Speaker relative efficiency/sensitivity when using a high pass filter

Is there a formula/algorithm/rule of thumb for calculating how a speaker's power requirements might change when the lower frequencies are handled by a subwoofer?  Specifically for a ported speaker with a supposed frequency response down to 35Hz and an a 89dB sensitivity with a second order crossover at 80Hz. I know it goes down but by how much? I recognize that power requirements increase as frequency decreases but is the difference enough to allow for a less powerful amp? I would think so.



If you set up the subwoofer as a subwoofer, not a substitute woofer, then you'll still need the same amount of power flowing to the main loudspeakers.  With a crossover at 80Hz the main loudspeakers will still have significant output at 40Hz.

I am using a second order high pass filter at 80 Hz yielding12dB down at 40Hz.  12dB is associated with a 16-fold power difference. This is my rationale for the inquiry.

If you want your main loudspeakers to have punch and power, I would not cut your main amp back too much, preferably buy more power! 

The sensitivity does not change. That is, the volume of output at 1 kHz relative to 2.83 V input remains the same.

However, since most of the voltage swing required in music is in the bass, cutting it out reduces the amplifier output for the same volume maybe by a factor of 2 in voltage, and 4 in power.


Makes sense. I’m sure the numbers won’t be exact but it means I may be able to go from my 400 W amplifier down to a 100 W amplifier. The speaker manufacturer recommends 200.

Post removed 

I have a Minidsp on order to use as a digital crossover, my Audio Physic Sitara 25 speakers are ported (89db / 36 Hz specification). I use with stereo subwoofers and Vincent SA31MK / SP331MK amplification.  I want to reduce the load on the power amp and speakers as the Vincent is class A for the first 10 watts. (Not sure if that means into 8 ohms ? as AP's are 4 ohm load then could be 10 watts or maybe 20 watts?). I will be experimenting and will add my experiences to this page.

@tcutter , if you take the bass out of a speaker with any high pass filter you increase the headroom of the amplifier driving the speaker but you do not change the efficiency of the speaker one iota, it remains exactly the same. Depending on where the crossover is in the speaker you may lower distortion at some frequencies. With a full range loudspeaker this can make a very noticeable reduction in distortion at moderate to high volumes certainly over 80 dB.

Understood, hence my calling it "relative efficiency".  I appreciate that your and Erik's replies are semantically more appropriate.

So it appears there is a decrement in the current/voltage required to drive a speaker to only 80Hz instead of 35 or so. I am wondering if there is a formula to determine what the quantity might be. My impetus is that requiring less power allows me to consider lower power amps, perhaps even making Class A available.


So it appears there is a decrement in the current/voltage required to drive a speaker to only 80Hz instead of 35 or so.

For music, this is correct. :) I would imagine if you started thinking 100W was OK you could do a 35 W amp after high passing it. Truthfully, 100W is overkill for most speakers and your average or modest listening room. I however am not on the Class A camp. I’m not especially drawn to those amplifiers, and the reduced wasted electricity and higher output of AB amps is a much better situation for me.

OTOH, if we are talking a sweet tube set up, say a 60 W Conrad Johnson or something, that's something worth thinking about for me. :)

I am thinking tubes as well but did not want to go down that path and incur/incite the commentary about there being plenty of high output tube amplifiers. Thanks for broaching it. I also want to entertain lower power AB SS amps.

I have a fondness for class A from my Aleph 3 days. Again, just wanted to have a better sense of my options, which appear to have greatly increased.

Most of the power in music is in the low frequencies. The speaker's "power requirements" don't change. How much power you need to drive the higher frequencies depends on where you cross-over. I'd guess that amps handling 100 Hz & up can be a quarter or half the power of whatever the speaker's "requirements" are. The speaker manufacturer's upper limit should be regarded as a safety spec. Exceeding that power could damage the speaker. There is no lower limit. You don''t lose sleep because you music system is turned off, do you? Happy listening.

@erik_squires --

"Truthfully, 100W is overkill for most speakers and your average or modest listening room." 

100W (depending on their specific iteration as an amp) may be deemed sufficient to quite a few, but as a blanket statement and going so far to call it "overkill" certainly holds no truth - not least with low to moderately efficient speakers as they're, by far, most commonly found.

To those for whom 80-85dB's max. at the listening position in a no more than moderately sized and -damped room is all they are ever going to need, and they may be plentiful, 100 quality watts or even less will do just fine. Setting the bar a little higher however with recorded material less compressed (typically classical music) and getting those peaks up to, say, 105dB's as something emulating a live event at the LP - reproduced cleanly, effortlessly and with impact, that is - 100W of most any kind with lower eff. speakers will come up short. 

A varying factor also for how those 100W will actually show themselves is the specific amp and its overall quality and PSU. I've heard below 50W Class-A amps handle difficult-to-drive speakers far better and sounding more powerful than with several hundred watts Class A/B or D variants.

Make the same speaker a far less difficult load by removing its (likely complex) passive filter and turn it into an active version, and the stated wattage of most any amp will sound fairly close to its specified nature. That's likely a scenario outside the reach and intention of this thread, but nonetheless it goes to show. 

If the approximation of clean sounding, live dynamics of acoustic or amplified events are a desired goal (and why shouldn't they be if a broader measure of Fidelity is regarded as important in this field of ours?), then 'overkill' could be seen as an expression where live-like SPL's are attained with headroom to spare, and thus "overkill" is not really overkill but rather what's necessitated to acquire sufficient, or at least some degree of headroom. For that to happen you need way more than the required output power to reach a given max. SPL, but many if not most operate with what's merely enough for a certain SPL ceiling, therefore failing to understand the importance of headroom. 

Of course it goes to show that more output power alone is not the only, let alone best way to attain headroom; we need efficiency as well to make the most of those wattages if thermal compression is to be taken seriously (which it must), but I guess that's for another discussion.  

@tcutter what are you using to high pass your speakers at 80 hz? I’m interested in doing the same thing. I want to relieve my speakers of some of that bass and open up my amp options. Thanks.

I love how @phusis refutes my claim, and then in a couple of paragraphs refutes himself.  Hahahaha, have at it guys, I've said my peace.

100 Watts is not enough, but it is enough.. ... but you can't tell by wattage... Funny.

@erik_squires --

"100 Watts is not enough, but it is enough.. ... but you can't tell by wattage... Funny."

And we also read and make of it what we want to, right? :) As I'm sure you can assess from my original reply I'm not, depending on the context, in complete disagreement with you, but that's not to say I refute myself. I merely try and point to scenarios where 100W can be more effectively utilized (if still not being "overkill" per se), but those are scenarios outside of your context, and so my main contention still holds. 

In pro this comes up in "bass managed" speaker placement in ATMOS systems.  When you roll out the bass of a small speaker, how much does the total SPL capability change?  The answer is you have to measure it.  We did so at the ATC factory and it only gains around 1dB total output SPL to use a HP filter (bass management).  There exists out there some manufacturers that state massive improvements in SPL when bass managed, I'm not sure how they arrived at these new measurements and conclusions.   So I think from a practical standpoint, you'll get a little improvement in total SPL by filtering out LF, but its less than you'd guess. 

@nymarty I am using a Devialet 400.  It has high and low pass filters along with time delay. I have a Dayton Audio SA1000 as my subwoofer amp with second order and fourth order high and low pass filters, respectively, at 80Hz but I am not currently using these. I would if I were to go with separates or an integrated with a tape monitor.  I'd lose the time delay feature of the Devialet but would hopefully make up for it with other attributes.  I could also use a miniDSP or equivalent which you might consider as well.

@lonemountain Do the small speakers you measured have considerable bass output? I would guess that a speaker that goes to 50Hz would yield less of a gain than one that goes to 35Hz. 

Similar but different question: with crossover (12 db/octave) at 200 Hz, how much (percentage) of the power goes to the low pass, how much to the high pass? 

Background: trying to determine (for class A or tube) what power rating for the amp I should eyeball for the high pass.