Power Relationship to Frequency band?

[willhart]

Hi.

Is there a simple formula for estimating the relative power requirements of different frequency bands?

I want to make sure I have the right power amps and drivers for a 4 way system.

For example I would like to work out where to split a narrow sub bass band and a wider Low Mid-band so that they both had similar power amp demands (1 stereo amp split across the 2 channels). Then work out how much smaller could the second amp be that is handling the Hi-Mid and Treble Channels?

As I said, I'd like to know how to estimate or work it out by a formula, rather than people's opinion on what works.

I also understand that the input signal would affect the outputs. I am talking for the purpose of live sound for various bands.

Any help much appreciated.

Cheers. Will.

 

[CharlieLaub]

I have seen (on this forum I believe) and participated in threads about this kind of question.

In the end, the answer (that I firmly believe) seemed to be this:
AVERAGE POWER follows a trend of highest in the midrange (200Hz to about 1-2kHz), lower in the bass region (below 200Hz), and trending down and ending up lower still by at least 6dB above 2kHz.

BUT THIS ALONE DOES NOT ANSWER YOUR QUESTION!
You want to know what power amps to choose. Music is not an "average" steady-state phenomenon, so average power isn't helpful. What you need to know is the PEAK POWER required in the various bands (e.g. for each driver).

It turns out that peak power is about the same across all bands, even for a teensy tiny dome tweeter (assuming the sensitivity of all drivers is the same). The increased POWER rating of the amplifier is just determining more or less the maximum voltage that the output stage can deliver into the typical 4-8 ohms loudspeaker load. The maximum voltage is what determines the peak of the waveform that can be cleanly reproduced.

So you need amplifers that have about the same peak power, but COULD have differing long term power delivery capability. For instance, NAD used to be famous for making amplifiers with undersized power supplies for the voltage that they can deliver into a load. This means that for a very short (e.g. 100 msec or less) the peak power can be delivered into the load, but very quickly thereafter the charge in the capacitors becomes drained quickly enough to drop the rail voltage enough to make the power output quickly sag. This is how you get an amplifier that can deliver 500W for less than 100msec but can only deliver 50W constantly (remember, music is NOT a constant signal).

If the system in question will primarily be reproducing very dynamic music then you can get away with an amplifier that has:
short term power >> long term power
If on the other hand the source will primarily be dynamically compressed pop music, then you should choose your amplifiers such that:
short term power ~ long term power

Finally, there is the notion that clipping an amp for the <100Hz range is less problematic than doing the same for the midrange, so you can probably undersize amps for this frequency range and not suffer too badly.

So, apart from scaling peak power by the sensitivity of each driver, the above should help you decide how to choose your power amps wisely.

 

[DPH]

To add though (trying to summarize prior threads about this), if one were to do an energy spectrum of music (not power!), it tends to monotonically decrease with frequency. This, coupled with sensitivity differences between various drivers means you can tend to put lower peak and sustainable power amplifiers in the higher frequencies.

Simply put, work backwards from the loudspeaker, and acknowledge that you can get away with a little less PSU up top (or a globally smaller PSU for a multichannel/single PSU amp).

 

[willhart]

Thanks for the info Guys.

In response to the 1st reply, It seems challenging to use the same amps across all bands.

Often in a balanced system with a big powerful 18" Sub, the treble will be handled by a single Compression Driver. Even a top of yhe range compression driver will be rated at 75W RMS whereas the Sub may be 1000W RMS. Surely using a big amp for both channels would mean the HF channel would either be under utilised on the amp or would risk damaging the CD?

I know power isn't the best measure for summarising all yhe properties of the various drivers.

But there is no way the treble drivers will have the same power handling capabilities as the Subs, but may often be more sensation!

 

[Max Headroom]

I have seen (on this forum I believe) and participated in threads about this kind of question.

In the end, the answer (that I firmly believe) seemed to be this:
AVERAGE POWER follows a trend of highest in the midrange (200Hz to about 1-2kHz), lower in the bass region (below 200Hz), and trending down and ending up lower still by at least 6dB above 2kHz.

BUT THIS ALONE DOES NOT ANSWER YOUR QUESTION!
You want to know what power amps to choose. Music is not an "average" steady-state phenomenon, so average power isn't helpful. What you need to know is the PEAK POWER required in the various bands (e.g. for each driver).

It turns out that peak power is about the same across all bands, even for a teensy tiny dome tweeter (assuming the sensitivity of all drivers is the same). The increased POWER rating of the amplifier is just determining more or less the maximum voltage that the output stage can deliver into the typical 4-8 ohms loudspeaker load. The maximum voltage is what determines the peak of the waveform that can be cleanly reproduced.

So you need amplifers that have about the same peak power, but COULD have differing long term power delivery capability. For instance, NAD used to be famous for making amplifiers with undersized power supplies for the voltage that they can deliver into a load. This means that for a very short (e.g. 100 msec or less) the peak power can be delivered into the load, but very quickly thereafter the charge in the capacitors becomes drained quickly enough to drop the rail voltage enough to make the power output quickly sag. This is how you get an amplifier that can deliver 500W for less than 100msec but can only deliver 50W constantly (remember, music is NOT a constant signal).

If the system in question will primarily be reproducing very dynamic music then you can get away with an amplifier that has:
short term power >> long term power
If on the other hand the source will primarily be dynamically compressed pop music, then you should choose your amplifiers such that:
short term power ~ long term power

Finally, there is the notion that clipping an amp for the <100Hz range is less problematic than doing the same for the midrange, so you can probably undersize amps for this frequency range and not suffer too badly.

So, apart from scaling peak power by the sensitivity of each driver, the above should help you decide how to choose your power amps wisely.

Good advice.
Ed Simon (Simon7000) made some surprising comments about LMH power requirements of stadium PA systems.
IIRC he backed up the above comments about peak capability, but added that because of air HF loss over long distances, even more peak power is required for mids and highs wrt to bass....Ed ?.
For home application I would stick with the advice given above....ie, run the same stereo amps for all of the drivers.
This gives a 'coherency' to the overall system....running different amplifiers may cause differing 'signature' over each of the bands that may 'play nice together' but also they may not.

Dan.

 

[arnyk]

Hi.

Is there a simple formula for estimating the relative power requirements of different frequency bands?

Simple? Depends what you call simple! ;-)

I want to make sure I have the right power amps and drivers for a 4 way system.

Monitor the amps for power output and clipping while operating the at the highest loudness you expect to use in the largest room with the most dynamic music.

If there is no clipping, then your existing configuration is fine.

If any of your power amps is being operated well below its capabilities, then it is over sized.

For example I would like to work out where to split a narrow sub bass band and a wider Low Mid-band so that they both had similar power amp demands (1 stereo amp split across the 2 channels). Then work out how much smaller could the second amp be that is handling the Hi-Mid and Treble Channels?

As I said, I'd like to know how to estimate or work it out by a formula, rather than people's opinion on what works.

I also understand that the input signal would affect the outputs. I am talking for the purpose of live sound for various bands.

Any help much appreciated.

There are a number of relevant variables, and they include items that are pretty subjective, such as what kind of music is involved, and what SPL levels you want to operate the system at.

Actually calculating what you are looking for involves knowing details about the crossovers, their corner frequencies, their slopes, the efficiency and frequency response of the drivers, and the spectral distribution of the music involved, as well as knowing some calculus.

Strictly speaking, the power delivered to each driver is the integral of the energy in the source material multiplied by driver efficiency and the product of the transfer functions of the relevant crossover band the and driver.

Are you up for that?

 

[AndrewT]

......................In response to the 1st reply, It seems challenging to use the same amps across all bands.

Often in a balanced system with a big powerful 18" Sub, the treble will be handled by a single Compression Driver. Even a top of yhe range compression driver will be rated at 75W RMS whereas the Sub may be 1000W RMS. Surely using a big amp for both channels would mean the HF channel would either be under utilised on the amp or would risk damaging the CD?...............

You did not read/interpret the answers he gave you.
He did not say that you need to use the same amplifiers for all the different drivers.

you need amplifers that have about the same peak power, but COULD have differing long term power delivery capability.

He said that for the same sentistivity drivers one needs to use roughly the same peak signal capability.

One finds that heatsink design and output stage design, very closely follows in proportion to AVERAGE power delivered.
If you then combine that with the typical (very different) driver sensitivities, you can easily end up with 1kW of bass power to 500W of mid range power to 50W of treble power to satisfy the reliability requirements for a reproduction system.

1kW into 95dB/W @ 1m gives ~125dB SPL, not allowing for peak nor for power compression.
500W into 98dB/W @ 1m gives ~125dB SPL, ditto do.
50W into 108dB/W @ 1m gives ~125dB SPL, ditto do.
All at 1m listening distance.
@ 10m listening distance subtract ~20dB from those SPLs.