In my article about Jensen wax/paper inductors and speaker crossover oil caps I mentioned the name Steen Duelund who was the catalyst in Jensen's development work. I was so impressed by these gizmos I had to contact Steen because I intuitively knew that something major was happening between his ears, and I asked him to write an article for our world wide brotherhood, and he did.

When I received his article I panicked, because I couldn't download it from my computer because it was so heavy. I called a local crane company and a large crane arrived the next day and helped me open the file…that is how heavy it is.

What you will immediately notice is that compared to the information you get about speakers from magazines and manufacturers this is Mickey Mouse compared to Einstein. But let me make this point…I insist that you go to this web site http:/ because what you will discover is that Steen is not a propeller head engineer, but a very serious music maniac who is searching for the Music Wholey Grail and is making absolutely no concessions to "normal", and that is a good thing.

This is another case where the Internet is revolutionizing the audio arts because it is creating a Hi-IQ path for those who have the capacity to deal with the paradoxes of the audio arts.


By Steen Duelund

This very ambitious title is meant in this way - you define the end, and I deliver the knowledge of, how to reach that end, by using the directions described in the following text and the text from "Components" , "How to build to the end" and "Loudspeakers in practise"

With sound reproduction it always ends up as a matter of taste it seems — why?

You are surrounded with a sea of sound waves from birth to death. The first many years the sound comes from natural sources. The main task in this period is to learn to connect the sound with its source an get meaning from these sounds. What you learn then is the base for your hearing.

Experience with music for every single person is built up from a mix of playing yourself, listening to others playing or listening to loudspeakers or when reached a certain age concerts either acoustical or amplified.

These many ways are so different in the resulting sound, that it is normal to listen to the contents of the music and not so much to the quality of the reproduction. It just has to be reasonably good and that means normally inferior.

For others and me the music only reach us if the reproduction is up to the highest standard concerning distortion in all its aspects.

Building to the final end, will be a rather complicated process, as it involves rethinking of all used components and technologies without exception, but less will normally do.

Normal used methods and components have been tried, and one by one, through the years, listened to, questioned, examined and discharged. This strange behaviour has forced me to find other ways. But first and foremost to find out why sound from loudspeakers always can be detected as coming from exactly that.

It has been a tedious and very expensive process, but also exciting and rewarding.

Fortunately I have been repairing defect loudspeaker units for many years. Thereby I have had opportunities to toy with, rebuild and change that very important part of them all. Here I must thank the loudspeaker manufacturer "Scan Speak" for their willingness to help this never satisfied old grumbler.

I have also been lucky to establish close connection with The Tobias Jensen factory, whose expert knowledge in capacitors, in winding techniques and vacuum impregnation has lead to development of a new audio capacitors, air coils and hopefully new resistors for use in loudspeaker crossovers.

Building loudspeakers has been a hobby of mine for nearly 25 years.

All energy has been thrown into the search for a loudspeaker, which could reveal all information hidden in the program material, whatever that might be. Sound reproduced in such a way, that you, actually with your eyes closed, can see the events stored for you - not only listen to, but almost experience as real actors and instruments.

To achieve that, it has been necessary to examine every part, from the loudspeaker units and backwards to the power socket, to find the sources of shortcomings, and really! There are many.

As a DIY-man, now mid fifty, it has been possible - with no financial director to stop me - to develop new components and technologies purely for audio purpose.

It hasn’t come easy, I can tell you, and has taken far too many years. First to hear, then to find the source of the disturbing parameters, and finally to develop new ways without them.

I’m too old to start production of all these findings. It is therefore much more reasonable to tell about them, and thereby inspire others to produce or use these findings.

The internet gives opportunities to communicate world wide with these rather few people, who realise, that building a good loudspeaker is much more, than to fix a box from 6 pieces of wood, put dampening material within, and place loudspeaker units on the front, equipped with as few filter components as possible. You just have to call it hi-fi and make it to look nice and you are a manufacturer of loudspeakers.

That is really what you get even from the expensive part of the market. No real innovations, none new ways, as if normal methods are the best - but designs and finish are very impressive. Sadly this is for the eyes not for the ears.

It seems difficult to build loudspeakers, which are more than 2-way, if you search the market. What has been gained, by these simple 2-ways constructions concerning recreation of a convincingly holographic picture of sound is lost, when more ways are chosen. Just consider how much energy has been put into the two way systems, to make them full range. None of them reaches the goal.

Close friends, who know to handle such things, have also done findings of faulty components and circuits in amplifiers, preamplifiers, CD-players and converters. My role in this has been to throw some new ideas into the arena and then listen to the changes and turn the thumb up or down. But also to keep the antenna high and receive the hidden messages, as it isn’t so straight forward as it may seem, even though the rules to follow are rather forthright, just hard to follow in practise. Habits of thinking and manufacturing are hard to fight.

The dividing network.

The main invention for a multiway loudspeaker to work properly at all, is a new approach to the dividing network.

This is needed if ways of building 2, 3, 4 and 5 way loudspeakers with the same manner of reproduction must be found.

In theory more ways should lead to better results, but practise has shown it otherwise. Normal filters and components are insufficient.

There is no way around the dividing network. There hasn’t so far been made a fullrange loudspeaker, which can reproduce the dynamics and transparency present at a realistic full range level. It has been tried for I don’t know how many years now, with none real break through.

With a well-constructed horn and a single loudspeaker, much can be achieved concerning experience, but full range and relaxing to listen to, it will never be. But they can be very spellbinding.

I have never really understood, why a divided system, where every single unit is optimised to its working area, suffer from absence of the ability, to take you by heart, and let you experience the event. The lack of that has driven me to construct and build again and again, to achieve that goal of excitement, fright, delight and nearness, possible to reach, when the stored music is brought to life in the right manner.

In that search, the dividing network at first seemed to be the culprit, but there was much - much more to come.

At the time for development of this, the personal computer came into economical reach, and the search started by the tiny ZX81. In use of this little machine the first solution came forward.

Its characteristics of linear frequency response, zero phase turn and possibility of linear impedance, the last determined by specific loudspeaker loads, got me hooked for many years, trying to use that theory with real loudspeakers. They could something very right. I learned a lot, but I couldn’t achieve, what I really wanted from that theory.

One Sunday afternoon I again toyed with the formulas - now on a QL, which I still use, when I by the merest chance found another solution hidden within the mathematics for the network, forcing all units to work in phase with each other, and much easier to realise. It had been there before my very eyes, in all that many years, and I hadn’t seen it.

The work from there was to find how this solution could be derived from simpler equations and it all ended up forming a brand new family of dividing networks, which luckily contained well-known members.

The dividing network in general

It can be said, that ordinary calculations on dividing network have no interest in the real world. They require linear impedance, linear frequency response and furthermore equal dispersion of sound to work properly. No unit can fulfil these demands, but it doesn’t really matter. Because

* Normally even that _ wavelength isn’t small enough, as the first irregularity will occur at around 1/6 the wavelength, but by a special construction of the diaphragm it can be stretched to _ the wavelength - even further. The resonance frequency must also be lowered and be kept at a Qt < 0.5.

First we must find the calculated response curves, which can be met, for a single unit. Then use them in search for the missing electrical filter parts we must add to the mechanically filter within the unit.

We know from the mathematics, exactly what the single unit shall do - we have the target for each of them and also for the whole system..

If the unit is perfectly manufactured, it will turn out to be a bandpass function with second order slope in both ends. It will also act as a minimum phase network, so electrical and mechanical filtering is equal. In the real world you will normally have a problematic first break-up point, which need to be taken care of, but that will be discussed later in "How to build to the limit".

Development of a new filter theory for loudspeakers.

In the literature you’ll find "the perfect filter" described as having linear response until a sudden abrupt cut-off. That is probably correct concerning telecommunication but it can’t be more wrong with loudspeakers. There the cut-off must happen in a very gentle manner, so let us see, how this can be achieved.

Here I can't avoid mathematics, but it is rather straightforward so jump out into it.

Special signs are used: * multiplication, / division,

It has been shown, that when you are working in the complex s-plane, in order to get linear phase and amplitude, the formulas for each unit in the dividing network must add up to give exactly one.

This is so for the expression: 1. H(s) = (1 + s)/(1 + s)

It equals one for any value of s.

S is the complex frequency (jw )=j*2*pi*f and H(s) is the frequency response in volt.

The "j" is a special number = the square root of minus one. It can be treated as other numbers, and will come forward as a whole number when an even exponent powers it, else it plays its main role in turning the phase.

The expression (1.) can be split into two parts:

Lowpass: 1/ (1 + s) smaller when s gets bigger and equals 1 when s is very small

Highpass: s/ (1 + s) smaller when s gets smaller and equals 1 when s is very big

When you let w in s=jw vary from zero to infinity, you have expressions for a well-known filter. In some circles it is appointed as the only usable kind of network, 2 way first order.

Remark that both expressions are _ when s=1, which is the dividing frequency.

This filter has a peculiar quality, as it doesn’t matter, how the units are connected - you may choose - in phase or antiphase.

For the last mentioned the expression is: 2.H(s)= (1 - s)/(1 + s)) (allpass-version)

The two versions sound alike and differ only in their total phase response, not clearly heard.

This filter will never work properly despite its good reputation. It demands units from another world. It is too simple. Remember that units are bandpass functions of second order by nature, so you really need amplification, if first order filtering should be realised, else the result will be of 3rd order.

To get higher order you can square the expressions. (1*1=1)

1a. 1.*1. H(s) = ( s2 + 2s +1 )/( s2 +2s + 1 ) and

2a. 2.*2. H(s) = ( s2 - 2s +1 )/( s2 +2s + 1 ) but you can also

3a. 1.*2. H(s) = (1+s)(1- s) /( s2 +2s +1 ) = (1 — s2)/(s2 +2s +1)

1a. and 2a. sound again alike, they just differ in phase (+ or -).

They have 3 parts in the nominator, and thereby lead to a 3-way system - second order for highpass (s2) and lowpass (1), but first order for the bandpass (2s).

It is possible to split the three parts into a 2-way version (quasi complementary), but I prefer the clear form, where every single part represents one unit.

B&O used the first expression - with a slight modification - in their famous fillerdrive system. That was the first attempt to look at all three units simultaneously. They left it again, probably because the demands for the bandpass unit are very high regarding bandwidth and sound pressure.

The third - in some papers called second order Linqwitz -Riley, is also well known for its linear frequency response and its mild turn of phase. This is equal for both low- and high pass in slope, but with a constant difference at 180 degrees. This is easy to fix by turning the phase of one of the units.

This filter is as such very good, the best when you want a 2-way loudspeaker.

The units can't fulfil the demands of the filter, as it is only 12 dB. You therefore must nullify the electrical filter function, when the units’ mechanical filter takes over. This can be done by resistors, parallel with serial components and serial with parallel components, and will work most beautifully.

What may interest you here, are the curves for the amplitude of the two units.

To make is easy for you to plot the slopes; the filter damping is given in two scales for you to mark on an empty measuring paper.

Second order two ways - Allpass (named Linqwitz-Riley)

Dividing frequency: 1 kHz, but can after drawing be copied up or down in frequency.

1/3 oktav



Normal paper



Low dB

High dB



Low dB

high dB



































































































































1 K














2 K







3 K







4 K







5 K







6 K







7 K







8 K



10.08 K




9 K



12.7 K




10 K



16 K




15 K







20 K



In this filter the cut-off frequency is also the centre-frequency, and what follows, is symmetrical around this. The normal definition of cut-off frequency is useless. The graphs meet where they meet - ruled by the mathematics.

The paper with the dotted line is the target for you to reach, when this version of the filter is used. Keep it reachable, it is all you need. I must emphasise here, that in addition of dB-values full level is only reasonably untouched if added levels are below —50 dB.

It can be a help to know the filter components that are to calculate, but don’t expect them to work properly due to unit characteristics. Neither amplitude nor impedance is linear, but the closer to linearity the closer you will come to the calculated values. Remember the need for cancelling the filter function.

2 way second order.

For this network Ln = 2 and Cn = 0.5 (n means normalised)

Remark: they are inverse of each other in value

For you to calculate you must know the value of Rdc and the centre frequency (-6.02 dB point in this filter).

Let’s say R=8 Ohm and cf=1000 Hz then

L= 2*8/(2*p *1000) H and C=0.5/(8*2*p *1000) F

It is common to have the results in mH and uF, so the value of H must be multiplied with 1000 and the value of F must be multiplied with 1000000.

The calculations can have some practical use, in letting your measuring device draw the curves for you, as a measure of sound level from a perfect loudspeaker, is the same, as a measure of voltage over a resistor with the same value as the loudspeaker. Just remember to use very good parts and avoid electrolytic capacitors.

This version is, as said earlier, perfect. It can be difficult for the unit used, to fulfil the demands, if the difference in size between the units used is too big. A 6-inch bass/mid with 1-inch treble is commonly used, but in my view the difference in size must be decreased.

It is believed, that one can divide another place in the frequency band and use the same type of filter once more to create a 3-way system. So it is done in the textbooks, but it is very wrong. Every single unit must "know" the existence of the others.

Filter functions are theoretically developed purely to lowpass filters, and thereby has a well-defined cut-off frequency. With this frequency in mind, it is possible to transform the lowpass filter to bandpass and-or highpass. This method is absolutely correct, if you want a single of these, but in a loudspeaker you want them all simultaneously, so we must have a theory for them all - no matter how many. In practice 3 or 4 way should be enough. I have also developed a 5-way filter, but I don’t think I ever will use that.

The equation that rules them all - 3 ways

Let us continue to develop the new type of filter, using the same technique as described above, where it led to well known types.

We will now look at expression 1a and 2a of the three previously mentioned

1a. (s2 + 2s + 1)/(s2 + 2s +1)

2a. (s2 - 2s + 1)/(s2 + 2s + 1)

The factor 2 in the part 2s is the inverse of the damping factor of the filter.

The damping factor of this circuit must then be _ which means, that it as circuit is critically damped. But you are free to decide the size of this damping, so we will change the number to a variable and name it with the letter "a" to look:

1a. (s2 + as + 1)/(s2 + as +1)

2a. (s2 - as + 1)/(s2 + as + 1)

With these two expressions you again can reach higher order by squaring. This process will lead you to a 5-way system.

I spent 6 years spare time working with that and didn’t reach my goal. No matter how accurate the theory was fulfilled, I still could hear the individual speaker unit.

You can also multiply them with one another, and then you achieve a very interesting result namely

s4 - (a2 - 2)s2 + 1 .

H(s) = s4 + 2as3 + (a2 + 2) s2 + 2as + 1

This expression is like a Chinese box, as it holds a number of well-known types and a lot of its own.

The minus at the coefficient to s2 in the nominator tells this unit to be connected antiphase to the others, if the value of the expression between the brackets is positive.


1. Its summarised amplitude response is always exactly 1

2. The units are in phase with one another at all frequencies if (a) is bigger than or equal to the Square root of 2

3. The step response is for (a) bigger than 2 without ringing

4. Its turn of phase can be chosen as a point to start

  1. Its amplitude slope is rounded - slowly reaching its highest slope. The higher (a) value the slower rounding.

6. The units have great overlap (correctional network is unavoidable)

7. When playing it is impossible subjectively to identify the single units as separate sources of sound.

8. It can be realised in full and doesn’t demand more of the units than it should be possible for them to deliver - dependant of the (a) value.


1. The displacement to one another is critical as they work in phase. They must fit within 1 mm from listening position. You are therefore forced to house the units in three separate cabinets, so you can optimise the distance to your listening position. In my views it really is an advantage. It is for you to judge. How you find these positions is described under — "How to build to the limit".

Again all you need is the curvature of the amplitude response for the three units.

But here we have a problem, I’m not to choose - you are. Therefore you must calculate yourself, if you want to see the possibilities.

In general it can be said, that the bass and treble roll off are 24 dB per octave asymptotically ruled by it Q, and likewise the middle but with 12 dB per octave.

The factor (a) decides it all.

The bandpass part -(a2-2)s2 has to be negative, so (a) has to be greater than or equal to the square root of two.

Let us look at some specific a-values, so you have something to choose from.

a=1.414214 (square root of 2)

With this value the bandpass fades away and you get a 2-way 4th order filter.

It is well known as the Linqwitz Riley solution (squared Butterworth).

The Q-value is 0.707 and will give ringing in the step response. This is heard as a focusing on the instrument(s), minimising the recorded sound from the surroundings.

a=1.732051 (square root of 3)

This choice gives you a three way Bessel transfer, to my knowledge never seen before, it shows some peculiar characteristics, as the three graphs meet in -9 dB on the centre frequency.

If you are to Bessel, this should be your choice.

NB! The cut of frequency in normal Bessel filters lies 1.732 times higher than the highest frequency with no phase turn. Here it is the centre frequency; so phase turn starts at Fc/1.732.


With this value you obtain the sharpest possible cut-off slope obtainable, when you want absolutely no ringing in the step response. The common point for bass and treble is -12 dB and the middle is dampened 6 dB.

Until now we haven’t heard so much of the mid-loudspeaker, as it has been dampened and more performed its role as a filler, to add what’s missing from summation of bass and treble. The tendency for higher and higher a-values is to tear open the middle part, making room for the middle to come forward, until it fills it all and nullify the whole filter function and it becomes full-range.

a=2.828427 (2*square root of 2)

With that value of "a" you get a rather straight lined phase turn What that means exactly has been subject to discussions, where we couldn't agree. By experiments it seems as this steady curvature of phase also means a steady sound picture.

Common point for bass and treble at -18 dB and mid is dampened -2.5 dB.


Here the middle band comes forward and the demands for the unit begins to be difficult to fulfil, but there are units out there, to be used with this high value of a.

The phase is disturbed a little, and this disturbance will increase for higher values.

Calculation of the three amplitude curves.

To do this you need a calculator.

First we have to change the s to jw in our expression, and put them in two groups: even and uneven exponents, it will look

H(jw )= w 4 + (a2-2)w 2 + 1 . .

(w 4 -(a2+2)w 2 +1) + (- 2aw 3 + 2aw )j

This process changes some signs, but so it is calculating with complex numbers.

The nominator consist of three parts:

w 4 for the treble - rename to t

(a2-2)*w 2 is for the middle - renamed to m

1 is for the bass - renamed to b

The denominator consist of two parts to form a complex number - renamed to

D1 = (w 4 -(a2+2)w 2 +1)

D2j = (- 2aw 3 + 2aw )j

The dividing into three expressions is shortened down to

t . + m . + b .

D1 + D2j D1 + D2j D1 + D2j

To get amplitude as well as phase, we have to find these expressions as complex numbers. t+tj and m+mj and b+bj.

d=D12 + D22

t=t*D1/d m=m*D1/d b=b*D1/d

tj= -t*D2/d mj= -m*D2/d bj=-b*D2/d

Amplitude treble: 20*log (sqrt (t2+tj2))

Amplitude middle: 20*log (sqrt (m2+mj2))

Amplitude bass: 20*log (sqrt (b2+bj2))

Phase: ATAN(tj/j) or ATAN(mj/m) or ATAN(bj/b)

In the expressions w =1 is the centre frequency, so you just multiply w with your chosen centre frequency to get the frequency in work. You mustn’t let that value be used within the equations.

It is now for you to choose a value of (a) and calculate for different w -values. To get a reasonable narrow punctuation, let’s say 5 points per octave you can multiply 1/64 with 2(1/5). The result from this again multiplied with 2(1/5) again and again till you reach w=32 and use the results as input for w in the expressions.

You should then have a sufficient number of points to draw the curves on an empty measuring-paper (remember to multiply the used w -values with your centre frequency).

To calculate the theoretical filter parts

The normalised values are only dependent of the value of a

They are called Ln and Cn (inductor and capacitor). To enlighten the termination of the component a further marking is used:

Lns means inductor in series, Cns means capacitor in series

Lnp means inductor in parallel and Cnp means capacitor in parallel.

The expressions are given in normalised form from amplifier towards loudspeaker unit.

Bass Lns=(2*a3)/(a2+1)




Middle Lns=2/a This has three different versions

Cns=a/2 I have chosen the easy one and

Cnp=1/(2*a) best to control, when not perfect

Lnp=2*a parts are in use. The two others can

Be found underneath.

Treble Cns=(a2+1)/(2*a3)




Alternative configurations of filter components used on bandpass unit.

Middle a. Lns=(2*a3)/(a2+1)2




Middle b. Cns=(a2+1)2/(2*a3)




These three versions of bandpass filter have the same slope and phase, but are slightly different in efficiency. These two versions are easier to work with, if your units aren't symmetric.

Again the Cn and Ln values are normalised to 1-ohm termination and centre frequency 1 Hz. For you to change that, you must decide loudspeaker impedance Z and centre frequency fc.

Then your L= Ln*Z/(2*p *fc) H

C= Cn/(Z*2*p *fc) F

This time the calculated coils and capacitors is of more use, they can of course be altered a little to correct larger tendencies as raising output, but it is advisable to fix that in other ways. Do you want perfect results you have to stick to your calculations.

In order to give you possibility to control your calculations, data is given to the solution preferred by me.


Dividing frequency is set to 1 kHz.

1/3 octave


Bass —dB

mid -dB















































































































































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12.7 K





16 K




















Filter parts calculated from amplifier towards loudspeaker unit.

Impedance = 5 Ohm, centre frequency 1000 Hz

bass middle treble

Ls= 4 mH Ls= 0.56 mH Cs= 6.3 uF

Cp= 57 uF Cs= 45 uF Lp= 0.44 mH

Ls= 0.5 mH Lp= 4.5 mH Cs= 50.6 uF

Cs= 5.6 uF Cp= 5.6 Lp= 4.5 mH

Calculation of step response

Some modern measuring devices use the step response to calculate from, so here is the expression for the whole system with (a) as only parameter.

At first we have to decide

a =(-a+sqrt(a2-4))/2

b =(-a-sqrt(a2-4))/2

S(t)=(-2*a*(a *e(a *t) - b *e(b *t))/(a -b )

S(t) is the step response dependent on the variation of t.

The drawn curve will look different than normal, as it also shows the turn of phase. (Remember the units are connected with different polarity)

FIGURE. All units are equally phased and will form the familiar response. The area of

every single triangle equals the energy present at a given frequency.

Further development of new filter topology.

For this we have to go back to the equations from start.

We had 1. H(s)= (1+s)/(1+s) and 2. H(s)=(1 -s)/(1+s)

We had 1a. H(s)=(s2+as +1)/(s2+as +1)

2a. H(s)=(s2 -as +1)/(s2+as +1)

We again multiply normal version with its allpass version and get:

H(s) = (s2+as+1)(1+s)(s2 -as+1)(1 -s)

(s2+as+1)(1+s)(s2+as+1)(1+s) giving the huge result

- s6 +(a2 -1)s4 -(a2 -1)s2 +1 .


This result can be simplified if (a) is substituted with (b-1), it’s just a number, to give

-s6 +(b2-2b)s4 -(b2 -2b)s2 + 1 . s6+(2b)s5+(b2+2b)s4+(2b2+2)s3+(b2+2b)s2+(2b)s+1

Which look familiar.

This expression shows again, that the polarity of the four unit have to shift - + - + , the signs of the four parts in the nominator.

We substitute s with jw and rearrange the denominator to give

+w 6 +(b2-2b)w 44 +(b2 -2b)w 2 + 1 .

(-w 6+(b2+2b)w 4-(b2+2b)w 2+1)+(2bw 5-(2b2+2)w 3+2bw )j

Which is a 4-way system of 6. Order.

This version has a most interesting slope of phase, when (a) is in the area of 6-7, in the altered expression where b is used 7-8. I have used this filter once, in a huge construction with the most fantastic result.

I wasn’t happy then, with the use of so many components, even if they were the best of my knowledge at that time. There has to be 6 of the kind on each unit, besides those used to correct the unit’s impedance and peaks. It was really overwhelming.

Normally one would say, "forget it", but here we come to the next point of the never-ending story - the components.

If we can develop these with a minimum of errors, or with defects, that at least serves the perception of sound, we are on the right track. For details on that matter you must look under "Components".

Back to the filter:

Calculation of the 4 amplitude curves.

The nominator consist of four parts:

w 6 for the treble - rename to t

(b2-2b)*w 2 is for the high/middle - renamed to hm

(b2-2b)*w 4 is for the low/middle - renamed to lm

1 is for the bass - renamed to b

The denominator consists of two parts to form a complex number, renamed to:

D1 = (-w 6+(b2+2b)w 4-(b2+2b)w 2+1)

and D2j = (2bw 5-(2b2+2)w 3+2bw )j

The dividing into four expressions is shortened down to

t . + hm . + hm . + b .

D1 + D2j D1 + D2j D1 + D2j D1 + D2j

To get amplitude response as well as turn of phase, we again have to find these expressions as complex numbers t+tj, hm+hmj, lm+lmj and b+bj.

d=D12 + D22

t=t*D1/d hm=hm*D1/d lm=lm*D1/d b=b*D1/d

tj= -t*D2/d hmj= -hm*D2/d lmj= -lm*D2/d bj=-b*D2/d

Amplitude treble: 20*log (sqrt (t2+tj2))

Amplitude |high/middle: 20*log (sqrt (hm2+hmj2))

Amplitude low/middle: 20*log (sqrt (lm2+lmj2))

Amplitude bass: 20*log (sqrt (b2+bj2))

Phase:ATAN(tj/j) or ATAN(hmj/hm) or ATAN(lmj/lm) or ATAN(bj/b)

In the expressions w =1 is the centre frequency so you just multiply w with your centre frequency to get the frequency in work. You mustn’t let that value be used within the equations.

It is now for you to choose a value of (b=a+1) and calculate for different w -values. To get a reasonable narrow punctuation, let’s say 3 points per octave you can multiply 1/64 with 2(1/3). The result from this again multiplied with 2(1/3) again and again till you reach w =32 and use the results as input for w in the expressions.

You should then have a sufficient number of points- a point at each 1/3 of an octave - to draw the curves on an empty measuring-paper (remember to multiply the used w -values with your centre frequency).

To calculate the theoretical filter parts

The normalised values are only dependent of the value of b and are called Ln and Cn.

To enlighten the termination of the component a further marking with numbers is used. See circuit.

The normalised values in letterform, former used, show to be enormous. This time we will go another way, and therefore select a value of (b) to transform the letters to numbers, which is to calculate.

You only have to find the normalised components for the bass, as the normalised components for the other units can be derived from these.

The filter components for the bass can be found from the denominator in s-form by a tricky division, here made easy for you to execute.



The coefficients (cp (p for power)) to the different powers of s is transformed to numbers by your choice of value for b.

c6=1 .................. =1

c5=2*b ................ = _____

c4=b2+2*b ........ = _____

c3=2*b2+2 ….... = _____ <--- your results

c2=b2+2*b ...…. = _____

c1=2*b ........…..... = _____

c0=1 ..............…... =1

The components drop out from the calculation from unit towards amplifier.

They are named as seen from the diagram. let’s calculate:

Cn3=c6/c5 =_____

d4=c4-c3*Cn3 =____

d2=c2-c1*Cn3 =_____

Ln3=c5/d4 =_____

n3=c3-d2*Ln3 =_____

n1=c1-Ln3 =_____

Cn2=d4/n3 =_____

d2=d2-n1*Cn2 =_____ (new d2=former d2)

Ln2=n3/d2 =_____

n1=n1-Ln2 =_____ (new n1=former n1)

Cn1=d2/n1 =_____

Ln1=n1 =_____

Normalised filter components from amplifier towards unit.

Bass Lns=L1 =_____

Cnp=C1 =_____

Lns=L2 =_____

Cnp=C2 =_____

Lns=L3 =_____

Cnp=C3 =_____

Low/middle Cns=C1 =_____

Lnp=L1 =_____

Lns=L2 =_____

Cnp=C2 =_____

Lns=L3 =_____

Cnp=C3 =_____

High/middle Lns=1/C1 =_____

Cnp=1/L1 =_____

Cns=1/L2 =_____

Lnp=1/C2 =_____

Cns=1/L3 =_____

Lnp=1/C3 =_____

Treble Cns=1/L1 =_____

Lnp=1/C1 =_____

Cns=1/L2 =_____

Lnp=1/C2 =_____

Cns=1/L3 =_____

lnp=1/C3 =_____

Again these Cn and Ln values are normalised to 1-Ohm termination and centre frequency 1 Hz. For you to change that, you must decide loudspeaker impedance Z and centre frequency fc.

Then your L= Ln*Z/(2*p *fc) H

C= Cn/(Z*2*p *fc) F

This time the calculated coils and capacitors are of more use due to their turn of phase, as their effect on level are difficult to measure precisely.

You must be very skilled with mathematics to subtract the inside components of the loudspeaker from the filter. But by measuring with your microphone placed very close to the unit, it should be possible to take away the last 2 filter components from high/middle and treble. This because the units themselves have 12 dB roll of.

If you have peaks in the frequency band you must correct them in a way so you keep the impedance linear - see "How to build to the limits" -, this takes 6 components, so units used should be selected with care.

In order to give you possibility to control your calculations, data is given to a solution.


Dividing frequency is set to 1 kHz.

1/3 octave

Filter parts calculated from amplifier towards loudspeaker unit.

Impedance = 6 ohm (all units) centre frequency 1000 Hz and b=7

bass low/middle high/middle treble

Ls=11.43 mH Cs=120uF Ls=0.211mH Cs=2.216 uF

Cp=120uF Lp=11.43mH Lp=2.216uF Lp=0.221mH

Ls=1.697 mH Ls=1.697mH Cs=14.92uF Cs=14.92 uF

Cp=15.16uF Cp=15.16uF Lp=1.67mH Lp=1.67 mH

Ls=0.243 mH Ls=0.243mH Ls=104.2uF Cs=104.2 uF

Cp=1.895 uF Cp=1.89uF Cp=13.36mh Lp=13.36mH

Calculation of step response

Some modern measuring devices use the step response to calculate from, so here is the expression on step-response for the whole system with (b) as only parameter.

At first we have to decide

a =(-b+sqrt(b2-4))/2

b =(-b -sqrt(b2-4))/2

L=((a -1)*(b -1)*(-2))/((-a -1)*(-b -1))

N=(2*a *(a +b )*(a -1))/((a +1)*(a -b ))

P=(2*b *(a +b )*(b -1)*((b -a )*(b +1))


S(t)=L*e(-t)+N*e(a *t)+P*e(b *t)

S(t) is the step response dependent on the variation of t from zero to?

Again the step response is without trigonometric functions and thereby without ringing.

Even further

For those out there, who as I find it amusing to search into the unknown, there may be surprises to find in the following expression.

H(s)= (s2+as+1)(s2-as+1)(s2+bs+1)/(s2-bs+1)


Here you have the possibility of working with two different Q´s and use (a) and (b) values that turn of some of the units.

There may be other ways, other basic equation to work with, than I have chosen.

Could this paper serve as inspiration for others to look into that area, I would have gained much from my work.

I’m not a great master of mathematics, as I much more am a person of practical skill equipped with an annoyingly sharp hearing too.

All I want is, that what is gained in practice must be expressed mathematically, otherwise you have gained nothing.

That is why, I have enormous concern about expressing myself, when it comes to wires, components and the human hearing. But I am not alone in this respect, even acoustic engineers face the same problem. There is no exact science in this department for now.

In the following you must forgive my use of experiences from listening.

Thereby I will enter into a strange world governed by my hearing, intuition, taste, feelings and even quantum mechanics that I really don't like.

But there has been no way around that, as all my experiences with sound have happened in my brain. That part of it all is for me to see the most important one. May yours work like mine.

The great audio puzzle of recreating the musical event left over to you — the listener.

It shouldn’t be so, but it is. The electrical line from microphone to storage medium is well understood and should follow the simple rule "Do not touch it" which seldom will be the case, the producer want to be heard as well.

From storage medium to the connectors of your loudspeakers you are the one and only to decide, how good that shall be.

"Just use your ears!" I would say, but by that remark we’ll jump right into a vortex of BIG problems — the division of the electrical signal into streams of bass middle and treble signals, transforming these streams into audio replicas by specialised transducers and putting it all together again.

In this process the problems are so many, that it seems the manufacturers have given up and guided their interest towards parts of the loudspeakers much more easy to handle ex. Appearance, price and intensity — playing loud is OK, when it is needed.

Listening to classical music it is often the case, just listen to Jon Leif’s "Sagasymphony" and "Hekla" BIS CD 730 and CD1030 or other of his earth-shaking works. There the energy is a must but also extreme clarity; else you won’t grasp the musical lines.

To illustrate the last mentioned I must direct your attention towards a marvellous recording of the duo Anthony Braxton and Niels-Henning Ørsted Petersen playing Charles Mingus’s "Goodbye Pork Pie Hat" on SteepleChase SCCD37003/4.

On this recording the line between noise and music is very thin. Probably one of the hardest recordings to open for musical enjoyment, I have ever owned.

To reach the heart/soul of the music — especially the unknown ones — the reproduction must have other qualities, than the ability just to play loud.

Let’s give it a closer look.

It you imagine sound as a close row of photographed flat pictures, then the broad lines are the bas the finer lines are the middle and the finest lines/details the treble. The degree of contrast equals the dynamic range and thereby the capacity to differ in level, the size of corns will show how well the three pictures are spliced and stacked together again to form the transparent sound-picture for you to listen through. The timely arranged row of three sound-picture-sets moving towards you at the speed of sound must stay in correct timely order else a mess will be the result.

A mess it is. The really impressive fact is that the human brain despite that has the capacity to redraw the distorted and missing lines. Our brain does an impressive work there, but it gets tired forcing the listener to do something else. It needs help, and the only one to give that help is the listener him-/herself.

Every part in a dividing network active as passive do influence on the electrical signal leaving an afterglow from what was to what is to what is to come. Those nearby smear every single sound-picture more or less. Therefore it makes good sense to improve on these overlaps if possible and it is.

The parts for the dividing network, the type of network itself and the used units are major culprits.

For the single parts the rules to follow are straightforward.

"An inductor coil must be an inductor coil."

"A capacitor must be a capacitor."

"A resistor must be a resistor."

It sounds idiotic, but is far from easy to achieve, especially when the low load, modern loudspeakers do present to the filter, is taken in consideration. 16 Ohm or higher should be a minimum by law.

An inductor coil MUST have low, very low resistance and capacitance — meaning that it by higher values will be heavy measured in kilograms of copper/silver and of the single layer band type.

Only if a resistor is in series with the inductor and no capacitor to ground between, this resistance can be built into the coil and a lot of copper/silver is spared.

The capacitors must act in the same manner with extremely low resistance meaning lots of conductive material. Again they will be larger and heavier, not much to do about that. Of course it goes for this part too, that a resistance can be built in as also inductance but then the free use of the part is heavily reduced.

From the great variety of types - stick to stack foils or variations on that theme if you can find them without plastics. The good old Micas works wonderfully well but they are far too expensive for greater values. Go for older types following the simple rule that bigger is better. A good sounding construction will be introduced from Jensen Capacitor in the near future. (An artificial stack foil, which regrettably only can be manufactured by hand for now.)

The resistors are a most problematic part to say it mildly. The harsh conditions within a passive network it must fulfil its task calls for new ways for power resistors. A solution IS found but further comments on it, I will ask Dr. Rosenberg to give.

A passive network needs spacing, so use bottom and backside of the loudspeaker box for it — the bigger the better. Also do not expect this important part to be cheap. I personally use more money on the dividing network than on the rest of the loudspeaker.

Returning to the analogy with pictures it is clear, that the three layer from at three way solution must fit timely together AND THEY DO NOT.

Just imagine a heavily broken mirror reassembled to form a whole mirror again but with its parts placed in different depths. By mirroring yourself you will see you and possibly also recognise yourself, but heavily distorted. This is the nature of phase-distortion, which of course must be avoided by all power.

It has been believed that amplitudes of different phase can be summed by vector addition, and that the results from that can be trusted. Measuring with a microphone confirms this believing to be true. But there is a great but, what hits our eardrum in the same time is not registered on the basilar membrane likewise. The basilar membrane introduces an 8-10 millisecond delay from upper treble to lowest bass and further we humans do listen with two ears by binaural hearing but do measure monaurally.

As far as I can see, there is only one way out of this conflict — "The phase coherent filter"

This is described below for those of you familiar with simple mathematics and transfer functions. I have tried to write it as simple as possible, but easy it isn’t.

The problems related to units will need a longer article of it own.

A Forum for new ways and wild ideas

In this chapter I will try to guide you even further away from the beaten track, not to confuse you, but to open your eyes and mind. There are more ways than anyone has even thought of.

Some of the shown constructions are just other versions — hopefully better and stretched even further than before. Other ideas are to my knowledge never presented before, but here they are, if you are interested in the best possible reproduction of acoustical music and prepared to improve your gear a quantum leap into the future.

The final step towards perfection

(Or as far as the dynamic loudspeaker can bring you)

In this part of the chapter new ideas of the room, the enclosure, and the dynamic unit will be presented.

Due to the quality possible to achieve following the way I suggest below, also an explanation on and the need of an absolute polarity is discussed.

For many years now the dynamic unit has been the one and only kind for the amateur.

The construction has through the years shown its potential as the best among other principles, but has never been able to produce sound that could cheat our brain.

One can always hear the source of sound to be a loudspeaker, if that is used.

Why can't our sense of hearing be fooled?

All possible sources for that have been searched for and examined ending at the dynamic unit itself and its baffle/enclosure. The problems lie inside that construction it self.

I have been circulating around this problem for many years now but having not seen it clearly.

Discussions with engineers through the years have - in deep respect of their knowledge - guided me away from, what my intuition told me:

There is something basically wrong with the dynamic unit.

Further also in our understanding of the room’s treatment of sound.

Measuring is too one-sided.

The way in which we at first use a microphone and then our eyes to examine the single results - level, phase and step response and more - is different from how the brain uses our ears and eyes.

The brain in reality uses four of its senses by an acoustical event: hearing, sight, somatic tough for lower frequencies and even the sense of smell simultaneously.

Reproduction of only sound in a room creates problems for the brains treatment of sound — missing two stimuli, as I’ll rule out the smell.

The sound simply can’t be interpreted as originating from natural sources.

The level and the belonging phase are in wrong order. In other words the impulses are pointing in a mix of correct and wrong directions, even if the dividing network does its job perfectly and the acoustic centres are correctly aligned — why so?

To clarify this I will define an impulse at a specific frequency as the positive or negative half of a sinus wave. Its turn of phase can then be seen as its direction on the circular plane perpendicular to the axis of time.

A sinus wave consists thereby of two impulses — equal in level — opposite in phase and connected in time.

The normally used step-response consists of a great number of frequencies but shows only the projection of the SUM of levels and its turn of phase related to the input.

A three-dimensional picture would enlighten the connected turn of phase. That is equally important as the level — maybe even more.

If we now turn our attention to impulses instead of level alone, then the problem is fairly simple. What goes into the microphone and comes out from the loudspeaker is not the same. What you hear from your listening position, is not the same as that coming from your loudspeakers and both should be.

In this transformation of sound (impulses) you’ll find three main culprits among a lot of others, dealt with elsewhere:

1. The loudspeaker units

2. The baffle/enclosure and

3. Your room

On this we hopefully can agree.

I know very well, that you could find a lot of other disturbances to take care of, but really all forces should be thrown into the loudspeaker to get that necessary part in order. It is the factual window you see/hear through. What ever you else should think of can then easily be heard and corrected.

That we still haven’t reached thereto is much more a question of carelessness than of ignorance, and an ever-lasting lack of money for research. Loudspeakers are of no interest for the military.


The price of the loudspeaker should mirror the price of the rest of your gear as almost equal. The reason is simple — the more quality gained from the electronic parts the more handwork must be invested in the mechanic/acoustical unit. A good loudspeaker has no easy way despite the manufacturer’s advertising of "The simpler- the better". It only for them is better and of course easier and cheaper.

In this crazy world you often must pay up to ten times the real price of manufacturing. Shouldn’t some of this enormous profit stay at the producer and creator of the product, which you are buying?

What follows - I’m sure - is forgotten knowledge. But I shouldn’t wonder, if I will be attacked by many people of far more knowledge than I have. They know of too many false "Truths" or can’t see the full consequences of, what they do know.

What you should keep in mind, is the simple fact that I have tried it, and it works.

If I’m right in my explanation of it, I of course can’t know for sure. But it seems plausible and it has at least helped me creating a considerably improvement of reproduced sound to my experience impossible to reach by normal ways.

Intuition against adopted rules the last will normally win.

The work of the brain is hard to examine even scientifically. But what, I for many ears have heard as wrong, has finally found an explanation apparently deeply against the adopted rules, but in fact present within them.

In the hope of you understanding the problems and exited to read on, we will go for a solution step by step.

The room is an amplifier

Normally a room is looked upon as a major problem for good reproduction of sound.

It is always the room, which is blamed, when the sound is lousy by demonstration of loudspeakers. — Shouldn’t they know the existence of that?

The rules from acoustics are used trying to silence the room as done in music halls.

Bass absorbers and other hocus-pocus are used in order to make the bass bearable to listen to.

Even the expensive DSP comes into question to regulate the bass (and more).

But really it is like using a sledgehammer to crack a nut.

The use of some rules from acoustics

A closed domestic room is a reverberant field for lower frequencies, especially from your position of listening, and will therefore act against the rules of a free field, where the intensity is reduced by 6 dB per doubling distance.

The intensity in your room can therefor be expressed as I= 4*W*(1-alpha)/S/alpha where

W is the source output power

S is the total room surface area

Alpha is the average room absorption coefficient (a complicated number and further dependant of frequency. It can be found using Sabine’s formula which roughly can be expressed as Tr=0.161*Vm/S/alpha where Vm is the volume in cubic metres.).

From these you can isolate S*alpha.

The intensity can now be expressed as

I=4*W*(1-alpha)*Tr/0.161/Vm - which shows the intensity’s rather direct dependency of reverberation time. The factor (1-alpha) must be taken in account, but plays a minor role in the area of bass.

You could now create deep gaps to reality by hard mathematical calculations. But do not!

The behaviour of the room can be found in a much simpler and far more informative way, "Think and understand".

A closed loudspeaker in a closed room

The two closed rooms are isolated from the outer world and can be equal or different in size.

The law of Boyle and Marriott P*V/T = k is valid for both rooms and governs the transformation of energy of sound to warmth.

They are connected to each other by a moving diaphragm governed by a magnet and an amplifier but also the two volumes, which both can be seen either as box or room.

The energy put into the loudspeaker unit and delivered to the two volumes must stay there, be distributed and preserved there. This is a universal law.

We normally don’t hear that as good because they as single resonators are poorly coupled to each other.

To make them be that, they must be forced to have the same resonance frequency and Qt. The loudspeaker must fit the room and not be a misfit monster.

When they do fit, then what is lost in the one box is gained in the other — a question of balance of the total energy.

The room acts in reverse to the loudspeaker box and vice versa.

The room serves as an amplifier for the loss of level from the loudspeaker and the loudspeaker as a microphone for the room. Any disturbance of the balance of energy will be fought if a possible way is at hand. Nature is conservative. In this fight the amplifier shows its work through its capacity to act as a short cut of the loudspeaker. Any resistance between the two will reduce the loudspeaker’s capacity to act as microphone registrating and fighting, what should not be there.

Fighting the increase of entropy demands energy. The possibility to transform the energy must be present inside the loudspeaker unit (the force-factor) and the amplifier must be able to deliver sufficient of it.

The basic demands for achievement of an extremely good reproduction of bass are simple:

    1. A closed cabinet
    2. A very low resulting Qt.(powerful magnet and coupling to it)
    3. A powerful amplifier, which follows the rule: power time load-impedance is constant.
    4. The use of the Linqwitz-Greiner bass equaliser, which makes the system work recreating the lost bass response due to the highly dampened oscillation at the resonance frequency as also any outer build up of resonances felt by the loudspeakers vibrating surface.

Measure the intensity (sound pressure) from your listening position and with your loudspeakers positioned, as you want them.

Measure again in their nearfield (2-3 mm). The nearfield response is the most precise measure of the unit’s behaviour as a piston you can get

Subtract their single responses, and you will get the room amplification for each of them.

These new curves contain information on every thing in the room and thereby nullifying the need of the factor (1-alpha). They reflect the actual treatment of the sound done by your private room.

.NB! By the measurement you should use one-third octave signals, thereby your measurements will be more in accordance with what you can expect to hear.

From here it is up to you to decide how deep you will go concerning time and money invested.

But at last, there is a method to achieve so perfect a reproduction of the bass and lower middle as possible.

Without knowing the answer for sure, the question is, if a general solution can be found to fit sufficiently to a greater variation of rooms. The little part that does the trick consists of only four capacitors and five resistors, so there shouldn’t be greater problems. Time will show.

It can be said here, that the adjustment of bass and treble is equally sensitive despite their very different directivity. Both must melt into a very wide midrange just as heard by a live acoustic event. Neither bass nor treble has a live of their own by normal not amplified music.

The future use of the DSP in reproduction of sound may very well rule out this problem. It also further could turn back the turn of phase done by the necessary filtering of the units. In this way the loudspeaker could be even more perfect with no turn of phase other than done by the airs transport of sound.

But I must admit that the way to the target by treating of symptoms is not that attractive to me as repairing of causes.

As you will see the room automatically will act as a low frequency amplifier with a low Qt and an amplification at12 dB per octave, until windows, doors, floor and ceiling are of no resistance for the low frequencies, and that means very low. It is into this build up of sound your loudspeaker must fit. When you buy clothes it must fit your body, when you buy furniture it must fit your taste and room, so why shouldn’t a loudspeaker fit to your room? — Now it is possible to make it do so.

To a given room one and only one loudspeaker concerning principle of housing, resonance frequency and Qt is correct. Playing loud — the loudspeaker must be big in size. Playing at normal level - the loudspeaker presented as the first construction in "Loudspeakers in practise" is all you need.

Irritating resonances that are insufficiently suppressed by the loudspeaker itself and heard from your position of seriously listening must be fought from the input signal and not on the problematic output. (It will be too late)

The housing of the unit must be the severely criticised closed cabinet (closed in the same manner as the room itself). No others will work due to their cut of characteristics.

The room will be interpreted as an amplifier as long as we are unable to direct the source of the keynote itself. It should therefore be valid up to around 400 Hz with decaying efficiency.

Answers to comments on this article

Friends have postulated that this governing of sound only to work at very low frequencies, where the room can be compared to a room of pressure. That is correct to be the main advantage, but think deeper.

The loudspeaker will of course fight only that, which it can register.

Standing waves will truly be split up into sectors by the increase of frequency, but still the loudspeaker will fight that part it can feel, and thereby also influence on the other sectors of it.

A standing wave needs time and stable conditions of reflections to build up.

The cause of a lesser capacity to fight standing waves is also caused by the passive filter. It reduces the output of sound from the loudspeaker unit so also the electrical output from it as a microphone.

I also feel the focus on standing waves to be wrongly emphasised. You can of course measure them, but you should be able to hear the timely difference of the two signals needed to build a standing wave — the direct and the reflected one. Waves pass through each other in the time domain and music also only lives in that domain. It is also so, that to any instrument overtones are attached, and somehow we hear and experience live music joyfully with no major disturbances related to standing waves even in churches.

So why focus so much on a steady state situation.

How the basic resonance frequency and the Qt can be calculated from the dimensions of the room and absorbing surfaces, I don’t know for now. But by the modern principle, "Try and error" you can find it.

Without knowledge of that formula you just as well can measure the bass in its nearfield and again from the listening position.

The difference between these is the room amplification. To find the difference you must redraw the curve from your listening position and find the middle value.

You will get an approximation by the whole process, but so also by a calculation.

You will in the same time get the reference for the slope of the level of your future bass loudspeaker in its nearfield. It simply is the mirror image of the room’s amplification. From this curve you can find the resonance frequency and the Qt of the best loudspeaker possible. See figure.

With an optimised loudspeaker-unit it has been possible to achieve a linear sound-pressure from below 1 Hz and upwards to 15 kHz within 5 dB, measured from listening position. It is really a very impressive but also a strange result referring to acoustics. But so it is.

The strange influence of the baffle (enclosure)

When a loudspeaker is measured at a factory, a large baffle is used. But for you probably a much smaller baffle will come into use.

In consequence of this you will loose sound pressure in the middle/low end of the frequency band at maximally 6-dB - mildly turned when a rectangular baffle is used.

I have always been puzzled of the phase of this decay. Why should there be any disturbance of that? The front wave isn’t disturbed at all.

I have therefore ignored that phenomenon, which only occur on distance.

But in the brain’s work with sound there is a clear improvement of the perspective, when this decay is partly compensated for (4 to 6 dB as the compensation must take into account the distance from the front of the loudspeaker to the walls, which serve as another baffle).

The only explanation I can think of is this:

An instant for a microphone and an instant for the brain are not always the same. Why so?

When we hear a specific sound, we turn towards it, ruling out the difference in phase of the sound from the two ears — we direct our hearing (the instant is equally the shortest possible).

Then we perform a closer listening — we are expanding the instant to a moment to include some immediate reflections. You focus on the event (and unwittingly change focus of recognition between wide-angel to telephoto ear-lens. With expanded time follows extended range of frequency)

In this procedure the brain also uses the sight to bring sound and sight in accordance and — BINGO! - Recognition. This procedure will, done again and again end in some sort of conditioned reflex in childhood.

Thinking deeper it wouldn’t be so strange if, when a person speaks to you, the immediate reflections from forehead and the upper body parts and sound from these are included in the brains moment.

If that is correct, as unnatural the brain also then will interpret a small baffle yes the whole enclosure. One can say, "the sound doesn’t look right" — confirmed by the sight of the loudspeaker. This goes also the other way around and forms your expectations of sound.

It will therefore help, if you hide the loudspeakers. But that isn’t enough. You must go deeper and further minimise the reflections from the cabinet. This can be done by directing all reflections away from your direction of listening, as the globe described by Olson, but the simplest and far the best way is simply to cover all reflecting surfaces by soft — thick felt.

Hiding the cabinet for your eyes as well as your ears will lead to a major improvement in fooling the brain.

Just as unnatural perhaps even detected as having a capacitive turn of phase the brain also interprets the loss of level, where the dispersion of sound slowly changes from a 2pi to a 4pi space. The loss can be compensated - not disturbing the impedance

This correction has a local inductive turn of phase, but still it helps my brain’s work with sound and this goes apparently also for others, who have listened to the construction, where this technique is used. Why and how I still don’t fully understand.

The main problem with this correction is its lowering of the efficiency, when it is done with passive components, but connecting two units in parallel will give the 6 dB needed.

The unit itself

A well-designed unit follows the rule of minimum phase, is a second order bandpass and should therefore cause no problem. But really it does.

The problems are many but the single unit’s bandpass property forced to be near linearity creates higher Qt of the resonances at the lower and the upper end of its frequency band.

These are minor problems, when the unit is filtered and therefore normally can be corrected by use of at least three passive components pr. resonance. But in the deep bass and the upper treble, they are untouched. In the bass a capacitive turn of phase is created likewise in the treble but inductive.

The brain somehow cannot recognise sound marked by these turns of phase as closely connected to natural sources, how minor they may seem to be. Any resonance put onto the signal will be judged as unnatural and not belonging to the music only to the loudspeaker. The two resonances in speak are practically unavoidable by dynamic units and are catastrophic for a natural reproduction of sound.

The cruel importance of this wrong behaviour and the possibility to repair it fully has been partly hidden for me until recently.

This solution I found by a sheer chance working on a smaller loudspeaker, stretching its ability to the outmost.

The problems and their solution are so simple, that apparently no one has ever thought of or described it, probably because it seems so deep in conflict with the science of acoustics.

A false "Truth" again has caused its hiding.

This time the false truth is the demand of linear level from 20 to 20000 Hz.

This may be a correct minimum demand for all links in your hi-fi but particularly not for the loudspeakers placed in a domestic room. A listener is not comparable to a microphone, therefore the loudspeakers behaviour should be directed towards the capacities of the human hearing. Information on that can be found from physiology of our hearing and psychoacoustics.

All domestic loudspeakers should therefore be an integrated part of that room and should of course use the amplification done by the room in a positive way. Don’t fight it — use it.

The factual bass response shall not be linear to 20 Hz — far less — the room for listening and not a false "truth" should guide its curvature.

To achieve that from different loudspeakers a Linqwitz/Grainer must come into use.

The demands for the bass unit is - in consequence of the theory - drastically changed from middle to very low resonance frequency and very much lower Qt.

The circuit can together with the room cure the catastrophic fault in the bass-unit and in the same time turn the problematic reverberation time of the room into an advantage supporting the lower and upper bass to no less than near perfection.

Why should we be satisfied with less?

Of course — if you should have a loudspeaker with the demanded data, then the circuit isn’t necessary.

For those who think they know much of standing waves by experience and therefore of course will doubt my findings, I must emphasise this:

When a loudspeaker is equipped with a powerful magnet, very low resonance frequency and further shortcut by a very low output impedance of the amplifier, it will keep a tight rein on the local build up of standing waves. It will act also as a microphone and from its position in the room regulate its impedance felt by the amplifier against any outer influence — also standing waves.

This happens simultaneously while it is playing. But the unit must of course not have any resonance of low frequency and high Qt built in, that would drown out the wanted behaviour of your room.

What then to do with the resonance in the treble?

To clear this up we must look for guidance from acoustics

The subject for this science is the sound itself and its properties under different conditions.

The main question for us hi-fi nuts should be this,

"What happens with sound when it is spread through air with a given humidity from a source to a listener."

The normal answer to this question is an astounded facial expression. But a friend Johnny Andersen, engineer in acoustics, thereafter has been a tremendous help for me on this subject and others.

The answer is - something happens and we experience this "Air-print" every day and all day, why we don’t notice it, but our brain does.

If we receive sound with a "box-print" we are unable to identify the sound as created by natural sources - unaided by our sight, when we are listening to music at home.

You have probably experienced how supportive the television picture is for the really lousy sound from the TV-set.

We can recognise and enjoy the sound from loudspeakers with our ears much in the same way as we do a picture of a naked model with our eyes, but why be satisfied with that, when you can get a virtual one.

To achieve highest fidelity the loudspeaker must react on the electrical

signal in exactly the same manner as air reacts on the sound itself.

If that were fulfilled, our gear would create the distance to the musical event, which we as listener are so accustomed to. All other parts needed to experience the events are recorded and hopefully not spoilt by the producer.

Also at this point of the preservation of sound we have the main problem with loudspeakers, the ones used in studios are simply too bad. They can play loud — Yes! — But their sound.

That their lousy sound is used to adjust the recorded sound before it’s stored on tape is scaring to say it mildly.

There is a tendency towards an inverse function of the amount of recording equipment to the true quality of the recording. Simple is beautiful, only too simple is ugly.

How is the "Air-print"?

This graph shows the "Airprint" at 20 degree Celsius, normal atmospheric pressure and a humidity of the air at 20, 40, 60 and 80%. As seen from the figure nothing happens in the bass region. Exactly that is gained using the room amplification.

The humidity plays a significant role, why in concert-halls this parameter is regulated under the musical performance.

The loss doesn’t seem much but reconsider; the curve is per metre.

If you are placed let’s say 15 m away from the centre of performance and the humidity of air is 40%, then 20 kHz is dampened with 15*0.57 dB = 8.5 dB and 10 kHz with around 3 dB.

This turn of sound leads us to the manufacturer of units for treble. They can now with this in mind bring forward older constructions with far broader high frequency band but not full level at 20 kHz. The demand for that has ruined the production of tweeters for at least the last two decades. But also I know, that they will not listen.

It is strange to me, so much talk is concentrated on the abrupt cut-off on the digital medium, when simultaneously it is repeated and apparently also accepted from units for treble. It is often a consequence of the wanted linearity. The left hand does apparently not know, what is done by the right hand.

What can easily be done about it on units at hand?

A simple solution could be to add a correctional circuit that threats the upper resonance as a peak. The impedance should stay undisturbed. It can’t be said more precisely for now. The variation is simply too big.

How much air it should simulate I don’t know either.

I will try to get the Linqwitz/Grainer to work in high frequency as it does in low.

Its dependency of distance apparently at 11 m can be expressed as a 4.order filter-function. But again it depends on the distance chosen. See figure

The curves below is calculated in accordance to ISO standard 9613

With a precision of +/- 10 % within

Temperature -20 to +50 degree C

Frequency 40 Hz to 1 MHz

Relative humidity of air 2% to 100% at 20 degree C.

A question of true quality

The quality possible to achieve by use of the methods above has focused the attention on the need for correct absolute phase

The cause and need of this are to my knowledge not described in the literature, though it has been discussed for decades.

I have always been very sensitive to this strange phenomenon, which far to many can’t hear because of inferior loudspeakers.

I will in the following try to prove that there is a difference, and how the brain treats it.

Looking in a mirror you’ll see your reflected image, but you quickly learned that it wasn’t you - though it IS you.

Shouldn’t it be the same with reflected sound? So you likewise know, what is the direct sound and what is reflected. I would be against your survival in more natural surroundings if you reacted to an echo as to the original sound, you would believe facing two enemies instead of one of the sort.

I’m sure it somehow is disturbed by its reflection, even if it is at 100 %, and that it can be reversed by the change of the polarity of your gear. To detect that a measuring instrument must be diode like sensitive and further treat the frequency spectrum turned heavily in phase meaning delayed dependant of frequency. Our hearing organ - not the eardrum — but the basilar membrane attached to the haircells stereochilia is exactly such a measuring device, where the phase is detected by neural active places in the length of the membrane. That this is factual can be seen from the delay on between 8 and 10 milliseconds from the oval window to apex.

To my ears this procedure turns the direct sound to reflection and vice versa.


To illustrate this, I have replaced the former picture of the impulse with its side-view - a vector. Thereby the axis of time can be replaced with an axis of frequency. Every mathematical instant the sound is normally seen as a single vector, but it is in music always a sum of many vectors, therefore it can be and will be broken up into impulses, so let’s take a look on a sound with time frozen. See figure

By listening every single impulse is registered — Either directly or indirectly.

From sound reproduced by a loudspeaker, the phase of the single impulse can be said to be relative and only together with the phase of other impulses they can be judged.

I must also emphasise here that deep bass are felt by our body nerves as well as by our ears even calculated to be of existence. (The missing fundamental)

My earlier postulated difference between an instant and a moment as time for closer listening, of course also goes for the brain’s treatment of phase, but with the detail hidden for you.

You’ll only hear a fully understandable result of that — if your loudspeaker is good — very good in its treatment of the phase.

If time should be added to the single vector shown, it would be seen as a full or partly circular turn of the vector, forming the well-known sinus curve.

Let us now say that the mark for the endpoint of the vectors is a ball — what would then happen, when it hit a wall? Yes! It will bounce back, why the rotation of the vector is changed.

But the brain is free to choose within the sound and do that in accordance with its sense of naturalness and danger.

Therefore the picture above can be seen as a counting work, with the high speed of rotation at high frequency and slower and slower rotation towards the bass. When the source of sound isn’t visible, the brain first stops its finding of the distance to the event, when the vectors are rightly turned why a picture of sound is recognised. Phase and delay are tightly connected.

In this the phase plays the important part. But we can’t be sure if the picture of sound is the right one.

This is why; a change of absolute phase is so easily heard the better the loudspeaker is made. It helps the brains work with the sound and you will feel that relaxing.

I have always felt this ability to be the final mark of quality. When you, listening to a loudspeaker, only fully can understand the one of the two possibilities, then your loudspeaker would be extremely good.

When the absolute phase is correct, specific instruments are playing placed inside a room with reverberation timely separated — when wrong, the room plays some instruments inside it with reverberation not separated in time.


The theory described above is found and proven correct by practical work with loudspeakers.

It must consequently force a new area to be developed within the field of science of acoustics.

Treatment of sound from instruments in great halls is marginally different from treatment of sound from loudspeakers in domestic rooms.

A domestic room is an amplifier, which will react predictably on its input.

What you’ll hear in a room will always be coloured by the "room-print", which beforehand can be removed from the input.

The net result will be the lower part of the "Air-print", where the level is untouched and reaches down to near DC.

In the middle band, where the length of the sound waves is comparable with the dimensions of the enclosure and baffle, you will get a "box-print". This can be dampened by mechanical means, so also that almost can be removed.

In the treble the practice of linearity is against the "Air-print". This must be added turned correctly in phase and in the same time the upper resonance of the tweeter must be fought.

In this way the loudspeakers will disappear as loudspeakers and instead play their part as air. Exactly that air missing from the recording of especially acoustical music.

Air is the medium of sound why an "Air-print" will cause no disturbance in your experience of music — even the recorded.

The possibility of wrong phasing can now be clearly heard and let’s hope that they know what they are doing by recording.

Listening to the MS-recording technique has shown it to be very disturbing by its disturbance of the absolute phase either left or right channel. It is only playable in mono so why not record it that way?

Apparently some of these important recording people cannot hear or do not know of these problems.

But some of them do. The sound from DVD’s is in many aspects marvellously well recorded. There is hope for the future development.

So is the law of progress in the audio world — two steps backwards and slowly a three steps forward.

Steen Duelund


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