May 14, 2011

Estimating maximum SPL for your subs

Predicting the maximum SPL of your subs in your room is not an exact science. Here I will provide a guide that will enable you to come up with a reasonable estimate. There are two parts to this estimation. The first is the output of your sub in a half space environment. This is what you would get if your sub was set up outdoors. The second is the output you would measure from the listening position in your room. For this exercise we will ignore room modes and simply consider room gain and attenuation due to distance. This should provide some kind of reasonable estimate that is valid up to about 40 Hz. Above that point the output will be dominated by room modes and estimates can be as much as 40 dB out.

Part 1 - Half space estimates

The half space output at 1m is based on the alignment and the total swept volume (VD). The swept volume is limited by power compression, driver excursion, and piston area. If you know the maximum swept volume, then you know the theoretical maximum output. However, real world concerns such as power compression, amplifier power handling and driver power handling may cause that maximum not to be reached.

A simulation program such as WinISD is a good starting point. You may find that a sub can output 120 dB in theory, considering a particular alignment and assuming 2kw of power and 32mm of one way excursion. In practice, we may only have 1kw of amplifier power, output is reduced by 3 dB to 117 dB. We may also find that the driver has 5 dB of power compression due to the heating up of the voice coil. The real output is 112 dB, not nearly as impressive. Any of these issues can be limiting factors.

For some real world measured examples are available:

Home Theatre Shack subwoofer measurements
AV Talk subwoofer measurements

Even if a sub of interest is not in either list, you can no doubt find something similar.

As these measurements are performed at 2 metres, 6 dB should be added to the output. This will yield a result that is comparable to simulations in a half space environment, except that compression is included. Ground plane measurements such as these, measure at 2 metres to counteract the 6 dB gain from the ground to closer approximate an anechoic result. Here, we want a half space figure.

SPL estimate

The table above suggests some typical half space maximum output figures at 20 Hz, and assume that adequate power is available and that no power compression is involved. If you have a small box, less power than required or port compression, you will get lower figures.

You may like to simulate your particular sub in WinISD. If you aren't familiar with this program, I've written a quick start tutorial. If you need to enter in a new driver, I suggest you also look at the post about how to do it.

1. Simulate the driver in the appropriate box size

2. Enter the maximum amplifier power under the signal tab

3. Check the cone excursion and reduce the signal until within xmax

4. You might like to add a High Pass (Rumble filter), especially if it's a vented box

5. View SPL

Part 2 - allowing for the room transfer function

Now the difficult part. If you have a speaker with some kind of output down to 20 Hz, you can work this out with some accuracy. Firstly, I'll cover the estimate where you have the option to take measurements.

1. Place the sub or speaker in the intended position and measure with the mic in your listening position with REW. View REW Quickstart guide if needed.

2. Take a ground plane measurement outdoors. Place the sub on the ground and the mic also on the ground at a distance of one metre.

Ideally you would keep the same level of gain in each case. If you adjust the gain for either measurement, the result becomes invalid.

You can now analyse the results. You will have to ignore peaks and dips in the response and look for changes in the bottom end which suggest gain. You may see greater extension in room which suggests gain. You may also notice that the level drops due to distance. If the sub was running with the same input power both times, you can then create a transfer function from say 20 Hz to the region before the first mode takes over.

Otherwise you can use an estimate.

One example

Let's take a Rythmik 12" sealed servo sub as an example. In the tests, this sub produces 95 dB @ 20 Hz. We will add 6 dB to get a true half space value, 101 dB. Looking at the table above, you can see the estimate is 99 dB at that point. Evidently it is slightly conservative.

I have measured this sub at around 36mm peak to peak excursion and the output at 3 metres was 95 dB. So in this case, in my small room it turns out that the ground plane measurement matches the maximum output in my room, which is small and lightly constructed, hence modest room gain is expected. Larger rooms and greater listening distances would see lower output. Concrete floors and masonry walls would increase the output.

Multiple subwoofers

Add a second subwoofer of matching output and you can get up to 6 dB increase in output. This increase can easily be achieved below 40 Hz even when the subs are spaced apart. At higher frequencies the interaction with the room tends to dominate and additional subs will tend to smooth the response without increasing the level.

How accurate are the estimates?

In reality there is no substitute for testing the sub in the actual room. However, if you are choosing a new sub with targets in mind or the room in question has not yet been built, an estimate is needed.

If you want a quick and easy estimate, you may like to start with the links to real measurements and find a sub which is close to what you have in mind. In a small lightly built room the maximum output measured will probably be close to what you will get at 20 Hz at 3m in-room. In a large room with similar construction, you may need to double up. Aim for around 6 dB extra to compensate. A more solid large room may end up with more output than a small lightly constructed room.

So how accurate are these estimates? Probably about as accurate as you need. Consider also that once placed in a real room, you introduce up to +/- 20 dB based on modal fluctuation. With that in mind, it is very difficult to know exactly what you will end up with. 

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