LOUDSPEAKERS 3, CROSSOVER FILTERS.

Edited August 2017.
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 2017.
I have no idea where you could buy SEAS drivers in Australia in 2017.
I doubt the SEAS drivers I used in 2000 would be available anywhere except from SEAS
in Norway.

But SEAS are alive and well in Norway, and their website lists all othe drivers made.
They show some "vintage drivers" listed at
http://www.seas.no/index.php?option=com_content&view=category&id=25&Itemid=254

I suggest the vintage drivers may be cheaper than latest ranges of "Prestige", "Excell", "Exotic".
A quick look at Madisound prices for Exotic drivers nearly caused heart failure, but Prestige
seemed affordable.

The drivers I used for Sublime speakers I made in 2000 were :-

Bass drivers are SEAS L21RNX/P
Mid-range drivers are SEAS MP 14RCY/P
Treble drivers are SEAS 27TF.

I might humbly suggest that the Prestige range of drivers will satisfy the fussiest audiophile.
SEAS have equivalents of what I used in my Sublime and Supreme from 2000. At that time I
purchased drivers directly from SEAS in Norway.

Peerless and Scanspeak drivers and made in Denmark may be available in Australia
at http://www.wescomponents.com.au
I would avoid drivers made in China. Loudspeaker drive units have to be made with high
quality control, and for tight magnetic clearances I prefered European manufacturers.
I often used Peerless made in Denmark which gave superb performance.

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 specifications.

TESTING EACH DRIVER.
Let me assume you have purchased a 210mm woofer, 125mm midrange, and a 25mm
dome tweeter, and that you want to know the impedance, acoustic response and sensitivity
of each for the intended frequency bandwidth, and for regions above and below.
Assume wanted bandwidth is :-
Bass, 20Hz to 250Hz,
Midrange, 250Hz to 3kHz,
Tweeter, 3kHz to 22kHz. 
The impedance and F response should be plotted on a graph with
A. Drivers hanging in air,
B. Drivers mounted in boxes,
and without any X-over filter R+L+C and for slightly wider F range than wanted to include
for resonances at each end of the bands.
Thus 4 initial graphs are made for each driver. DO NOT trust the data given by manufacturer.

You need a reliable pink noise generator and bandpass filter with 36 bands with Q of about
12 for each band, and which produces equal average amplitude for each band when measuring
the pink noise source between 22Hz and 22kHz. The distribution of pink noise source energy
must be equally spread between 22Hz and 22kHz, and if this is not true, or the Q of band of
BPF is not equal, you are completely wasting your time building speakers.

The testing environment must not have high reverberation and can be a large room in a house
> 150 cubic meters with carpets, curtains and furniture and clutter which minimize room effects
on the response. Room effects will ruin all attempts to measure acoustic response using sine
waves which will give response errors of + / - 12dB. Pinknoise errors with reflected sound waves
can give up to + / - 3dB, errors, but if a calibrated electret microphone is used in 4 different
positions at average distance of 3M from a single speaker, the results become accurate where SPL
is averaged for each band. This is explained fully in loudspeaker-response-testing.html

The 12 graphs will lead you to understand your drivers. I found it could take several days of
ful time work to get any pair of speakers to sound well. Crossover coils will have to be wound,
and you must have a stock of many bi-polar electrolytic and some polyester or polypropylene C.
5W and 10W rated resitors are also needed, along with 10mm plywood for circuit boards, 16mm x
4 guage brass cupboard screws for terminals, and some 1.2mm bare copper wire for board tracks.
Do not bother trying to make printed circuit boards which can only suit mass production, and
which are not able to be altered while optimising the cross overs.
Be prepared to make hundreds of calculations with pocket calculator and to plot paper graphs
and be accurate at all times, and be quick, youse ain't got all damn week. Get it done, and get
it done right, which means you need to critisize your work 100% of the time.

The Z graphs for bass and midrange in a sealed box will have a single peak for Z below wanted
crossover F. The dome tweeter has no air connection between rear of dome and box, but will
alsogive resonant peak below Fo.

Ported bass reflex designs are always better than all the rest if the Fs > 28Hz. The port length and
dia can change the box resonant F which should be between two Z peaks in response. So a typical
bass speaker may have Z peaks at 17Hz and 50Hz up to 30r, with null between peaks equal to
nominal speaker Z.
Where the bass speaker data includes all Theile and Small parameters, the box size and port
dimensions can be calculated with a program freely downloaded :-
http://www.linearteam.dk/default.aspx?download=winisd

For most midrange drivers there is no need to have a ported box and something sealed and
about 2 to 7 liters is often OK. 

To avoid possible damage when testing tweeter, use a series C of 39uF for 6r0 midband.
The F cut off = 680r, and large vac at 100Hz won't overheat the fragile voice coil.
There is no need to use more than 1Vrms applied to any driver, and amplifier Rout
should be < 0r4.

Some general ideas about crossover filters :-

First order crossovers with single L or C in series with a driver never give enough attenuation
of frequencies outside the intended bandwidth. I have always used second order with L+C
or C+L, and usually "over damped", ie, the driver R load is less than 0.707 x reactance XC or
XL at Fo.

The crossover F for any C+L or L+C for second order high pass or low pass filter,
the resonant frequency for C and L is 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.

At Fo, reactance of C = reactance of L. 

For a Butterworh filter without any peaking in response and for most rapid attenuation towards
maximum of -12dB/octave either before or after -3dB pole,
the R load of speaker = 0.707 x XL or XC at Fo. The phase shift at -3dB pole is either + 90 degrees
for a high pass C+L filter or - 90 degrees for a L+C low pass filter.

For example, for a bass speaker with Low Pass Filter, LPF, and L 2.4mH, C 55uF,
Fo = 5,035 / ( sq.rt [ 2.4mH x 55uF ] ) = 438Hz.

Reactance XL = L x 6.28 x F, where XL is ohms, r, L in Henry, H, 6.28 is constant 2 x pye or 44/7,
and F is frequency.
For this case, XL = 0.0024 x 6.28 x 438 = 6.60r.

Reactance XC = 159,000 / ( C x F ) where XC is ohms, r, 159,000 is constant from 1,000,000 / 6.28,
C in uF, F is frequency.
For this case, XC = 159,000 / ( 55 x 438 ) = 6.60r.

For a "maximally flat" Butterworth F response, the R load = 0.707 x XL or XC = 0.707 x 6.6r = 4.66r

The L and C values chosen for a simple second order filter could be a wide variety of L&C for the
the same Fo, but may be dertermined if R and the crossover F is known.

if R = 4.66r, and Fo = 438Hz, then XL and XC = R / 0.707. 0.707 = 1 / square root of 2.
Therefore XL or XL = 1.414 x R and for this case 1.414 x 4.66r = 6.6r, and from this L and C is calulated :-
L = XL / ( 6.28 x F ) = 6.6r / ( 6.28 x 438Hz ) = 0.0024H = 2.4mH.
C = 159,000 / ( XC x F ) = 159,000 / ( 6.6r x 438Hz ) = 55uF. 

Fig 1. L+C passive LPF bass crossover filter.

Fig 1 shows analysis of possible wave forms for Sublime bass speaker units I made in 2000.
The response curves show why it is impotant to have the correct R load following the L+C low
pass filter input network.

Notice the high Q with R = 30r. If there was 1Vrms input at say 20Hz, then 2.4mH has low
inductive reactance and 55u has high capacitive reactance, so the amp drives the speaker
though low winding resistance of the 2.4mH choke, and little current flows in 55uF.

But as the F rises, increasing current flows in 55uF, and the total input current in L is sum of
current in 55uF, 5r6 + 47uF, and speaker driver.
But if the load load after the L was 30r only, and input = 1.0Vrms, a peak in response
is seen at Fo 438Hz where Vac at output of L = 5.0Vrms, and this is across the 55uF, and
XC = 6r6 at 438Hz, so current in 55uF = 5Vrms / 6r6 = 0.758Arms. There is also current in 30r
= 0.2Arms, so total Iac = 0.958Arms.
But with 1.0Vrms input, and 0.958A input current, the input impedance = V / I = 1.0V / 0.958A
= 1.04r, and this a much lower load than the nominal speaker driver impedance and is enough
to soon damage an amp if left running with 438Hz sine wave. The Vac across the L4 2.4mH
could be expected to be XL x Iac = 6r6 x 0.958A = 6.3Vrms.

I am not sure of the phase shift of Vac across C with respect to input where L+C have no load
at Fo, but where the Q = 0.7 and the R load = 0.707 x XL or XC ar Fo, the phase shift at -3dB
point and at Fo 438Hz = -90 degrees.

Where the load R = 0.707 x XL or XL at Fo 438Hz, the response is -3dB, so if input = 1.0Vrms,
expect to see 0.707Vrms across 55uF and R load = 4.66r. The current in C = 0.707V / 6r6 = 0.107A,
and in R = 0.707V / 4.66r = 0.152A, so lotal current in L must be 0.258A, and if Vin = 1Vrms, then
input Z at Fo = 1V / 0.258A = 3.86r, which happens to be less than R load.

The input Z to 2.4mH + 55uF + 4.66r will be close to 4.66r at say 10Hz where the Rw wire resistance
of L forms an R divider to cause a slight loss of Vac at R load, which is negligible if Rw < 5% of the load,
say < 0.23r.

As the F is increased, the input Z with 4.66r drops to a minimum of 3.86r then rises at 6dB/octave
where XL increases to 66r at 4,380Hz and XC reduces to 0.66r at 4,380Hz.

if the bass speaker and midrange have the same R load and LC and CL input filters have same
Fo, and same Q, then input Z would start at 4.66r, drop to 1.93r at Fo, then rise to 4.66r above Fo.
The two speakers would have phase shift difference of 180degrees. To avoid a bad dip in acoustic
response at Fo, the midrange should be connected with opposite phase.
The response overall around the crossover region for any bass and midrange can be anything but
a nice flat theoretical curve, and all sorts of tricks must be used to tweak the phase response.

The low Z dip to 1.93r at 438Hz is completely unacceptable! This Fo is a region of high audio energy,
and thus Fo should be overlapped and perhaps the total Zin does not drop to less than 0.7 x the
lowest Z for the driver. The SEAS bass has wide region each side of 200Hz where Z = 7r0, so
minimum Zin should never be below 0.07 x 7r0 = 4r9. Its not so easy to get Zin always above 4r9,
and I have nominated Zin = 4r5, which tells everyone they MUST have an amp capable of driving
a 4r0 load.

The effect of crossover filters lowers the load and thus the SEAS data figures for L21RNX/P
sensitivity of 87.5dB/W becomes meaningless, and maybe real sensitivity is 85dB/W/M.
The SEAS data graph for response below 100Hz was done with 20L sealed box and you may
expect a much better response with a ported box of 55L.

If you make your own speakers and cross-over filters, there are many traps for those
with the confidence of the unexperienced.

Allow me to explain more basics.
1. Assume ALL speakers and the filters used will be driven by an amp with low output
resistance of 0.4r maximum, so that if a speaker is "4 ohms", the damping factor = 10.

2. All L+C or C+L second order filters will behave as series resonant networks with Q well above 1.0
unless they have R connected across the L, or across the C, or in series with both L+C.

3. For all 3 way speaker systems, bass LPF and treble midrange HPF will both be between 200Hz
and 500Hz, and both may be at say 250Hz, or bass at around 450Hz and midrange at 250Hz.
Once Fo is chosen the speaker R load with equalizing Zobel at Fo is measured, and XL and XC are
calculated to be 1.414 x R load. If R load = 4.66r at Fo 438Hz, XL = XC = 6r6, and for 438Hz,
L = 2.4mH, and C = 55uF.

4. The same procedure is trialled for all other drivers and Fo, and the in the 3 way system there
will be a total of 4 Xover filters, LPF for bass, HPF + LPF for midrange, and HPF for tweeter.

Crossover design usually clashes with human "common sense", and gives queer and unacceptable
amp load values and non flat responses unless one gradually improves understanding and
discipline with practice. I don't have room here for a book about L+C series or parallel resonant
networks. Do not assume anything.

5. Its better to over damp an LC filter than allow R to be too high which always gives an unwanted
peak in response.
if you look at the curve for Q = 0.5 with R = 3r3 for 2.4mH + 55uF, you see that the response from
LF upwards gives -3dB pole at 270Hz, and the response is nearly identical to a first order filter with
2.4mH feeding 4r0 without the 55uF. But as F rises to say 1kHz where bass cone resonaces could
be a real problem, the 55uF will give much more attenuating for the unwanted sound from bass above
say 500Hz. Sometimes I have used series L+C+R tuned for say 1.1kHz instead of 55uF to get a
deep but R damped null and maybe another series L+C+R for 3kHz. Just what is used depends on
how horribly the bass speaker perfoms above 300Hz. Old speaker designs from 1960s often had
bass crossing over to midrange at 1kHz, with tweeter crossover at 7kHz, and the sound was usually
hopeless for massed brass or violins or voices because of intermodulation effects.

Therefore each driver in a 3 way speaker system should pass only one decade ofr frequencies,
30Hz to 300Hz for bass, 300Hz to 3kHz for midrange, and 3kHz to 30kHz for tweeter.
--------------------------------------------------------------------------------------------
Fig 2. Sublime speaker crossover network.

210mm SEAS Bass driver has mid band Z minimum of 6r7 at 120Hz.
To see all driver data in .pdf from SEAS, bass driver SEAS 21RN4X/P
Midrange driver SEAS MT14RCY
Tweeter driver SEAS 27TFF

Use of any alternative drivers listed in above crossover will not produce a satisfactory outcome
and what I show here is a guide to how you must think about the speaker building.
The box sizes for Sublime and Supreme will work very well for a large range of 200mm dia bass,
125mm midrange, and 25mm dome tweeters. But the crossovers for Peerless or other brands
may be entirely different.

Its Fs = 27Hz, and SEAS data shows ZFs = 88r. The data tests were done with 20L box and
microphone at 0.5M away. What you measure with 55L box and microphone at 3M will resemble
real world use and be different to data, and I found the ported 55L box gave MUCH higher bass
output than the SEAS data curves indicate.

L4 = 2.4mH, XL = 0.75r at 50Hz, so at F below 50Hz the driver is connected virtually directly to
the amp. C6 = 55uF, XC = 58r at 50Hz, so negligible amp current is wasted in C6 at below 50Hz.

L4 2.4mH + C6 55uF form second order LPF with Fo at 438Hz, above the LF region.
At 438Hz, XL = XC = 6r6, and bass driver Z is about 7r0 at 438r, and with slight loading of Zobel
R8+C7, response is -3dB at just over 400Hz. 
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 remains at
same level as at 300Hz. I found the SEAS bass units very nice to work with, and without the
common disappointment of having poor LF output due to Fs being too high, or having poor reflex
reaction with ported box, or having low sensitivity at low bass F.

Bass driver Z rises to 8r5 at about 400Hz and increases due to voice coil inductance at higher F.
The Zobel network for impedance equalization is R8 = 5r6, and C7 = 47uF which gives Z ( R+C )
= 8r0 at 604Hz, and ultimate Zobel Z = 5r6, slightly less than theoretical value of about 7r0.
The Seas bass drivers have aluminium cones with very high Q resonances above 5kHz which must
be well supressed with action of L4+C6 which gives -43dB attenuuation at 5kHz.

140mm SEAS midrange driver has Z = between 6r0 and 7r0 for its midband region from 300Hz to
1.2kHz. L2 15mH + C2 300uF + R3 3r4 form series resonant network with Fo = 75Hz.
The Q is reduced by R3 3r4. L2 15mH does not need to have thick wire and Rw may be 2r0.
The R value for damping L2 + C2 resonance is total of L2 Rw + R3 = 5r4 approx.

C1 86uF feeds driver R = 7r0, + R 1r0 and LF pole is at about 231Hz, and below the cut off
for bass driver at about 350Hz. It is a first order filter. But below 231Hz, the effect of L2+C2+R3
is to much reduce low bass signal at midrange. The crossover overlap still gives a flat response and
there was no need to reverse the phase connection of midrange with respect to bass.
As F rises, the loading effects of L2+C2+R3 become negligible due to XL2 = 282r at 3kHz.

L1 0.26mH and C3 6u8 have Fo at 3.79kHz, where XL = XC = 6r2. I found using R4 1r0 in series
midrange and parallel C3 6u8 gave a well controlled HF attenuation for HF above 3.5kHz.
There was no need for a Zobel R+C across midrange.

27mm SEAS tweeter driver has Z between 6r0 and 7r0 in its midband region at about 8kHz.
There is a Zobel C5 2uF + R7 6r8 to make the speaker load 6r8 at all F above 20kHz.
C4 3u3 + L3 0.5mH form HPF with Fo = 3.9kHz. XL = XC = 12r2. The tweeter R plus series
R5+R6 give load of about 8r7, and the Zobel C5+R7 load = 9r0 at 3.9kHz, so that total load
at 3.9kHz = 4r5, and this reduces Q < 0.5 for LPF C4+L3. So the phase shift at HF crossover
Fo is low, similar to first order filter, so the tweeter has same phase connection as midrange
and bass.

Where you have a LC LPF or CL HPF loaded with the mid band Z for 2 speakers, the input Z at Fo
dips to less than the midband Z, possibly from say 7r0 to 5r0. But if the bass and midrange have
overlapping crossover F, not at the same F, then minimum Z in can be kept above 4r0. At above
1kHz for midrange and tweeter, with over damped C+L HPF, the minimum Z can also be kept above
4r0. The end result gave the Sublime minimum Z = 4r5, and average or nominal Z = 5r0.

Unfortunately, the changes to available driver models since 2000 means you must source SEAS
drivers which are close equivalents to what I chose in 2000 to give similat performance with
crossover filters which will be similar to above schematic. I am confident that newer driver models
listed in 2017 would produce fabulous sonic results, but the principles of applied experience
with crossover filters is still needed.

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 https://www.wes.com.au
But some are not now available.

Many drivers are available at
https://www.wes.com.au/product_list.aspx?&id=0&pcr=WES-04D&cid=WES10918N&tsb=&tsm=&searchstr=&type=Category&value=Speaker+Drivers+Audiophile&bname=&byp=1&Path=K6WOvrM7yDGJsbKYFM1l%2b53cP8HUT0Dxg%2bPOAn2YvT1VRAenDWMFTJG3Hh1cs5QMNoEWmGfHXoo%3d

Fig 3. A useful chart to explore LCR filters :-

Fig 3 shows HPF and LPF for attenuation per octave = 6dB, 12dB and 18dB.
Perhaps the most useful are 12dB / octave.
C1 = 113,000 / ( R x F ) , 113,000 is a constant, C1 = uF, R = ohms and F = Hz.
L = 225 x R / F, 225 is a constant, L = mH, R = ohms, F = Hz.
The results give a Butterworth response with no peaking and gives the same results
where R = 0.707 x XL or XC at Fo.

SUB-WOOFERS.
I am not a huge fan of using sub-woofers because I found building full range speakers with two boxes
for bass from 22Hz to 300Hz gave better bass quality than having a pair of bookshelf speakers able to
get down to say 100Hz with all bass from a single sub-woofer often placed where room allowed, or a
wife allowed, but which gave a very non flat F response between 22Hz to 120Hz. Very many so called
sub woofers do not manage any output below 45Hz. I was sometimes called out to measure the response
of systems with a sub-woofer and I find the sub woofer cut-off F point has been wrongly chosen, and
that when the sub is used, a number of dips in several narrow F bands occur because of phase cancellation
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 he purchased a pair of my Sublimes which gave him much better bass and 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 certainly could produce very low F.
Having a sub with 120mm cone is almost 100% useless.

The only time high 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.

Fig 4. Blank sheet for plotting Frequency vs dB levels.

For those not used to "thinking in dB", relative V levels may be expressed in dB.
If the reference level = 1.0V, then +3dB = 1.414V, +6dB = 2.0V, +9dB = 2.83V, +12dB = 4.0V.
Relative dB levels may be calculated where V1 = 1V = 0dB, and another V2 = 5V.
The difference in dB = 20 x log of ( V2 / V1 ) = 20 x log ( 5 / 1 ) = approximately +14dB.

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