LOUDSPEAKERS 3, CROSSOVER FILTERS 2012.

Crossover filter for Sublime speaker explained, some dreadful theory stuff,
and a subwoofer recipe at the bottom of this page.

Crossover filters present a HUGE CHALLENGE !!!!

Unless you have a lot of knowledge and practice, and you have an oscilloscope,
wide bandwidth voltmeters, signal generators, calibrated microphone, and possibly
PC spectral analysis program to display response graphs then you are wasting your time
trying to make good speakers. There is just no way anyone can build good
speakers using ears, guesswork and ignorance as tools.

So YOU MUST be able to design and build the crossovers to suit the the selection
of drivers you choose.

WHERE TO BUY DRIVERS.
Because I am in Australia, if I wanted SEAS drivers I have no idea where I could get
them. After googling, I found places listed as SEAS sellers in Oz, but their websites were
piles of bullshit and drivel instead of a simple list of what they stock, and with the prices.
I went to the SEAS website at http://www.seas.no
Once there, it seems they have a varied range of drivers, "Exotic", "Excell", "Prestige",
and that's probably the order of expensiveness and I might humbly suggest
that the Prestige range of drivers will satisfy the fussiest audiophile. They have
equivalents of what I used in my Sublime and Supreme from 2000. At that time I bought
drivers by dealing directly with SEAS in Norway.

The best driver supplier I know in Australia is at http://www.wescomponents.com.au
The have a large range of Peerless and Scanspeak drivers. Included in their stocks are
some made in China, and which you are welcome to try, but I won't find the time.
Loudspeaker drive units have to be made with high quality control, to get tight magnetic
clearances and I prefer European manufacturers.

Never ever buy any drivers for which there is no clearly legible response graph
and a full set of Thiele&Small parameters, Fs, VAS, Qts, and all that techno stuff.

TESTING EACH DRIVER.
Let me assume you have purchased a 210mm woofer, 130mm midrange, and a
25mm dome tweeter, and that you want to know the impedance, acoustic response
and sensitivity of each for the range of frequency bandwidth intended.
Let me assume you wish bass to be between 20Hz and approximately 250Hz,
midrange between approx 250Hz and approx 3kHz, and tweeter between approx
3kHz and 20kHz.
The impedance and response should be tested over a slightly wider bandwidth,
Bass = 5Hz to 1kHz, Midrange = 5Hz to 10kHz, Tweeter 1kHz to 20kHz.

SIX graphs should be drawn for impedance, Z, for each driver hanging in air,
and then mounted in the box with approximate port length if any.
What one finds is that the resonant Z peaks in the box at the low end of the BW
will be different to the Fs in free air, and usually the mid band lowest Z is similar
between free air and in box measurement. The mid band Z is of MOST interest.

THREE graphs must be prepared for acoustic response of each of the three drivers
mounted in the boxes *without crossovers* and using say 1Vrms signals at all F
from a good amplifier with low Ro < 0.4ohms. To avoid accidental damage to a
fragile dome tweeter, use a capacitor in series with tweeter to give a LF cut off
at 700Hz. 

The testing of impedance
and response is covered at my page at
Loudspeakers 4, response and impedance.

IMPEDANCE EQUALIZATION.
Each driver will generate a typically shaped Z curve with Z = coil resistance at
very low F, then a peak of resonance just below the bandwidth intended, then Z
dropping to a minimum in the middle of the band, and then Z rising at the top of the
band.
At resonance, the inductance L of the driver coil plus its springy mechanical suspension
causes the driver Z to act like an L and C parallel network in series with the mid band
Z which is usually slightly below the wire resistance. As F becomes higher, the driver
begins to resemble a resistance R in series with an L which has a reactance X which
can much exceed the R.  
For the crossover filters to work correctly as intended, the effects of resonance and rising
Z with increasing F should be countered by adding R+C or R+L or R+L+C series networks
to make the Z appear to be closer to the mid band Z for ALL of the bandwidth intended.
This is especially true where you want to use first order filters, just an L in series with bass,
and a C+L in series to drive a midrange, and just a C to drive a tweeter. Such simple
filters are rarely satisfactory. Where a second order filter is chosen, there may be no
reason to use impedance equalization because the C after the L plus available
driver damping resistance will act to give the wanted signal attenuation rates.

SUBLIME EXAMPLE.
Suppose the mid band Z of a midrange driver = 6 ohms at 500Hz. The Z at this F will have a
mainly resistive property, unaffected by reactive behavior at extremes of bandwidth.
It is good practice, IMHO, to make the driver behave as a mainly resistive element for
more than all of its intended bandwidth.

Let me assume you have a SEAS midrange as I show in Fig 1 crossover filter for my Sublime.
The LF resonance Fo for the mid driver in the small sealed box is at about 75Hz, and nearly
two octaves below the intended crossover F1 at 250Hz. The Z at Fo may be 30 ohms.
To exclude bass signals from the midrange, a series C1 is used, and value here is 86uF.
At 75Hz, XC1 = 25 ohms. When in series with a driver with Z = 30 ohms, there is far too little
wanted attenuation. So the C2 300uF plus L2 15mH plus R3 3r4 are added to form
a series resonant circuit with Fo at 75Hz. The Z of the L+C at Fo will be very low, perhaps an ohm.
The 3r4 acts to keep minimum ZLC about equal to the driver mid-band Z.
With the C1, R3, L2, C2 in place, the driver's unruly resonance at 75Hz is terminated by a shunting
R3 of 3r4. The real R is 3r4 plus the wire resistance of L2. At 75Hz, the speaker looks like resistance
of less than 6 ohms, and with XC = 25r, attenuation is about -12dB, and what we want, because we
need to stop midrange cone movement at low bass F so we don't spoil the sound in the
wanted bandwidth. In my Sublime with SEAS driver, there was no need to use impedance eq
at the high end of the BW, because XC3 shunts the driver's increasing Z as F rises.
L1 plus C3 act as the second order filter. The crossover F2 at the high end of the BW is indicated
by the possible resonant F between L1 and C3.

if you need to know the possible Fo between any L or C value, it may easily be calculated
Fo = 5,035 / ( square root of [ L x C ] )
where Fo is in Hz, 5,035 is a constant for all equations, L is in millihenrys mH, and C in in uF.
So, for 0.26mH and 6u8, Fo = 5,035 / ( sq.rt [ 0.26 x 6.8 ] ) = 3,788 Hz.

Notice that the Fo is close to the wanted crossover F of 3kHz.
The L&C values chosen for a simple second order filter could be a wide variety of L&C for the
the same Fo, but we wish that the L&C we choose will suit the amount of resistance or R
in the circuit.
Confusing? I thought so, I can see you say "WTF......"
Well, I did tell you LCR behavior is queer. So allow me to explain more basics.
First of all, assume ALL speakers and the filters used will be driven by an amp with low output
resistance of an ideal 0.4 ohms maximum, so that if a speaker is "4 ohms", the damping factor = 10.
Secondly, all L+C or C+L second order filters will behave as series resonant networks with Q > 1
unless that are damped by an R placed across the L, or across the C, or in series with both L+C.
Thirdly, the R value cannot be any old value, and should suit the XC or XL at the Fo. Now L1 and C3
shown in Fig1 have Fo = 3,788Hz, and at this F the XC = XL = 6.2 ohms.
If there was no "terminating" load R connected to the L&C then they would act like a short circuit
at 3,788Hz, and perhaps the amp would smoke. At Fo without any R, the impedance of the series
L&C is much lower than either the XC or XL at Fo. So with a given fixed voltage applied, the voltage
appearing across either L or C will be much higher at Fo than the input voltage. Queer but true.
BTW, parallel L and C act differently, but equally queerly. Don't assume anything.

Now if the R is a higher value that XC or XL at Fo, the response will be peaked at Fo across the C.
C has one end grounded and shunts the driver. so with high R, an unwanted peak in the response
occurs because of the crossover inadequacy. If the R value is reduced to 0.707 x XC or XL at Fo,
then the response of the driver will become free of any peaking, and be what is called maximally
flat, but with a sharpest possible knee of attenuation to the -3dB response point, with -12dB
per octave attenuation rate. Such a nice looking curve for a low pass filter might even sound OK, but
don't assume it will, or that it will suit the acoustic response profile.
In this case, the R would need to be 0.707 x 6.2 ohms = 4.4 ohms. if the R value is lower
than 0.707 x XC then the filter behaves as an over damped filter, and the sharpness of the
attenuation slope is reduced, but the ultimate rate of attenuation still becomes -12dB / octave by
say 5kHz which is what we would want.

In order to have the right amount of R at a given high F crossover Fo, then we could try
using an R+C series network across the driver to maintain its mid band Z no matter how high
F becomes for the applied sine wave signal. 
By reading the graph you draw of the driver Z, you can identify mid-band Z, and see where
Z rises to 1.414 x mid-band Z. So if the driver is say 6ohms at 400Hz mid-band, and say 8.5 ohms
at say 1.5kHz, then to make the driver appear to be 6 ohms at all F above 400Hz we need R be
6 ohms and XC = 6 ohms at 1.5kHz. C is easily calculated,
C = 159,000 / ( R x F ) where C is in uF, 159,000 is a constant for all equations, and F is
measured where Z has risen by factor of 1.414.
In this case C = 159,000 / ( 6 x 1,500 ) = 17uF. In theory, the SEAS midrange I used in 2000
could have had 6r + 17uF strapped across it, but after testing the acoustic F response and the input
impedance including the crossover as shown the R&C Z eq at the higher F was not needed,
or gave no response improvement, so, it was left out. But in many of my other design efforts,
the R&C appear across the midrange.

The midrange plus tweeter crossovers have selectable volume levels relative to the
signal applied to the bass. R1 and R2 form 2.35 ohms series resistance to attenuate the
mid-treble by 3dB and allow the bass to have more prominence. Everyone finds this a very
useful feature, because many small rooms tend to produce too much mid-treble and not quite
enough bass. The speakers were tested in my large room which favors bass.
The added series R is not enough to upset the filter behavior.

The acoustic level of bass at 60Hz should be the reference level for all F above 60Hz.

To ensure the speakers measured fairly flat from 60Hz to 20kHz, but without the R1, R2,
there were added R to mid, see R4 1ohm, and R5+R6 = 1.7 ohms in series with
tweeter. Luckily the sensitivity of the SEAS bass, mid and treble drivers were
fairly close, and the crossovers fairly easy to get right.

Let us consider the SEAS Tweeter. Mid band Z = 5 ohms at 5kHz, and Fo peak
at low end is at 1.2kHz and 10 ohms. I chose not to worry about the low end Zeq network
because crossover F > 3Fo. The Fo for C4 3u3 and L3 0.5mH = 3,920Hz.
XL = XC = 12.3 ohms. Mid band Z rises to 7 ohms at 14kHz, so for the R&C eq
network if the R was 5 ohms, then C = 1.6uF
in practice, I found using 6R8 plus 2uF gave better acoustic response, so that is what was used.
Now the tweeter load of around 5 ohms at 4kHz acts to "overdamp" the C4 & L3 filter and
cause much less phase shift at the crossover Fo.
The added R5+R6 1.7r to reduce excessive tweeter output combines with mid-band 5 ohms
of the tweeter to give an adjusted mid band R load = 6.7 ohms. The critical R value for the
C&L filter would be 8.7 ohms, but with 6.7 ohms, the filter phase shift is reduced at the -3dB
point. I would have played around with R&C values to get the best F response. I sometimes
connect the midrange in opposing phase to bass and treble because the signals around
crossover regions should always be additive lest a response trough occur due to cancellations
along with poor imaging. In the Sublime case, phase coherence exists for all 3 drivers,
and some overlapping is done to get an overall best response.


The acoustic response must always triumph over any pernicious attempt to force the design to
always conform to overly simplistic theory. 

The 6r8 plus 2uF plus 1r7do manage to equalize the Z at above 14kHz to be 8r5, a pure R
load which all amplifiers will "see", without any tendency for HF oscillations.
 

Let us look at the SEAS Bass driver. Bass has mid band Z minimum of 6.7 ohms at 120Hz.
Its Fs was 27Hz with Zo = 70r, but there is no need to reduce this high Z. The L4 + C6 low pass
filter has Fo at 438Hz, way above the LF region. 2.4mH has XL = 0.75r at 50Hz, so at F below
50Hz the driver is connected virtually directly to the amp. The box Fb is 31Hz, and in the box of
55L the two Z peaks are at 21Hz and 47Hz, and Z averages 15r between 20Hz and 80Hz,
entirely benign. Sensitivity is good and low bass output is nicely high. I found these bass units
very nice to work with, and without the disappointment of having poor LF output due to
Fs being too high, or having simple poor sensitivity.
Bass driver Z rises to 8.5r at about 400Hz. I have R8 = 5r6, and C7 = 55uF, theory value
would be 59uF, but all near enough. The ugly HF resonances in these SEAS aluminium coned
bass units occur at above about 5kHz, but with the second order filter any chance of some HF
signal across the bass is impossible. The XC6 and XL4 at 438Hz = 6.6 ohms. The equalized
bass speaker Z of around 6 ohms at 438Hz gave the best acoustic response in combination
with the midrange which extends lower than the bass in an overlap. The overlap is OK
because the midrange has little contribution to bass below 250Hz, and phase coherence
was wanted, and there was a need to keep overall input impedance of the completed speakers
above 4 ohms.
Where you have an LC low pass filter loaded with the mid band Z, then at F well below the
crossover Fo, the Z in is just voice coil R, plus any wire resistance of the L choke. But as F
rises towards crossover Fo, Z drops to about 0.7 x mid band Z and then rises at 6dB per
octave as the XL of the choke rises.
Where you had an LPF and HPF centered at the same Fo, and if the mid band Z was say 6 ohms,
you could have each producing minimum Zin of 4.2 ohms at the same F so you'd have combined
Zin of 2.1 ohms. Its all too easy to have it even lower, and this low Z can destroy amplifiers.
F region between 100hz and 500Hz is where most audio power occurs, so if bass and midrange
crossover together at the same F in this region, you can have an awful problem.

THE OVERALL Z of the Sublime worked out OK and minimum was 4.5 ohms. 

Fig 1.
sublime-crossover.gif

Unfortunately, the changes to available driver models over the last 10 years
means that whatever crossover schematics I used only 5 years ago are now
not correct for drivers made now, so I can only give the method you must use,
and I am not able to give you a schematic giving best possible performance
using different drivers to those SEAS models listed in Fig1.

Perhaps you are now trapped, because either you buy expensive well made
speakers, or you spend an enormous amount of time to learn the theory and to
acquire sufficient equipment to proceed competently. There are no short cuts.

The one-box design shown in Drawing 3 at my loudspeaker DIYer page
used Peerless drivers purchased from w
escomponents.com.au back in 2006.
They no longer appear in the WES catalog.


Fig 2. A useful chart to explore LCR filters :-
LCR filter chart.

SUB-WOOFERS.
I am not a huge fan of using sub-woofers because I try to ensure bass speakers provide

the full bass frequency range from 20Hz to 300Hz, so there is no need for a sub-woofer
which usually produce
from 20Hz to selectable F between 40Hz to 100Hz.

Sub woofers are often very difficult to properly place within a room and get good
integration with normal bass units which might only reach down to say 50Hz.
It has not been unusual when I have measured systems that I find the sub woofer cut
off point has been wrongly chosen, and that when the sub is used, a number of dips
in narrow F bands occur because of phase effects so that bass becomes worse,
not better, hence the perception of implausible sounding bass that just doesn't
sound right.

However, I had two clients who both started with Vienna Acoustic 'Mozart'
speakers
with only 2 x 125mm dia drivers in little 22 litre enclosures. Despite this, they
made good bass down to 60Hz. Both clients
independently concluded their sound could
be improved by adding the missing octave below 60Hz. Both had tube amplifiers I built
for them for their main amps, and both used a solid state amp for the subwoofer.
Both found the sub made an improvement.  But because the Vienna Motzart are 2 way,
not 3 way, there was the tendency for the small drivers to have muddy midrange because
of having to handle bass plus midrange F.  One of these clients finally woke up that he
could sell his Motzarts to a relative, and then buy my Sublimes, and then he had real bass
and finer midrange. He kept his sub, but it wasn't essential any more, and when he moved
to a house with a bigger sound room, his sub just gathered dust.

The sensitivity for sub bass is much lower than above the crossover point because a
large amount of energy is produced by the port on the sub and not by the front of the
cone. As cone area is reduced, the need for power increases as frequency reduces,
while the speaker excursions must increase. The larger the sub bass driver, the easier
it is to maintain high acoustic levels of very low bass without so much cone movement
or amplifier power. I have seen a sub with a 450mm dia driver, and it sure gave rumble
in the jungle.
The only time the big power is needed might be for movies with deliberately high levels
of very low bass. Although teenagers using dad's hi-fi set might try boosting bass up as
high as humanly possible.

SUB-WOOFER RECIPE.
The driver was a single 300mm Peerless XLS subwoofer driver. One Watt gives 90.6dB
SPL at 117Hz, but the same 1 Watt gives only 83dB at 30Hz, so you need a good amp
for between 25Hz and 60 Hz. However, for music, when you measure the average
power a sub needs below 60Hz, it is never more than the main amp.

The sub enclosure I have made with 33mm thick MDF. Internal volume = 86.5 litres,
not including the port which can be a 100mm dia pipe of 380mm long, or a
rectangular port 88mm x 88mm x 380mm formed in a corner of the box with scraps,
or a "shelf slot" port of about 320mm wide x 24mm thick x 380mm long.
The port shape can be any shape as long as the cross section area and length
are the same.

SUB-WOOFER DIMENSIONS internally were 530mm x 510mm x 320mm.
In the samples I made I used a "shelf" port, so that the port  "hole" was slot
24high x 320mm wide and 380mm mm long and using a spare piece of 33MDF
to form the "shelf" across the 320mm direction.
I had a joinery shop cut up a sheet of 33mm thick MDF for me and at my workshop
I glued the pieces together by standing them up on each other on a generous bead
of glue while keeping everything perfectly square and held together with masking
tape as I went.
When the 4 sides and and bottom were glued, I waited a day for glue to strengthen,
then glued in the port shelf and top which was then ready for cutting out the speaker
hole with a jig-saw.
Next day I carefully drilled lots of 8mm dia holes around the joined sheets about
70mm deep at 120mm centers to allow 80mm long dowels to be slid into the holes
on plenty of glue to hold the glued panels together better.
No screws were used.
The ends of the dowels were sawn off and planed smooth, holes filled, all external
edges were given a pencil round and all well sanded down. I applied 3 coats of a
water based grey metallic acrylic paint.
The driver and its terminals were installed.

One channel of a solid state amp was employed to power the sub.
I built a special active filter to accept the stereo signals from the preamp and filter
out the bass signals as a mono signal with 3 switchable cut offs could be chosen at
30Hz, 45Hz, or 74Hz.
The initial attenuation rate past each pole is gradual because there are 3 cascaded
6dB/octave filters each driven with a simple emitter follower solid state signal amp,
but an additional fixed filter with a pole at about 200Hz gives an ultimate attenuation rate
of 24dB/octave.
There is not much sound below 50Hz in most music. The sub should be set up in what
is the best position to give a flat response at the listening seat between 25Hz and
say 100Hz, something which is very difficult to achieve without properly measuring
the response. Most audiophiles will just guess the box into a position that can be
approved by their suffering wife, who probably is at a complete loss to understand
the need for a sub. But at least she might get a nice place for a vase of flowers or a lamp,
or heaven forbid, a picture of her mum.
Phase of the sub output can be reversed by swapping speaker cables, and thus
get a better transition of response between low bass and sub bass.
While listening to a variety of music, the levels for the sub and the adjustment for cut
off frequency can be made for the best sound without sub "bloat", or too much sub bass
which sounds dreadful.
When the main amp is switched off so only the sub is left to work with bass signals,
there should only be a bit of what sounds like very unmusical rumble, with voices
only just discernible when the 74Hz cut off is selected. One learns easily most people
can survive without a sub-woofer for music. But a sub is good for movies on the
HT system because movie makers have deliberately engineered low bass
signals into the sound track to create a creepy atmosphere, or for explosions.
For myself, I prefer a better story with less explosions.

To Loudspeakers 2, DIY.

To Loudspeakers 4 testing.

To Loudspeakers 1, new from 2000.

To Loudspeakers directory.

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