Calculating required amplifier power and resulting sound pressure levels for a given loudspeaker design

[Dandy]

Hi Everyone,

I am planning to build a loudspeaker based on the HifiBerry Beocreate Amplifier module. Since that amplifier is fairly limited in output power (30-60W max power depending on impedance and THD requirements), I would like to simulate what sound pressure levels I can reach with it through a specific chassis/enclosure combination.

Since this is an active system, I would opt for a closed enclosure with active low frequency amplification, since that, in my opinion, allows for a compact enclosure, with fairly deep bass and steep lower cutoff frequency (i.e. low subsonic stress on speaker).

Now, what always puzzled me a bit about speaker and amplifier design/selection was the amount of amplification power I'd need to reach a certain sound pressure level (at given distance, e.g. 1m). I need this information so I can properly select the right speakers (in a given enclosure volume) for the (fairly weak) Beocreate.

I also would like to know, for the mid range and tweeter section, at what crossover frequencies I should separate them and how I can simulate what sound pressure levels can be reached this way (taking into account their electrical and mechanical/acoustical limits). Especially for tweeters, often the limit is not mechanical but electrical stress (by overheating of wires or materials). Can this (electrical stress) be simulated at all with typical information from the producer?

Digging a bit deeper, I found this article, explaining the topic in more detail. I am aware, that some spreadsheets are provided with this article, but I would like to know if there is a simulation software which can also simulate the behavior of loudspeaker configurations at various amplification power levels, so one can see at what levels and frequencies which of its chassis run into trouble and starts becoming the limiting factor.

How are you approaching the problem of selecting the right speakers and/or amplification power and crossover frequencies so that the system harmonizes?

 

[kiwifi]

I am pretty sure that WinISD can estimate the loudness of a given driver + cabinet combination. Larger cabinets are more efficient (require less power) to achieve a given loudness. Aim for Qt (cabinet + driver) of 0.707

 

[Dandy]

Thanks a lot! I had a look at WinISD and it did exactly what I needed. It can even take equalization into account (to actively extend the lower bass).

 

[Willem]

But do realize that average power is a lot less than what is needed for the peaks in music with a high dynamic range. The power output that you mention would only be adequate with quite efficient speakers, for near field listening, or for high passed speakers combined with powerful subs.

 

[AwesomeSauce2015]

Thanks a lot! I had a look at WinISD and it did exactly what I needed. It can even take equalization into account (to actively extend the lower bass).

Keep in mind, if you set WinISD to have 100w of input power and then add +3db of EQ to the (wherever), you'll now be simulating 200w of power into the speaker at that frequency.
If you are trying to do bass boost EQ, with only 60w of what I like to call "when the stars and multiverses align" power, you're going to be disappointed unless you have very efficient speakers, or unless you are using the system on a desk inside a tiny^tiny room...

 

[Waxx]

I use winISD for that indeed, and activate limited by xmax and use voltRMS as watts are a relative power indicator. When a driver goes out of xmax the bass start to distort more severe and altough the driver will go louder, it will be with high distortion (that is luckely harmonic). Also count that passive crossovers can eat a lot of sensivity. well optimised take at least 1 to 3dB, bad ones sometimes take 10dB

The theoretical needed clean volume is by most in the hifi industry set to 102dB per speaker, but higher is often better as you have more headroom. So for 60w I need at least 85dB sensivity (after crossover) to be safe for a clean sound. This means with a passive crossover i need at least 88dB sensivity and take care about my crossover to not to loose to much sensitivity. With dsp it's the EQ that does the same and need the same precaution.

I often do with lot less in my own system but that is because i have a small room and like harmonic distortion (in the right dose) but all my speaker systems (mostly diy) easely go +102dB clean with the right power from the amp. It's the amps i use that are lower power and i'm aware of the limitations of that (that i don't mind).

 

[AwesomeSauce2015]

The theoretical needed clean volume is by most in the hifi industry set to 102dB per speaker, but higher is often better as you have more headroom.

Personally, my requirement is 105db/speaker cleanly over the intended range @ listening distance. Once those factors are in play the power requirements go nuts.

I'd say to avoid using the amp OP posted unless they were planning on having 95+db sensitivity over the whole range... Or unless they don't care about getting that loud.

 

[fineMen]

The theoretical needed clean volume is by most in the hifi industry set to 102dB per speaker, but higher is often better ...

I use winISD for that indeed, and activate limited by xmax and use voltRMS as watts ...

I personally assume that the requirement is grossly overstated for many. For me a long-term pleasant listening level lies somewhere around 74dB plus some 10dB, or 20dB max of headroom stereo in-room. That's about 10dB less (max dyn/ incl/), and hence a factor (!) of 10 less amp power. With a reasonable design a speaker box of 50 liter of internal volume would need 10 to say, 30Watts per channel. Even the back then infamously low-efficiency KEF speakers were specified at 82dB/watt. KEF appeared quite elaborate on that topic with a still today highly appreciated engineering approach.

But hold on. If You're talking about using WinISD please consider that the numbers given are meant to tell which level could be achieved within the limits at exactly that frequency. It mostly hits the excursion maximum for the bass driver first. But with music, or even random noise ( Apollo13's launch ) it is not exactly the bass that defines the perceived loudness. To the contrary. Bass contributes only little to the listener's SPL experience because of the Fletcher-Munson curve.

In short, the max SPL shall be computed considering a wider spectral distribution of Your choice. At least, as music depends (!) on harmonics one shall add a minimum of 6dB to that number, which is given by the excursion limit of the bass.

 

[puppet]

Just keep an eye on the excursion limits and consider using a high pass filter/cut off even on a sealed enclosure to gain you some head room.