Matching Amp Power To Speakers

[flemingmras]

Here's another one I see a LOT of.

There's a false equation going around that's been going around for quite some time. The equation is:

Power=Volume

OK in this lesson we will deal with some psychoacoustics, dBs, power and speaker sensitivity. Some math will be involved as well.

All speakers have several ratings. Among the most important are Power, Impedance, and Speaker Sensitivity, which seems to be the most overlooked rating.

Pro audio speakers have 4 different ratings. They are:

Continuous Power
Program Power
RMS Power
Peak Power

Continuous power is the amount of power the speaker can handle going through it continuously. The test for this is done with pink noise, which is every frequency in the ISO spectrum played simultaneously. For example, my mains cabinets are rated at 400 Watts Continuous Power. This means that they can handle a pink noise signal at 400 Watts CONTINUOUSLY, 24/7. However, the music that will be running through the speaker, which is commonly called the "program", is not continuous. It has starts and stops. Therefore, the starts and stops allow time for the speaker to cool down before it has to work again. This means that with actual program material, the speaker can handle more power.

This is where the Program Power rating comes in. Program Power is 2X the continuous power, and half of the Peak Power rating. Using the speaker in the above example, since the Continuous Power rating is 400 Watts, the Program Power will be 2X this at 800 Watts. And since Program Power is 1/2 the Peak Power, this means that the Peak Power handling of the speaker is 1600 Watts. This is the amount of power the speaker can take on momentary peaks that occur within the system.

RMS(Root Mean Square) Power is 70.7% of the Peak Power. Given a signal that reaches 1600 Watts right at the tip of the peak of the signal, the RMS Power of this signal would be around 1130 Watts. RMS and Peak Power just specify how much the speaker handles on peaks only.

A lot of guys get into the whole "Oh we don't need that much power, we don't have to be that loud" when actually, it's best to have more power than you need. This will result in a system that can get plenty loud, yet sound very clean and clear with no possibility of clipping, which can damage both amps and speakers. So what they do is they take a cab that's rated for 400 Watts Continuous Power and run it on an amp that only puts out 150 Watts@8 ohms, thinking they'll never exceed the 400 watts and they won't blow their speakers. Well actually with this setup you stand more of a chance of blowing your speakers than if you overrated the amp. This is because there won't be enough power to drive the speaker to the point where it sounds it's cleanest and loud enough, which causes guys to turn up. Eventually they hit clip and say "Bye bye" to their speakers, and they can't figure out why or how they're blowing them.

The most overlooked speaker rating is speaker sensitivity. This rating here along with the max power handling of the speaker is going to determine how loud the system is going to be. Speaker sensitivity specifies how much power it takes to get the speaker to produce a certain amount of volume given certain power levels. Speaker sensitivity is measured in units of dB SPL(Decibels of Sound Pressure Level), and it is measured 1 meter away from the speaker on axis, with 1 watt of power going through the speaker. It will be specified as dB SPL(1w/1m), or Decibels of Sound Pressure Level at 1 watt of power 1 meter away. This is where the math comes in.

Example Speaker: 400 Watts Cont. Power
800 Watts Program Power
1600 Watts Peak Power
99dB SPL(1w/1m)

Now for a 10dB increase in volume(which is perceived by the human ear as being twice as loud), you must increase the amp power by 10 times.

We know at 1 meter away with 1 watt of power it will produce 99dB on axis.
So increase the power to 10 watts, and the speaker will produce 109dB at 1 meter away on axis.

Go to 100 watts, and it will produce 119dB at 1 meter away on axis.

Go to 1000 watts, and it will produce 129dB at 1 meter away on axis.

Now everytime we double the output power, that will result in a 3dB increase in volume on axis. However, the speaker handles a MAX of 1600 Watts, and thats only for momentary peaks. No way will it handle double the power at 2000 watts. So now we must calculate the volume with these equations:

Power dB

Pp/1w Log x 10=Power dB

V2 is the peak power while 1w is the 1 watt of power used to measure the 99dB at 1 meter away.

1600 Watts/1 Watt=1600 Watts

Log 1600 Watts=3.204

3.204 x 10= 32.04

So there is 32.04dB difference between 1600 Watts and 1 Watt.

Now add 32.04 to 99dB:

32.04+99dB=131.04dB at 1 meter away on axis

So our max rated SPL for this speaker would be 131.04dB, which is WAY beyond the threshold of pain.

When selecting an amp to drive a speaker, always use an amp that can put out the Program Power rating of the speaker. So for this speaker an amp that puts out 800 watts per channel at 8 ohms would be the correct amp to use. With this much power, with just that one speaker we can produce a volume of:

800 Watts/1 Watt=800 Watts

800 Log=2.9

2.9 x 10=29

29+99=128dB of on axis volume at 1 meter away

Now everytime you double your distance away from the sound source, you lose 6dB of volume, which is perceived as half as loud.

So go 2 meters back and you'll be at 122dB on axis.

Go 4 meters back and you'll be at 116dB on axis(now you're just over half as loud as where you started

Go 8 meters back and you'll be at 110dB on axis

Go 16 meters back and you'll be at 104dB on axis

Now this is all on axis(coming from the direct center of the speaker) volume. As you move over to the sides, you'll start to lose some volume, as you start moving closer and closer to the edge of the projection area of the speaker.

But as we can clearly see, for most small venues, matching this speaker to it's Program Power rating will produce MORE than enough volume before clip, resulting in greater headroom and clarity. And that's just for one speaker.

For subs...most people run mono subs since you can't depict what direction frequencies below 100Hz are coming from. So you'd typically use a smaller amp and bridge the amp for double the 2 ohm rated power for each channel at 4 ohms. However, when running speakers in parallel, this power gets split between all the speakers. I run two subs parallel and my amp puts out 1600 Watts total power into 4 ohms, so each speaker gets 800 watts of it, which is actually 100 watts above rated program power for my subs.

By matching amp power to the speaker's program power rating, your system will have PLENTY of volume and you won't be able to use all of it. Also, your system will be clean and clear with LOTS of punch. However, when you don't have enough power you can't turn up, but if you have more than you need, you can always turn it down.

Jon