Power needs across audio spectrum in active setup

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I've been doing some thinking regarding power amp needs towards assembling my 4-way active setup and I'd like to share it to get your feedback. Looking forward to learning!

Somewhere, maybe in Floyd Toole's book, I remember the reference to 350Hz being the midpoint in power needs for audio. Assuming all drivers have the same sensitivity. Allow me to approximate said midpoint to 320Hz to simplify the rest of my reasoning. So 50% of the power used in reproduction is needed for the first 4 octaves, and 50% for the other 6 octaves.

Let me assume power won't be an issue below 320Hz as I have dedicated subs plus 400W class-D driving dual 10" midbasses per side. My concern is mostly power for the midrange.

Big assumption: if the lower 4 octaves in the audio spectrum consume 50% of power, I´ll venture 40% of the spectrum consumes 50% of the power. Extrapolating: at the 40% point of the top 6 octaves is the midpoint in power consumption. In other words: the amount of power needed for 320 to about 2kHz is the same as from 2kHz to 20kHz. Assuming drivers with the same sensitivity. Would love to get feedback on this.

Let me assume the tweeter will have 104 dB sensitivity and will be xo at 2kHz. While the midrange will be 97 dB sensitivity, of course running from 320 to 2000Hz. Hence, assuming tweeter and midrange amps are the same brand/model, the midrange amp will be the limiting factor.

Let's further assume the amp is a 2A3 SET delivering up to 4W, but I want to design for up to 2W to keep distortion low.
One midrange driver will deliver 97dB SPL at 1 meter using 1 Watt, and 100dB at 1 meter using the 2W I want to use as limit. Let's also assume a benign impedance curve.
Adding the second midrange driver (the one on the other speaker) it adds 3dB, so both together will be playing at 103dB SPL driven by 2W and measured at 1 meter in open space.
The listening position is at 2.4 meters, so 103+20*log(1/2.4)= 95.4 dB SPL at the listening distance with 2W, in an open space.
Adding 4.5dB as an estimated room reinforcement, I arrive at 99.9dB from the midranges at 2W at the seating position. Call it 100dB SPL.

That was the midrange, which is the limiting factor. Assuming the tweeter can keep up since it has higher sensitivity and driven by the same amp, it would add another 3dB SPL, so midrange driven by 2W plus matching tweeter would be delivering 103dB SPL at the listening position.
Along the same lines, midbass and subs running below 320Hz are also keeping up, so adding another 3dB SPL.

So I could expect such a system to be good to play up to 106dB SPL at the listening position if I wanted to limit midrange amp power usage to 2W. Is all this correct?

106dB SPL would be RMS, right? How should I factor in dynamic range in the music?
I usually listen at 85dB SPL C-weight, sometimes like to turn it up to 90dB, and rarely go to 95dB. I understand ideally I should build 20dB headroom, so ideally 115dB and at a minimum 105dB. Should I consider the full 4W amp capability for transients, therefore adding another 3dB, so the system would be capable of 109dB SPL peaks? But at 4W the amp is probably distorting so maybe I should steer away from that even for transients?

Your feedback will help me understand how close to the limit I would be with this amp and driver combination. Maybe I should consider other drivers or setups (such as MTM, arrays), or another amp. Definitely want to design a matching combination of amp and midrange.

Thanks for the patience and looking forward to your feedback!
 
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Your research and calculations are beyond me, but I essentially am facing the same question and tried asking for input in one of the threads discussing the sound qualities of First Watt amps in the Pass Labs forum. I wanted to know which First Watt amp designs would work especially well in the mid bass frequency range and mesh well with the sonic character of the amps I use for the midrange and above. No feedback yet.

I’ve been playing with horns and dipole for several years and had an active setup right from the start. Didn’t like MiniDSP because no matter what power supply I tried there was too much noise from it with my Oris 200 horns and the Fostex, Lowther or Tang Band fullrange drivers I was using. I bought a used First Watt B5 and have been using that for a two way system with active separate sub.

It took me a while, but I eventually built a dipole bass panel modeled on NPs SLOB article. I had to scale the baffle down and that meant that the sensitivity dropped. I hoped that (6) 91.5dB 8” drivers per channel with some bridged Rotel HT amps would be enough to keep up. The amps were putting out over 100 Watts according to manufacturer’s specs. I had to crank the bass gain setting on the B5 all the way up to get close to matching levels of the Oris horns with my DX3s driven by ACAs or my recently finished F2J monoblocks. They’re rated at 8 and 5 watts respectively.

Now I want to experiment with some Edgar horns I have and try a 3 or 4 way system. I’m asking the question what amp can I build for a mid bass horn that can keep up with my F2J driving a high efficiency driver in the Edgars?

I doubt I will have any problem with sub and bass up to 200Hz or so. I recently scored a great deal on (4) Acoustic Elegance dipole 18s and a pair of Hypex Fusion 2X500 Watt plate amps.

My intention was to build a conical adapter I modeled in Hornresp for a pair of the Oris 200 horns I have and try a B&C 8pe21 driver with it. I have (4) drivers, but haven’t figured out how to model a multi entry adapter. With one driver Hornresp is giving me a 110dB flat response from 200-800Hz.

The drivers I have for the Edgar horns are Radian 760pb neo and Dynaudio D54. They are rated at 111.5dB (in Radian’s test horn) and 96dB respectively. I don’t know what it will take to keep up with them.
 
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s.e.t.

A typical 2A3 s.e.t. doesn't posses enough oooomph to drive anything other than a compression driver, or a very hi-efficiency tweeter.

To drive a mid-range cone at around 97db/w, you will need at least a 5 watt Class A amplifier. I have a transistor (home brew) 5watt s.e.t that works *okay* but my 50 watt, class A push-pull has more punch. And that's with 99db/watt

The octave with the greatest density of acoustic power, is that of between 250-500Hz. 355 is dead center. 320 is okay, but speakers with crossover frequencies of 380Hz can sound pretty good.

Crossing at 250Hz, while an ideal way to keep the vocal range intact, can provide some challenges, due to the extreme amount of acoustic density. The only way I could ever get that to work, is by horn loading an 8 inch driver that is especially suitable for horn loading.

There are many paths to audio nirvana. Some guys use a pro 12, or 15 inch, used up to about 700Hz, and then cross to a compression driver/horn combo. Filtering the sub frequencies, below, say 80Hz, takes all the strain away from the pro 12, or 15 inch driver and it can deliver a nice presentation of acoustic energy, in a typical sized living room.

Use an active analogue crossover only if you wish to have the ultimate listening experience.
 
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acoustic power distribution

acoustic power distribution
 

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1) Assuming the tweeter can keep up since it has higher sensitivity and driven by the same amp, it would add another 3dB SPL, so midrange driven by 2W plus matching tweeter would be delivering 103dB SPL at the listening position.
Along the same lines, midbass and subs running below 320Hz are also keeping up, so adding another 3dB SPL.

So I could expect such a system to be good to play up to 106dB SPL at the listening position if I wanted to limit midrange amp power usage to 2W. Is all this correct?

2)106dB SPL would be RMS, right? How should I factor in dynamic range in the music?
I usually listen at 85dB SPL C-weight, sometimes like to turn it up to 90dB, and rarely go to 95dB. I understand ideally I should build 20dB headroom, so ideally 115dB and at a minimum 105dB. Should I consider the full 4W amp capability for transients, therefore adding another 3dB, so the system would be capable of 109dB SPL peaks? But at 4W the amp is probably distorting so maybe I should steer away from that even for transients?
1) The different ranges don't "add" in level, each bandwidth has it's own independent sensitivity and output.
2) The sensitivity and power are assumed to use RMS figures, a sine wave signal of 1 watt (2.83 volts into 8 ohms) will result in "X" sensitivity, dB SPL on your meter.
Your dB meter will probably not register the full level of "peak" readings of transients.

Using room gain probably is not valid for mid/high calculations.

97dB at 1 watt less 7.6 dB for distance loss puts level to 91.5, bringing power up to 40 watts could achieve 106.5 dB peaks, slightly above your "minimum requirement".

That said, you may not ever actually want to listen as loud as your "minimum requirement", so 2-4 watts per driver might "get 'er done" ;^).

Art
 
Yep, many agreements.

Other than 1) 'The different ranges don't "add" in level, each bandwidth has it's own independent sensitivity and output. "

My understanding is that even non-correlated sound sources add to make higher SPL.
I know I've measured this looking at SPL driver by driver, then whole speaker.

Here's a calculator for such...it says to me, if i split the spectrum into three equal thirds having the same SPL, combined SPL will measure +4.8 dB.
Adding acoustic levels summing sound levels 10 combining addition summation sum decibel levels or SPL of up to ten incoherent sound sources audio logarithmic decibel scale identical summing 1/3 octave spl full octave sum sound pressure level noise so


Definitely not as the OP was portraying, but there is SPL gain for sure.
Make sense?
 
1) The different ranges don't "add" in level, each bandwidth has it's own independent sensitivity and output.
2) The sensitivity and power are assumed to use RMS figures, a sine wave signal of 1 watt (2.83 volts into 8 ohms) will result in "X" sensitivity, dB SPL on your meter.
Your dB meter will probably not register the full level of "peak" readings of transients.

Using room gain probably is not valid for mid/high calculations.

97dB at 1 watt less 7.6 dB for distance loss puts level to 91.5, bringing power up to 40 watts could achieve 106.5 dB peaks, slightly above your "minimum requirement".

That said, you may not ever actually want to listen as loud as your "minimum requirement", so 2-4 watts per driver might "get 'er done" ;^).

Art

THANK YOU for taking the time to address where the reasoning is flawed. That way I learn!

Excellent point to not include room gain for midrange/treble. Will [not] do.

Also understood the point about sensitivity and power assumed as RMS. I was wondering about your comment "as loud as your minimum requirement". Kind of sounded like this is not sensible. Would you mind elaborating?

Looking forward to the discussion with mark100 about the addition of SPLs from different frequency ranges. I see SET friendly speakers such as Tekton The Perfect SET spec'd at 96dB sensitivity and 8 ohm, "optimized for SETs with 8-12 Watt RMS" to cover the whole spectrum and can't help wonder if three 4-Watt amps wouldn't deliver the same if set up actively than a 12W amp driving the whole speaker.
 
1)I was wondering about your comment "as loud as your minimum requirement". Kind of sounded like this is not sensible. Would you mind elaborating?

2)Looking forward to the discussion with mark100 about the addition of SPLs from different frequency ranges. I see SET friendly speakers such as Tekton The Perfect SET spec'd at 96dB sensitivity and 8 ohm, "optimized for SETs with 8-12 Watt RMS" to cover the whole spectrum and can't help wonder if three 4-Watt amps wouldn't deliver the same if set up actively than a 12W amp driving the whole speaker.
1) Although having dynamic headroom available is a good thing, most listeners don't seem to use all that much, as evidenced in Pano's "How much Voltage (power) do your speakers need?" poll, where 71% of respondents came in under 5 volts, about 3 watts.
2)Non-correlated sources definitely add in SPL, but each individually driven transducer(s) output is limited by it's sensitivity and power.
Going from 12 watts to 4 watts would be a reduction of -4.77dB headroom in each individual band, although combining the spectrum of three equal thirds having the same SPL, combined SPL will measure +4.8 dB.

Although the average of the power spectrum (acoustic power distribution) of orchestral music may look like some of the graphs presented, the peak requirements across the spectrum are ultimately equal, if the driver's sensitivities are equal.

In other words, if any given frequency uses the full range of headroom available to it in the recording medium, it's output will be clipped if the amp/driver combination can't deliver it.

This leads to another perceptual observation- Mark100 could easily detect loss of headroom (clipped transients) that I previously found I could not detect until the playback level was uncomfortably loud to me.

The difference between the two sound files in this article is 6dB, 1.3dB more clipping than the difference in clip point between 12 and 4 watts.
Peaks vs RMS - Keeping Peaks in Their Place | Prosoundtraining Peaks vs RMS - Keeping Peaks in Their Place

Funny, today I had Bonnie randomly play back those sound files at a low level (about 60dBA) and correctly identified them correctly 6 out of 7 trials. (1C, 2U, 3U, 4C, 5 wrong, picked un-clipped when it was clipped, 6U, 7C)

If you can readily detect the difference between the files, you probably want more than 4 watts behind your mid/high drivers :).

Art
 
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This is a great graph. I wasn't aware of this. What's the book? Great point.

The graph from post #8 is from a book I read, from many many years ago, when I was first learning this hobby. It is called, "How to Build Speaker Enclosures" by
Alexis Badmaieff and Don Davis.

The graph attached to this post is from The Radio Engineering Handbook.
 

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I developed a spreadsheet exactly for this reason, although I never was able to validate the empirical results from it. It does give me at least the proper order of magnitude (the electrical side of things is a bit more iffy, but to my limited knowledge seems to be somewhat useful). You can use fewer than 4 channels if you want, just set the HP/LP frequencies to appropriate values. For example, if you want to do a 2-way active, just set the bottom 2 channels (of the allowable 4 channels) to have crossover points at 20 Hz and 25 Hz, which renders them basically useless.

I've attached it as a zip file as xlsx does not seem to be a valid attachment format.
 

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2)Non-correlated sources definitely add in SPL, but each individually driven transducer(s) output is limited by it's sensitivity and power.
Going from 12 watts to 4 watts would be a reduction of -4.77dB headroom in each individual band, although combining the spectrum of three equal thirds having the same SPL, combined SPL will measure +4.8 dB.

Although the average of the power spectrum (acoustic power distribution) of orchestral music may look like some of the graphs presented, the peak requirements across the spectrum are ultimately equal, if the driver's sensitivities are equal.

In other words, if any given frequency uses the full range of headroom available to it in the recording medium, it's output will be clipped if the amp/driver combination can't deliver it.

Art

Thank you. I think I now got what you were saying. Will listen to the linked clipped files today.

It sounds like I'm ath the edge in terms of having enough midrange efficiency/power available and maybe should look for a more efficient midrange or more amp power.
 
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10 inch mid range

I have just recently put together another system. The mission on this one was to be essentially a modular stack; hence a relatively small foot print.

The mid-range is a ten inch unit. It's an Altec ER-10, which, as it turns out is an exceptional unit. It is linear between 80 and 6k Hz. This pair was sourced from an older audio buddy of mine. he must have had these stored away for many years, and who ever used them before, allowed the sun to bleach out the color of one of the cones.

I am able to use it from 250-6K Hz. No cone cry and superb sound quality. Now, for the first time in many years, I can understand what all the fuss is, about that
"Altec Sound".

The ER10 is 99db/watt and I am sure I am experiencing some baffle step-loss, but it does not seem to bother me at all. While it's the same 99db/w as my big horn system was, it does not grab as much air. None-the-less, I am able to drive it with my 5 watt, single-ended, Class A, zero-feedback amplifier to very loud levels.
 

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