Evaluating specifications and characteristics
of QRD-Diffusers

by ThingMan - December 2014
revised version: 16-8-2017 ThingMan

dit artikel lezen in het nederlands

Theory and practice
differ in a diffuser
in a way that,
practically spoken,
manifests as
a huge advantage !

The following considerations hopefully bring practically useful insights in the acoustic characteristics of QRD-diffusers. Specifications, reviews and plans of such diffusers, found on this site, might then be seen in a wider perspective.

The fundamental fact is this: the practical working range of a given QRD-diffuser turns out to be about 1,75 times bigger than its theoretically calculated boundaries, and this is a huge bonus with useful implications !
Theory and practice differ here in a most beneficial way.

From the beginning this phenomenon has been reported by all users. It was of course also noticed and investigated by manufacturer RPG, after which the phenomenon has been described in their deep-digging book on diffusers in 1990.

Conclusion: your ears don't cheat at this point!
A diffuser with sufficient
maximum well depth (MWD) will also have a significant impact on low- and lower-midrange frequencies. Part of this extended range is not covered by the specs; it is well below the lower boundary of the working range... This is both quite obvious and useful.

Realizing the full 100% of efficiency (more on this later on) should be inherent in a
classic QRD-design, that has no dimensional restrictions. Such restrictions can easily occur in a diffuser that has a folded deepest well.
While efficiency can be regarded as an indication of the quality of a given diffuser, it can only be interpreted as such, when read in the right context and with a correct sense of proportion.
So please, continue reading. There's not a lot, but it's crucial in diffuserland.

After reading this article, you will also find the DIY-page on folded-well diffusers
easier to absorb. This page, written in English, can be found

Working Range -- theoretical and practical

the four parameters of any QRD
are visible in the image above

a symmetrical and an asymmetrical version
of a classic QRD-7 design

Theoretical Working Range

A diffuser's theoretical working range is a fundamental parameter that can be pre-defined. This parameter
can be the most important criterium to choose a given model, but it can also make way for another aspect of equal or higher importance in a given situation, such as
periodicity (more on this later).

In a QRD-7 one period or panel width consists of 7 wells, separated by rather thin fins
(they can be 'infinitely thin').
Most QRD's have symmetrical design. This means the odd 7th, non-deepened well is divided in two equal parts. These half side-wells are then mounted as the sidewalls with half side wells, together defining the 7th well on 0-level.

With classical QRD-designs, shown below left, the designer usually has a choice of
different depth-sequences with each N-number. With a folded-well diffuserdesign only the use of unmodified depth-sequence is feasible. This imposes no limits on the design whatsoever, as an efficiency of 100% can be realised with almost any design.

Below is an overview of all depth sequences of QRD-diffusers up to N=31.
These are: QRD-7 / 11 / 13 / 17 / 19 / 23 / 29 & 31.

Juggling with depth-sequences can be useful when custom-designing classical diffusers for a unique acoustic situation. Good diffusion with 100% efficiency can be realised with every depth sequence though, so there are no real limitations when you're stuck to unmodified depth sequences (Mod-0).

The actual working range of any given QRD-diffuser -- see drawing on the left -- is determined by four parameters, always interconnected and interrelated:

  • maximum well depth (MWD)
  • well width (WW)
  • N-number (= total number of wells per period)
  • chosen depth sequence (drawing above)

MWD defines the bottom-end of the working range
WW defines the
top-end of the working range
N-number determines the
maximum attainable working range (in octaves)
Depth sequence allows
small shifts of the working range

MWD defines the lower limit of the working range.

the larger MWD,
the lower the bottom frequency of the working range will be.

However, with MWD of, let's say 25cm, the design formula will result in a deeper bottom frequency with a QRD-7 than with a QRD-13.

Also, identical MWD's in different depth sequences will also result in different bottom frequencies for the working range.

One may safely conclude that one and the same MWD will result in different bottom frequencies for the working ranges, all depending on the chosen N-number and the chosen depth sequence.
Freely available diffusercalculators do
not take this phenomenon into account. For them an MWD of 25cm will
always result in identical lower bottom frequencies of the working range, regardless of the chosen depth sequence.

WW defines the upper limit of the working range.

the smaller WW,
the higher the upper frequency limit of the working range will be.

Here we see the same shift as with the MWD: a given well width in a QRD-7 will result in a lower top-end of the working range than the same well width when applied in a QRD-17. And by choosing different depth sequences, the same well width will always result in different upper limits.

It seems very seductive to design a diffuser by choosing a considerable MWD, like around 30 cm or so, and to pair this to a rather narrow well width of, let's say, 3 cm. Perfect!
Unfortundately the proportion of WW and MWD has its limits.

The perfect proportion of WW and MWD (100% efficiency) is related to the chosen depth sequence and the N-number. The success of this proportion in different designs is reflected by a corresponding percentage.
In the specifications, this percentage is the
efficiency of the diffuser.

For a given QRD-7-4/7 Mod-0 with 100% efficiency this proportion, based on N-number and depth sequence, is simply: MWD should never exceed 4 times WW.

Other N-numbers need other proportions.
This can directly be seen in the diy QRD-13 design, bottom left.

an asymmetrical QRD-13
in real life
and in sketch

With a QRD-7 design
incorporating optimal proportions
between SW and MSD
and an unmodified depth-sequence
the theoretical working range
ALWAYS spans 2,75 octave
regardless of the chosen SW or MSD
The perfect proportion between WW and MWD can be compromised in two ways:

by exceeding the maximum feasible design boundaries
for correct proportions (overdimensioning);

not realizing the maximum feasible design boundaries
for correct proportions (underdimensioning)

When exceeding...
the design boundaries, the ideal proportion is also exceeded and compromised, either by too big an MWD, too small a WW, or both.
This means bad diffuser design. Diffusion is compromised, because homogenity in the working range has become more or less corrupted.
Exceeding makes the specs look better though, because both the working range and the efficiency seem to increase. Efficiency even exceeds 100%, which is impossible.

When not realizing...
these very same ideal boundaries of diffuser design, the MWD is too small and/or the WW is too big. The design is underdimensioned.

may indicate bad diffuser design, but this not necessarily always the case...
... because it may also indicate a case of deliberate custom-design, limited in size and proportion for some particular reason. It cannot have the correct parameters to optimise the proportions all the way to 100% efficiency.
But -- and this is quite crucial -- the
remaining diffusion can be of impeccable quality, even if it occurs within a limited working range, because no limits were exceeded in the design. On the contrary!

The N-number...
of most available diffusers is 7.
The conclusion that diffusers with higher N-numbers exist is correct -- that is, with more wells per period. The depth sequence table revealed this earlier on...

A folded-well design indeed allows higher N-numbers, but everything quickly becomes very complicated, en then impossible to design on the drawing table.

A QRD-11 with folded well can be realised.
This proces the plan for the prototype, below,
which is scale-correct on pixel level! (1 pixel = 1mm).

A QRD-7 design with an optimized proportion of WW and MWD ALWAYS has a working range that spans 2,75 octave, regardless of the chosen WW or MWD.

It is possible to design QRD's with a theoretical working range that exceeds 2,75 octaves. Choosing different depth sequences will change both ends of the working range, but will never change
the proportion between WW and MWD! The net result will always be a working range of almost 3 octaves, no matter which depth sequence was chosen.

The best option for expanding the working range of a diffusers is to choose a higher N-number -- a QRD-11, -13 or even -17 and -19 belong to the possibilities. Without a doubt these panels (periods) will be quite wide , because it makes a big difference if 7 wells of 4 cm wide are incorporated in the diffuser, or 19 of them... A QRD-19 will thus have a panel width of almost three times that of a QRD-7 with identical well width.

Interesting data come up when theoretically perfect diffuser designs with different N-numbers are compared.

Note: MWD and WW are 100% in the comparisons below.
Only the N-number changes, and therefore fully determines
these theoretical working ranges:

QRD-7: max. 2,75 octaves
QRD-11 max. 3,5 octaves
QRD-13 max. 3,7 octaves
QRD-17 max. 4,25 octaves
QRD-19 max. 4,4 octaves

the practical working range
of these 4 allround diffusers
turns out to be 1,75 times bigger
than the theoretical working range

It became evident that only a QRD-11 would be feasible in the folded well concept. Higher N-numbers are not really suitable for the trick with folded wells.

This is not a problem in itself. Essentially you don't need more than good QRD-7's for homogeneous diffusion in the frequency range where it counts most -- the range of harmonics up to 4kHz.

On the left you see a table in which WW and MSD (in centimeters) of 4 allround QRD-7 diffusers is shown. Although the dimension for WW do not really differ that much, they still cover the complete range in which you normally wish diffusion to occur.

Diffusers with high N-numbers will quickly encounter physical problems, when the rule of periodicity or 'repeating the pattern' is applied. The next section on "
Homogeneous Diffusion and Periodicity" explains this parameter.

And finally, you will need a lot more physical depth to create a QRD-11 that has diffusion
down to 300Hz, than you need with a standard QRD-7!

Practical Working Range
Up to now we've always considered the
theoretical working range of the diffuser. In all QRD7-4/7 mod-0 models this range spans 2,75 octaves, corresponding with 100% efficiency. Lower and upper boundaries of the working range are defined by the MWD and the WW respectively, and they are the most important design parameters on the drawing board, as they define the target for the diffuser to be designed.

From the practical application of diffusers -- starting slowly after the invention of the QRD-diffuser by Manfred Schroeder in 1972 -- it appeared the working range was clearly bigger than indicated by the design formula (theory).
So much bigger that it is not just a little extra, but a real bonus.

Under controlled and specific circumstances the performance of a diffuser surface can be measured and diagnosed, and these measurements support the finding heard.

The practical working range of a QRD-7 equally extends
on both ends and becomes at least 1,75 times bigger
than its theoretical working range.

Of course the practical working ranges of diffusers with higher N-numbers will expand correspondingly than their theoretical counterparts.

This means the practical working range of a QRD-7 with perfected WW / MWD proportion spans over 4 octaves. This is wide enough to span most of the sound- and space-determining components of the soundfield in the midrange, and sometimes quite a portion of the higher midrange as well (in case of a narrow well width), or an expansion at the bottom-end of the working range, in case of a larger maximum well depth. These variables can be found in the table on the left.

Unfortunately it is not possible for a single diffuser to cover the whole musical range, unless we're talking fractal diffusion. But diffusion above 5kHz is more like treating flutter-echo than diffusion. So forget about fractal diffusion for the moment, because all you need is couple of decent QRD-7's...

The 4 allround FWD's, offered to you in a download, have working ranges with an overshoot to the next one.


Homogeneous Diffusion and Periodicity

increasing degrees
of homogeneous diffusion,
visually projected

an extended working range alone means nothing,
if it doesn't include homogeneous diffusion.

Practice is a lot more abstract though, because homogeneous diffusion cannot easily be made visible, nor can it be measured at home with a microphone and software on a laptop.

Homogeneous diffusion is the (fortunate and) automatic result of successfully merging two conditions, both on completely different terrains:

  1. right dimensional accuracy
  2. periodicity or repeating a pattern

Right dimensional accuracy is
first of all a matter of correct design, as discussed under "
Working Range".
Right dimensional accuracy is also the result of good craftmanship at the sawmill, followed by a sufficiently accurate assembly of the wooden parts. The physical part of the deal... very important indeed.
In the context of a factory-environment, all this would not present real problems, but for a home builder it might still be quite a challenge!

When all conditions of dimensional accuracy are met, periodicity is the last condition to be met, in order to generate homogeneous diffusion.

It is impossible to generate homogeneous diffusion on a given surface
by applying just
one diffuser or "period" to cover it.
This doesn't work, not even when it is a QRD-11 or, for what it's worth, a real QRD-19 of 150cm wide!

The solution is simple and independent from the N-number:

It takes at least three, rather four joined periods to create a surface that generates sufficient homogeneous diffusion in time and space, and within the specified working range.

left: periodicity (5 x QRD-7)

right: non-periodicity (1 x QRD-19)
So a given diffuser surface, regardless of its location or purpose, is ideally 'covered' by at least four joined diffusers or periods.

Often the available physical width for diffusion purposes is limited.
But even when this isn't really the case, any early reflectionzone in home-conditions requires not much more than 1 meter of diffuser treatment.

Example from practice:
As an example we assume there's 145cm of width available to create a diffuser surface.
To realise homogeneous diffusion as possible you must cover this surface with
four identical periods, so the total width becomes 145cm.

The idea will be clear: the correct choice of a model is sometimes determined by the maximum width of the surface to be treated.

Another example from practice:
We now have a maximum of 160cm available to create the desired diffuser surface on the wall behind the loudspeakers. Counting from the middle we have 80cm on both sides of that center line. In this case one could choose any of the allround FWD-models on this site, except the biggest, since at least 4 periods of these models will cover the area.

One can only really benefit from the significantly larger working range of a QRD-19 (4,4 octaves in theory and 7,5 in reality!) when at least four periods are applied in joint configuration. An ideal QRD-19, having a useful working range, will be close to 100cm wide. Therefore you need a surface of at least 4 meters wide to generate homogeneous diffusion with a QRD-19. Not really a diffuser for the sidewalls, unless in very large rooms. It would indeed be quite a large room to benefit from this... at home hardly any situation can offer the right circumstances for a QRD-19 to shine, no matter how attractive the working range may seem. Those who build custom-diffusers may however experiment with anything that can be built.

And just to be sure:
Two diffusers, 62cm high and stacked on top of each other do NOT represent 2 periods!
This would still be one period of width; height simply consists of two separated panels instead of one.



high efficiency isn't the last word
in quality of diffusion
a design can deliver;

efficiency says everything
about the success of the proportion
between the MSD and the WW

After reading the information written above this section, on "
Working Range" and "Periodicity", you will be able to appreciate the efficiency specs of diffusers.

All-important conclusion is this: efficiency doesn't always indicate the quality of diffusion the design can deliver.

A diffuser with an efficiency of 50% can deliver totally homogeneous diffusion, even if it is within a 50% reduced working range. This working range will theoretically span 1,4 octaves, in case of a QRD-7, while it could (and should) have been 2,75 octaves. Yet within this 1,4 octave of working range there is as much homogeneous diffusion as with a perfectly designed diffuser with an efficiency rate of 100% !

The efficiency rate is a quality score that comes from the calculation formula on proportions between
MWD (maximum well depth) and WW (well width).

As such it is a design parameter, only functioning as a design target in the calculation stage of designing diffusers.

an efficiency rate of 100% expresses the realisation
of the perfect proportion between MWD and WW.

the result in a QRD-7 is always a working range of 2,75 octaves,
the maximum attainable range,
in which homogeneous diffusion is possible
provided the periodicity rule is also respected.

efficiency below 100%
does not necessarily mean harm
to the quality of diffusion itself;
it just needlessly limits
the maximum working range
that's potentially possible
with the design

When fysically designing a diffuser with folded wells, WW and MWD must be manipulated in order to meet the desired proportion, by applying various panel thicknesses, and sometimes "fillers". Unfortunately, making-it-fit is often not possible at all, at least not with a targeted well width, nor with a slightly smaller or bigger well width.


Frequently Asked Questions

There are not many, just a few quite
important questions...

stretching a diffuser with fabric
leads to destruction of much
of the diffuser's capacities,
and creates many unwanted
membrane absorbers,
which is quite bad

Frequently Asked Questions: Can Diffusers be stretched with Fabric ?

Quite often the question raises whether diffusers can be stretched with fabric. Thus they become visually invisible. The question is very relevant, because the perspective of having to paint various diffusers is usually not attractive.

Stretching with fabric obviously seems to be
an attractive alternative to painting;
but unfortunately it isn't... !

By stretching the front of the diffuser with fabric, no matter how heavy or light, every deepened well becomes a small but tuned absorbing element. Many small membrane absorbers are actually created, and as there is a repeating pattern of well depth, there is also a repeating pattern of fully identical, selective, powerful and tuned absorption. Unwanted absorption as well, RPG could conclude and describe in their research on this.

The added absorption will probably not be much of a problem, when applying 4, 6 or 8 big diffusers in your room. Only when applying large diffuser surfaces, this unwanted selective absorption will definitely become a nuisance of the first magnitude.

Much worse however is the fact that the diffuser's efficiency and power to diffuse is largely destroyed or compromised by turning it into an unwanted membrane absorber, and of course that is very bad.
You will have made or bought diffusers that don't really diffuse in the end...

In such cases diffusion is probably not the first choice. Not enough diffusing power will remain to be enthousiastic about. Absorbing measures might be a better choice to treat those surfaces.

Well... there might just be one tiny possibility, only reluctantly admitted... as it is still not an ideal and still somewhat counterproductive measure!

By stretching the fabric at least 5, even better, 10cm in front of the diffuser's face, no powerful membrane absorption occurs.
Definitely not.

The potential of the diffuser will still be compromised, no matter how 'transparent' the fabric may be. In short: this is a compromise one might be able to live with -- one that's still better than no diffusion at all. This cannot be said about the first method of stretching the fabric directly against the front of the diffuser.

Diffuser specifications will not be fully met when using fabric in front of diffusers. How much compromise and loss of performance will occur cannot really be predicted on a grey scale or in a number.
My own experiments with fabric at 10cm in front of the diffuser's face indicate a substantial loss of diffuser-potential, yet what remains is still perfectly good diffusion.
No distortion noticed.
Subjectively spoken I would say that 30 to 40% of the diffuser's potential vanishes in thin air, when they are placed behind fabric. Perhaps diffusion is too valuable for this...

painting diffusers is usually not
a job that brings lots of joy

diffusers in MDF with lacquer carrying foil
reduce the paintjob
to just one layer of finishing paint

painting will still be a drag,
yet you should realise
it is a one-time-only job...

Frequently Asked Questions: Then what's the best way to finish Diffusers ?

The best way to finish diffusers is definitely painting or spray-painting.
Both are one-time-only jobs, and so is normally the purchase of diffusers. They should last an audiophile life long.

Many customers indicate they think this single labour investment is more than worth while, and get themselves in the mood for painting a long weekend (or two). Others prefer to do bussiness with a spray-painter. More expensive and with potentially better results than hand painting, although I have seen astonishing examples of home-craftmanship as well.

No-finish is not an option, I think. In dedicated listening rooms with somewhat dark moodlighting and brownish or other earth-like colours, an untreated but neat MDF diffuser might perfectly blend. However, if a lot of untreated mdf is present in the listening room, upper-mid and treble will suffer. In that case a hard finish will be unavoidable.

In home-theatres the level of finish-in-black is often less critical. I've seen well finished diffusers with one layer of cheap black latex paint.

Untreated (normal) MDF requires a ground-layer of paint, sometimes even two, although it might be too much asked in the case of decorating diffusers...

A finish with rock-hard transparent paint for woodfloors is possible as well. It can be applied directly on untreated MDF or on top of a layer of colour paint. This paint is rock-hard, and the harder a diffuser surface is, the better its diffusing performance!

In short: finishing the diffuser is in fact a must, also acoustically spoken.