Selecting speakers and amplifiers for an application

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When Biamp engineers sat down to analyze the performance needs of the modern conference room, they looked at the full signal path and realized that most installations have far more amplification power than is needed for a typical conference room. Most meeting participants are seated less than 10 feet from a loudspeaker. At this distance it is possible to deliver exceptional playback quality with far less power than is typically installed. In this article we will run the numbers and show why this is true.

To do this, we will need to:

establish the target volume we need to provide at the listener position
determine the maximum distance from the loudspeaker to the listener
specify the loudspeaker we will be using for the room and note its ratings for sensitivity, ohms, and power handling
calculate the minimum amplifier needs based on the above

Target volume

Typical voice volume

We will begin by determining the reinforcement needs of a conference room by walking through the relative volumes involved. This will establish the target volume.

How loud is the voice of the person seated across the table from you? This spoken-word volume is the logical baseline for conferencing reinforcement levels.

Let's rephrase the question: how loud does a conference reinforcement system need to be? Spoken word from the far end of a conference system should arrive at your ears at about the same volume as the spoken word of participants sitting in the room with you.

The typical continuous (RMS) volume of a voice is about 70dB-SPL(A) at 1 foot (0.3m). However, a voice is not a constant-volume signal, sometimes it peaks higher than its continuous volume, as much as 12-18dB higher. So, the typical peak volume of a voice can be as high as 88dB-SPL(A) at 1 foot.

Ordinarily, we stand further than 1 foot away from people when speaking. Due to the inverse square law, we lose 6dB of volume every time the distance is doubled. So, at 2 feet apart, the typical voice is 64dB-SPL RMS and 82dB-SPL peak. And if we move to 4 feet apart, the typical voice is 58dB-SPL RMS and 76dB-SPL peak. A distance of 4 feet is a normal distance, so we can use these levels as our target voice volume. To play it safe, we'll round up these values to 60dB-SPL RMS and 78dB-SPL peak as our target volume at any listener position, since this is the typical volume that we'd expect from an unamplified talker at a distance of 4 feet.

Loudspeaker-to-listener distance

In many applications, ceiling speakers are 6 to 9 feet (1.83 to 2.75 meters) from the listener. We can use 13 feet (4 meters) as a worst case and work out our power needs based on that.

Remember that we need to achieve 60dB-SPL of continuous volume and 78dB-SPL of peak volume at our listener position. And our listener position might be as far as 4 meters from the nearest loudspeaker. In order to achieve those levels at the listener position, how much volume will we need at a distance of 1 meter from the loudspeaker?

The inverse square law states that we lose 6dB for each doubling of distance from a source, conversely we can add 6dB each time we halve the distance to the source:

60dB-SPL continuous / 78dB-SPL peak, at a distance of 4 meters
66dB-SPL continuous / 84dB-SPL peak, at a distance of 2 meters
72dB-SPL continuous / 90dB-SPL peak, at a distance of 1 meter

So, now we need to choose our loudspeaker and amplifier, keeping in mind that they must be able to provide 72dB-SPL of continuous volume and 90dB-SPL of peak volume.

Loudspeaker sensitivity

Speakers are rated by their sensitivity. This is a measure of how much volume they can produce per watt of input power.

The standard measurement is made from 1 meter from the speaker, with a 1kHz tone and 1W of power. A "typical" conferencing ceiling speaker will be be rated for around 85 to 92dB-SPL (1W, 1m). Using this sensitivity value you can determine how loud your playback will be when you hit the peak power rating of your amplifier. Higher sensitivity values are more efficient since they show that more volume is generated per watt of power applied to the speaker. It's often less expensive to buy more efficient speakers than to buy more powerful amplifiers.

Biamp's online Amplifier Calculator will help you translate the speaker sensitivity specs to the real world applications.

Amplifier requirements

Here are a couple of handy rules you can remember with respect to converting amplifier power to dB-SPL:

2x the power (amplifier wattage) = +3dB-SPL
4x the power = +6dB-SPL
10x the power = +10dB-SPL

Let's quickly re-state our objectives. We need to find an amplifier that satisfies the following requirements:

Provides 72dB-SPL of continuous volume at a distance of 1 meter from the loudspeaker
Provides 90dB-SPL of peak volume at a distance of 1 meter from the loudspeaker
Assume the loudspeaker we've selected has a sensitivity of 90dB-SPL (1W, 1m).

The math works out very easily for the peak volume requirements. We needed 90dB-SPL at 1 meter, and the sensitivity of the loudspeaker is 90dB-SPL at 1 watt, 1 meter. This means that we need 1W of amplifier power to achieve the desired peak volume.

To achieve 72dB-SPL of continuous volume, we'll need far less than 1W of amplifier power. If you do the math, you'll find that we only need 0.016W of amplifier power to satisfy the continuous volume requirements.

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Here are some example output levels correlated to the Biamp AMP-450P and TCM-1A PoE+ amplifiers.

For a speaker rated at 90db-SPL (1W, 1m), measured at 1 meter (3.28 feet):

90db-SPL at 1W (speaker sensitivity value)
92dB-SPL at 1.58W (This is the target peak SPL we were looking to achieve in the sample room)
93dB-SPL at 2W (2x the power = +3dB)
96dB-SPL continuous at 4W (4x the power = +6dB) (AMP-450P with 4 channels driven, or TCM-1A with 2 channels driven)
99dB-SPL continuous at 8W (2x the power = +3dB) (AMP-450P with 2 channels driven, or TCM-1A with 1 channel driven)
100dB-SPL at 10W (10x the power = +10dB)
102dB-SPL continuous at 16W (2x the power = +3dB) (AMP-450P with 1 channel driven)
103dB-SPL at 20W
105dB-SPL peak at 30W (AMP-450P and TCM-1A per channel peak output rating, 8-ohm)
106dB-SPL peak at 40W (TCM-1A per channel peak output rating, 4-ohm)
107dB-SPL peak at 50W (AMP-450P per channel peak output rating, 4-ohm)

As stated, these SPL values are measured at 1 meter (3.28 feet). We need to verify our calculations for listener distance from the speakers. Let's do it here:

For sound radiating in free space there is a loss of 6dB-SPL per doubling of distance (slightly less in enclosed environments, varying by frequency)

if listeners are 2m (6.56ft) from a speaker the SPL drops by 6dB-SPL
if listeners are 4m (13.12ft) from the speaker the SPL drops by 12dB-SPL

Calculations reveal a speaker rated at 90dB-SPL (1W, 1m) powered with a 4W amp will provide 96dB-SPL at 1 meter (3.28 ft), 90dB-SPL at 2 meters (6.56 ft), and 84dB-SPL at 4 meters (13.12 ft). These are RMS values.

In the Reinforcement Needs example above, we decided 80dB-SPL(A) was a sufficient peak value for the room.

Speaker rated 90dB-SPL (1W, 1m)	Amp provides 4W continuous, 30W peak	Peak Target Volume = 80dB-SPL
Distance = 1m (3.28 ft)	96dB-SPL continuous, 104.77dB-SPL peak	Headroom beyond peak target volume before exceeding amp's Continuous rating = 16dB 96dB-SPL - 80dB-SPL Headroom beyond peak target volume before hitting amp's Peak rating = 24dB 104dB-SPL - 80dB-SPL
Distance = 2m (6.56 ft)	90dB-SPL continuous, 98.75dB-SPL peak	Headroom beyond peak target volume before exceeding amp's Continuous rating = 10dB 90dB-SPL - 80dB-SPL Headroom beyond peak target volume before hitting amp's Peak rating = 18dB 98dB-SPL - 80dB-SPL
Distance = 4m (13.12 ft)	84dB-SPL continuous, 92.75dB-SPL peak	Headroom beyond peak target volume before exceeding amp's Continuous rating = 4dB 84dB-SPL - 80dB-SPL Headroom beyond peak target volume before hitting amp's Peak rating = 12dB 92dB-SPL - 80dB-SPL

Speaker rated 90dB-SPL (1W, 1m)

Amp provides 4W continuous, 30W peak

Peak Target Volume = 80dB-SPL

Distance = 1m (3.28 ft)

96dB-SPL continuous,

104.77dB-SPL peak

Headroom beyond peak target volume before exceeding amp's Continuous rating = 16dB

96dB-SPL - 80dB-SPL

Headroom beyond peak target volume before hitting amp's Peak rating = 24dB

104dB-SPL - 80dB-SPL

Distance = 2m (6.56 ft)

90dB-SPL continuous,

98.75dB-SPL peak

Headroom beyond peak target volume before exceeding amp's Continuous rating = 10dB

90dB-SPL - 80dB-SPL

Headroom beyond peak target volume before hitting amp's Peak rating = 18dB

98dB-SPL - 80dB-SPL

Distance = 4m (13.12 ft)

84dB-SPL continuous,

92.75dB-SPL peak

Headroom beyond peak target volume before exceeding amp's Continuous rating = 4dB

84dB-SPL - 80dB-SPL

Headroom beyond peak target volume before hitting amp's Peak rating = 12dB

92dB-SPL - 80dB-SPL

A 4W amplifier provides 4dB-SPL RMS more than is needed at the 4 meter (13.12 ft) position, and 10dB-SPL RMS more than is needed at 2 meters (6.56 ft). Remember that +10dB-SPL means twice the perceived loudness, so this amp is really overkill for the room.

The peak power requirements calculated for the room fall well below the continuous power rating of the 4W amplifier.

Note that these values were calculated for a single speaker in a free field environment. We are not boosting the numbers to account for half-space loading gains for speakers mounted in a ceiling, or for multiple speakers on a shared circuit reinforcing one another due to increased radiating surface.