The input circuit

The input circuit consist of a summing amp to allow a stereo input to the sub. The input signal can be provided both by a line level from a dedicated subwoofer output on the preamp or an extra preamp output, or by speaker level taken from the speaker terminals on the amplifier.

The signal passes a first order high pass filter C1, C2, P1 which cuts away undesired DC levels on the input. A low pass filter consisting of R3, R4, C3 cuts off frequencies above 10 kHz which is of no use in this construction and would only bring instability and noise. The summing amp inverts the signal.

Input circuit.gif (7009 bytes)

The lower cut off frequency can be calculated by:

With the given components this gives a fn = 22,7 Hz. This is ok for this small speaker but for a larger sub you'll need to get a lower fn using larger C1 and C2 (2,2uF gives fn = 10,3 Hz).

The low pass filter

From the summing amp the signals goes into a second order low pass filter, which cuts off frequencies that are handled by the main speakers.

I have chosen a second order filter, as this will match a sealed box roll off characteristic. If you are using the circuit together with a vented system then just close the vent (roll a couple of socks and pluck them in the port/vent), this will give you a sealed box instead.

The filter is the well known Sallen Key filter, for which the components can be bound by:

Where R1 = R2 = R.

For a Butterworth response Q = 0,707

We would like to be able to shift fc from lets say 30 to 160 Hz with 80 Hz as the center frequency.

With fc = 80 and R1 = R2 = 10k we get C1 = 282,5 nF and C2 = 140,1 nF.

These are not standard but can be obtained by using capacitors in parallel:

C1 = 100 nF // 150 nF // 33 nF = 282 nF

C2 = 68 nF // 68 nF // 4,7 nF = 140,7 nF

Now by making R variable we can shift Fc. We'll use a 5 k resistor in series with a 22 k lin potentiometer for R

low pass filter.GIF (5257 bytes)

P2 is used for adjusting the cut-off frequency. By using a 5 kohm resistor in series with the 22 kohm linear potentiometer the cut-off frequency can be adjusted  between 30 and 160 Hz. By using a linear potentiometer the cut-off scale is almost logarithmic. On the figure bellow the cut-off frequency has been calculated as a function of the potentiometer position (blue curve). The purple line equal the logarithm of the cut-off frequency, for the scale to be logarithmic the line must be linear (straight). As can be seen this is not far from being true.

low cut scale.gif (5225 bytes)

If you are using other components you can use the excel sheet for calculations, just press here to get it.

dial.gif (3066 bytes) Using the components shown here, the marking on the dial should be as follows. You can of cause use more than 5 markings, use the excel sheet to calculate up to 23 points.

Phase inverter

The circuit includes a phase inverter, in order to make a better match with the main speakers that will be placed at a distant from the sub therefore introducing a delay or phase shift. The phase match is especially important in the cross over region to get a flat frequency response. The phase inverter is of cause a bit crude in the sense that only two settings are possible, an adjustable all pass filter would be far better, but less simple and must therefore wait till another time! You can do a lot in sense of matching by physically placing the sub in the most optimal way.

Some adjustment must be foreseen!

Phase switch.GIF (3144 bytes)

The circuit for the inverter is straight forward.

Power supply

The equalizer circuit will normally be build in together with the power amplifier in the sub it self, and the easiest way to power the circuit is of cause to connect it to the power amplifiers power supply. Op-amps only handles up to 15-18 VDC and an regulator is therefore necessary, this will also reduce the noise somewhat. The regulator is build around two transistors and some passive components. It is quite basic, reducing the number of components, and does not use feed back. We could have used an integrated circuit such as the LM78xx/LM79xx series but the presented circuit is cheaper and just as good for this purpose.

R12 and R13 must be calculated to match the input voltage from the power amp:

To get a stable voltage over the zenner diode we need some thing like 2 mA running through it so R12 = R13 = (Vin - 10V) / 2 mA

When using the 25 W amp Vin is 25,5 V and R12 and R13 is therefore 7,75 k ohm (~7k87 as 1%).

PSU.GIF (5153 bytes)

A simulation of the power supply was conducted, using +-25,5 VDC as input but with an 2 V AC signal superimposes. The load was put to 500 ohm between Vcc/Vss and Gnd (which resembles a n output of +-20mA). As can be seen below the signal was reduced by 62,5 db above 30 Hz for the negative side and by 75,5 db for the positive side. This is not best possible result, but it's quite respectable and good enough for this application. Remember that the op-amps are quite insensitive to PSU imposed noise, and the relative low gain of the circuit together with the relative high input signals (line level) no hum should be detectable due to the PSU. Better results could be obtained by using transistors with higher Hfe.

PSU_SIM.gif (6335 bytes)

The circuit and part list

circuit.gif (9896 bytes)

Here is a simulation of the whole circuit + the simulation of the woofer. The resulting system is the orange line V(23). The -3 db points lays at about 33 and 85 Hz, quite close to predicted.

Sim_sys.gif (6681 bytes)

It is seen that the low frequency roll off is of 3. order. This is because the overall equalizer gives a 2. order roll off but the input capacitor C1/C2 gives an additional 1. order roll off.

Part list

R1 * C1 1 uF MKT IC1 TL072***
R2 * C2 1 uF MKT IC2 TL072***
R3 100k C3 not used    
R4 100k C4 68 nF MKT T1 BD139
R5 10k C5 68 nF MKT T2 BD140
R6 10k C6 4,7 nF MKT    
R7 10k C7 100 nF MKT SW1 One pole switch
R8 5k11 C8 150 nF MKT    
R9 5k11 C9 33 nF MKT D1 10V Zenner
R10 10k C10 470 uF E-lyt** D2 10V Zenner
R11 1ok C11 470 uF  E-lyt**    
R12 7k87 C12 100 uF/16V  E-lyt P1 47k stereo log pot.
R13 1k C13 100 uF/16V  E-lyt P2 22k stereo lin pot.
R14 1k        
R15 7k87        
RA1 10k CA 1 uF MKT    
RA2 10k CB1 56 + 5,6 nF MKT    
RB1 23k7 CB2 56 + 5,6 nF MKT    
RB2 23k7 CC 180 nF MKT    
RC1 48k7        
RC2 48k7        

* R1 and R2 can be calculated when the output power of the connected power amp is known use the Excel sheet (Input mixer) to find the needed value. In the case of the 25 W amp R1 = R2 = 133k.

** C10 and C11 must be chosen to withstand the input voltage. With the 25 W amp chose 35V.

*** A double op-amp has been chosen because there are a lot of types to choose from (compared to quad or single), if you want to experiment. TL072 is not the best op-amp but for this use it is a good choice.

To get the Spice simulation file click here.

DSC00002.jpg (109479 bytes)

Picture of the pcb with components.

The PCB layout is available in post script and HP Laser Jet compatible printer file (can also be printed on HP Deskjet printers).

PCB Layout Post Script PRN File
Component Mounting Plan Post Script PRN File
PCB Layout and Component Mounting Plan together   PRN File

When printing the PRN files, just write:

    copy "filename".prn lpt1

in a dos command window. This will copy the file to your printer (if it is connected to lpt1 ..... most likely).

The Enclosure

The enclosure is build with dimensions as a cube. The woofer is firing downwards, facing a bottom plate instead of the floor itself. The bottom plate provides protection to the speaker under transport. The enclosure is made of MDF which I think is both easy to work with (you can have it cut for you at the hardware store) and as it is quite heavy it also sounds quite good.

Box outline.GIF (6019 bytes)

The box is glued together, only the bottom plate is fastened with screws, to allow removal. Make sure the box is completely air tight as this is paramount in order to make it work as predicted.

Cabinet Part list

Pieces Dimension [cm] Thickness [mm] Material
3 27,5 x 27,5 19 MDF
2 27,5 x 19,3 19 MDF
2 23,7 x 19,3 19 MDF
4 2,5 x 2,5 2,5 Wood

Initial Tests

The mini-sub has now been tested, and it has become clear that the small 6.5" woofer needs more than 25 watt to perform properly. The small amp simply is not capable of delivering the voltage needed to drive the digraph to the limits. One should also remember that we have boosted the lowest frequencies by some 12 db's. The woofer and equalization circuit was tested with a 150 W power amplifier and now the small woofer was actually capable of quite a lot of bass. A single 6.5" woofer will never be able to support a THX system but it with a little more power than the 25 W amp it is capable of supporting a small satellite speaker set.

I think that if the woofer itself was more efficient and maybe somewhat larger like a 10" woofer, the 25 W amp would actually be quite enough.

This leaves me with the question of getting more power out of the mini-amp design! I'll get working on that. I think that it could be modified quite easily to give something like 75 -100 W quite easily, but it would of cause raise the cost as well, not least for the power supply. ....... stay posted!

References

Ref. 1 J.E Benson: Synthesis of High-Pass Filtered Loudspeaker Systems, Part 1. JEAS 1979, Volume 27, Number 7/8.

W. Marshall Leach Jr: Active Equalization of Closed-Box Loudspeaker Systems. JEAS 1981, Volume 29, Number 6.

Ref. 2 "Adaptable active speaker system" Electronics World February 2000 (Author not stated!)