Friday, July 19, 2013

Audio Calculator for Speaker Requirements

I have now completed the first version of the Calculator for Speaker Requirements, for home theater and sound reproduction.

By entering data for room and speakers, the sound pressure level can be estimated to verify if the speaker configuration has sufficient output to meet the chosen required listening level.

A graphical presentation shows the current status, and provides point and click access to each speaker configuration section.
Speakers that do not meet requirements are indicated, it is easy to get an overiew of the current situation.

Speaker Calculator status image

The most difficult part was to decide how to calculate the reverberant sound field contribution - the sound that is added by the room itself.
The chosen method is approximately valid for relatively small rooms that are acoustically well damped, with reasonably normal height-length-width relationship.
For larger spaces or odd room shapes the model may be less accurate.

With this tool it is quite straight-forward to check whether a chosen speaker set will be usable, and also see how much amplifier power is needed.

This is very useful for subwoofer configuration - add or remove different subwoofers and see the results immediately.

It is easy to see that the most difficult requirement is the subwoofer.
Reference level with a nice house-curve lift at the lowest frequencies will require massive output capability, most likely several powerful subwoofers must be used.

Tooltip provides additional information for many of the different data items.

Master Volume Listening Level

The loudest listening level is selected, this forms the foundation for the rest of the requirements.

Level can be chosen from a set of predefined values.
There is a reason for not using just a number to be entered - the range of values now reflect the level of accuracy one can expect, there are also descriptions for the different levels, and steps of 3 - 6 - 10dB are appropriate, as these levels provide suitable steps in loudness to span the range from reference (quite loud) to a lower -20dB.

Now, these are meant to be the systems maxiumum design requirement - that does of course not mean that one always must listen at these volumes.
Even -20dB may be too loud sometimes, and for quiet movie or documentary both the dialogue and sound effects should be clear and easy to understand at, say, -40dB.
But you don't dimension the home theater for that.

Room data

Dimensions and acoustic data for the room is used to calculate the resulting sound.

Here the reverberation time T60 may cause some uncertainty, regarding what value should be entered.
If the theater has not been built yet, how can you measure it.
The answer is, you do not need to measure it, you determine the value instead, and thereafter fix the room with acoustic treatments to reach that value.

A T60 around 0.25 or lower is nice for the smallest rooms, 40-60m3, or 12-20m2.
Larger rooms have longer reverberation, 0.3 and up to 0.4 can still be usable for rooms up to 40-60m2.

Speakers and room

Distance from listening position to speakers determines how much attenuation there is in the direct sound.

Speaker directivity is the radiation pattern of the speaker:
 1: Omnidirectional 4π radiating. Subwoofer or normal speaker at low frequencies.
 2: 2π radiating. Recommended for wide dispersion surrounds (180°).
 3: Dipole, and normal radiating. Recommended for mains L,R with low directivity - direct radiating mid and tweeter. 
 4: 45° radiating. Recommended for mains L,R with higher directivity - horns, waveguides.

The critical distance, calculated based on room data and speaker directivity, is displayed.
This is the distance where the reverberant field and the direct radiated sound are equally loud.
Beyond this distance, the sound from reflections around in the room will be louder than the sound that comes directly from the speaker.

Subwoofer configuration

Defines how to calculate subwoofer sound pressure level.
When main and surround speakers are set to Small - routing the sub frequencies to the subwoofer, the required capacity for the sub must include the added signals.

House curve means a customized frequency response target with a boost at the very low end, starting typically at around 50-100hz, full level at 20Hz.
Clearly this will also add to the required spl form the subwoofers.

Since the main and surround channels are very unlikely to have full level low-frequency content, the level of contribution can be adjusted.

Loss means correction from 1m/2π specification to in-room at listening position.
The actual correction will vary according to room construction and size, and subwoofer location.
A range of typical values can be selected, and when set to "Use distance" the spl is calculated using reverberant field and room data.

Speaker Requirements

Sensitivity for the speakers must be specified, as measured at 1m with 2.83V.
Often specified as dB SPL/1m/1W, as 2.83V equals 1W into 8 ohm load.
Some speakers are 4 ohm, and in some cases sensitivity is given for 1W into 4 ohm, then add 3 dB and you have the sensitivity for 2.83V.

Actual SPL at listening position is calculated using the entered Actual Power.
The Power calculated is the required power to reach the required spl.


Four different subwoofer types can be selected, in any reasonable number.
The configuration table allows for quick and easy overview of different subwoofer configurations.

For subwoofer specification, the maximum spl at 20Hz, measured at 1m distance 2π (groundplane) must be used.
Make sure the value you use is a real, measured value, and not some marketing number.
Most subwoofers will be a lot more powerful at higher frequencies, like 60Hz, than at the lowest 20Hz and below, so be aware of getting the right spl number, you want the one for 20Hz.
If the specification is for 2m groundplane, just add 6dB to that value to get the 1m/2π.

For existing and new installations

The calculator is useful both for new and existing installations.
Due to flexibility in what data may be entered, there will always be a way to get approximate information about performance.

Monday, July 1, 2013

More on Compact Subwoofer Technology

The Compact Subwoofer Technology is a design method for small horn subwoofers, presented in the article available on the Kvålsvoll Design web pages.
The article describes briefly what it is, and how it works, read the entire article there, it is also available for download as .pdf file.

Now I will discuss some of the more practical implications of the small horn
designs, and give some examples on what can be achieved, in real subwoofers.

Several subwoofers have been designed, and some of those have been built and

The very small 6-14 subwoofer was designed to be compact, at the expense of
low frequency output capacity.  Design specification, output capability: 30Hz,
100dB (1m/2pi).
The 6.14 subwoofer. A very compact 30Hz, 100dB design.

This means it is not a real, full bandwidth subwoofer, and can not play powerful
 bass in a larger or even medium sized room with the physical authority and feel that larger systems have.
However, the small size have some advantages, and the output is enough for low and mid volume tv or movie, and music.
With two of them in a small room they played loud enough to have a gentle physical impact on the cannons in the Master & Commander movie.
Being small and nice looking, it is easy to find a place for them, they will also often fit under a sofa.
Another advantage of small size is that they are easier to move around for measurements and testing.

Utilizing a small 6.5" driver, this design really pushes the limit for output from such a small woofer.

30Hz extension is not enough to get the solid weight of low frequency effects in movies, and nowadays there are lots of music that also benefit from extension down to below 20Hz.
The difference really has to be experienced.

The T138 (left) is a real subwoofer with true 20Hz capacity. As we can see, it comes with a price.

Now, compare the size of the 6-14 to the T138.  This is a real subwoofer.
Extension to well below 20Hz, design output 112dB/1m/2pi at 20Hz.

Small is a relative term.
Even though the compact subwoofer technology enables very good performance for the size, it still can not beat the physics of low frequency sound reproduction.
More output at lower frequencies will still require a larger box.

SPL requirements

How much output does one need, then.
Let us assume movie playback at reference level on a calibrated system, we can calculate the theoretical maximum sound pressure level from the subwoofers, when bass management routes all LF to the sub, including LFE track:

Source SPL ref (dB) N Sum N (dB)
L 105 1 105
R 105 1 105
C 105 1 105
SL 102 1 102
SR 102 1 102
RL 102 1 102
RR 102 1 102
LFE 115 1 115
Sum SPL (dB)


We see that maximum sub output may actually be 124dB.
However, we can make some assumptions that lowers this number considerably.
First, it is unlikely that there is full level content at 20Hz and below.
And, if there are any other sounds playing at the same time in the front and surround channels, some of the headroom is used for that signal, and thus can not have low output at maximum.
For most of the time, we can assume it may not be necessary having more than 115dB capability.

But, since we would like to have some reserve headroom for a nice house-curve with some boost down at the lowest frequencies, that must be added.
Let us assume +6dB.
We still end up with 115dB + 6dB = 121dB.

To achieve this kind of output will require some powerful subwoofers.
We need the real thing.

4 decent subwoofers is no overkill..

Simulations of the S4 subwoofer, a nice, 62l net volume/97l external design, shows output capability at 108dB/20Hz/1m.
Around half the size of the T138 pictured above.
Now, assuming we loose 3dB on average in-room from the 1m output to th listening position, we see that 4 of these subwoofers can give us 117dB:

Source SPL ref (dB) N Sum N (dB) SPL diff LP1 (dB) SPL LP1 (dB)
S4 108 4 120.0412 -3 117.0412

0 0

0 0



Sum SPL (dB)


Also consider that the output increases some up in the mid-bass range.
This should be a good start for a nice subwoofer setup.

Advantage of small horn - the compact subwoofer technology

To achieve the same output with sealed box subwoofers would require more subwoofers, and a lot more power:

Source SPL ref (dB) N Sum N (dB) SPL diff LP1 (dB) SPL LP1 (dB)
Sealed 50l 100 10 120 -3 117

0 0

0 0



Sum SPL (dB)


We see that using a driver with similar parameters in sealed boxes requires 10 subwoofers, and that is not really practical.
(For sealed simulation: mms increased to 2x, mounted in 50l sealed enclosure, driven at same voltage level, excursion xmax = 16.8mm).

An alternative could be to use larger vented boxes, but bigger boxes are more difficult to place, likely it is easier to find space for four smaller boxes than one or two monster-cabinets.
There is another advantage to using several smaller subwoofers as well - when located spread around the room they tend to even out the frequency response.
But that is a different subject on its own, so we can get back to that later some time.