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# The First Watt is the ‘Loudest’ - Amplifier Power vs Speaker Efficiency

We get asked this question all the time; I have speaker ‘xyz’, how much amplifier power do I need?

This question comes down to a couple of considerations:

1. How efficient are your speakers?

2. What is the size of your room?

3. How loud do you typically listen?

1. Factors that Determine Amplifier Power

1.1 Speaker Efficiency

Speaker efficiency is simple.

It describes how loud a speaker plays for a given input power and at a given distance. It is measured as SPL (Sound Pressure Level) in decibels (dB) typically at 1-watt of input power and at 1 meter distance from the speaker.

For example:

88dB @ 1W/1m

This figure of merit helps boil down the question; for a given input power, how loud does my speaker get?

Speakers which are more efficient will transmit more sound into air (higher SPL) for a given input power.

The distance from the speaker is listed in the measurement because for every doubling of distance from the source, the SPL reduces by 6dB. This is true regardless of the speaker. 1 meter is the standard so different speakers can be easily compared.

It is also worth noting that SPL in dB is a (logarithmic) ratio.

From the equation above, the measured sound pressure level is divided by a reference sound pressure level to get a ratio. The value of this ratio is computed to dB.

So, what is the reference?

SPL_Reference is a value of 20uPa (micro-pascals) which, corresponds to a pressure wave in air at the threshold of human audibility. Therefore, we compare a speaker’s pressure capability to lowest sound pressure that humans can hear.

This reference was found through acoustic studies averaging the hearing characteristics of a large number of participants.

1.2 Room Size

Room size matters because a larger room requires more sound to fill it. As described previously, regardless of the speaker, SPL drops by 6dB every time the distance to the speaker doubles.

This is true for both the distance to your walls (a boundary for the sound) and the distance to your listening position.

If you place speakers in a large room, then it is generally safe to assume you are sitting further from them compared to a smaller room, and the sound has farther to travel before it reaches a boundary.

1.3 How loud you listen

If you play loud, then you need more amplifier power than someone who plays music much quieter. Acoustics studies have found that approximately 10dB SPL increase is perceived as twice as loud by our ears.

2. Amplifier Output Power vs SPL

Considering moderate room size and moderate listening levels, speaker efficiency will be the largest factor in determining the required amplifier power.

For every doubling of amplifier power, a speaker can produce 3dB more SPL.

For example, if you have a 96dB efficient speaker and currently use a 1W amplifier, increasing to 2W amplifier will make the same speaker produce 99dB. Since speaker efficiency is rated with 1W of input power, then 99dB would be the maximum SPL this speaker is capable of at 1m distance with a 2-watt amplifier.

With 100W amplifier this speaker would be capable of 20dB more SPL than the 1W case for an output of 116dB at 1m.

If the amplifier power were then increased to 200W, the apparent gain in SPL would again only be 3dB, or 119dB max SPL.

Notice this time, it took +100W to only gain 3dB.

SPL vs amplifier power is a logarithmic relationship. Inversely stated, amplifier power must be exponential to for SPL to increase by a constant amount.

In Figure 1, the gain in speaker SPL vs amplifier power ratio is plotted. Notice that for increasing amplifier power, SPL increases at a slower and slower rate. This is the ‘problem’ with amplifier power, it takes exponentially more power, to continue to increase SPL.

Using Figure 1, if we increase our amplifier power by 10x, we gain 10dB SPL. However, it takes 100x amplifier power (another power factor of 10) to gain 20dB SPL!

4.1 The First Watt is the ‘Loudest’

The exponential amplifier power vs SPL relationship shows that the first watt is the most effective in producing SPL. Every additional watt of power is less and less efficient at producing SPL and therefore speaker volume!

If we look at this from another angle, the base efficiency of a speaker is much higher than any realistic increase in amplifier power we could throw at the speaker to double its dynamic range.

A modest 80dB efficiency loudspeaker with 1W of amplifier power will produce 80dB at 1m. However, the same speaker with 100W of amplifier power will only produce 100dB. Adding a 1000W amplifier now produces 110dB.

Using our example of an 80dB efficient speaker (quite low by most standards) it would take a power increase of 100 million to double the dynamic range compared of the first watt of amplifier power!

Granted this would be deadly loud assuming a speaker can reproduce this; but the example highlights that the first watt of amplifier power produces a bigger change in SPL dynamic range than any additional amplifier power.

It is for this reason, that higher speaker efficiency requires exponentially lower amplifier power to drive them to normal listening volumes. If you want to play loud or are running out of amplifier headroom, the best solution is to get more efficient speakers.

Adding more amplifier power is fighting a losing battle.

4.1 Pros of Speaker Efficiency

Besides having a larger dynamic range for a given amplifier output power, speaker efficiency also has a benefit of greater audio accuracy.

As stated before, speakers which are more efficient will use the given amplifier power more effectively, producing higher SPL. This also means the driver does not need to physically move as much to produce the same SPL as a less efficient speaker.

If we think of a subwoofer, we can visualize the cone moving in and out to produce low frequencies. This linear displacement is called excursion. Large excursion is highly undesirable for clean linear response since the amplifier must overcome the moving mass and cone acceleration to control the speaker. There is also a maximum slew-rate (excursion vs time) for the cone based on the spring constant of the suspension, the moving mass, and the force factor of the speaker’s magnetic motor.

These factors mean at higher excursions, the speaker’s inability to accurately follow the input signal of the amplifier causes an error compared to the signal coming out of the amplifier. This tends to blur the low end leading to boomy sounding bass with little detail in the low end. It is amazing how much detail there can be in low frequency audio content when the speaker can reproduce it accurately.

Large excursion also produces higher distortion (harmonics) than what would appear from the output of the amplifier. This is caused by breakup modes and/or rocking modes where the cone surface bends and deflects. It is no longer acting like a true piston.

In fact, speaker distortion is almost always an order of magnitude larger than the distortion produced by any amplifier. This fact makes amplifier distortion almost meaningless, yet speaker manufacturers never list their THD specs!

Higher efficiency speakers solve all these problems by using a larger fraction of the amplifier power to produce SPL.

4. Amplifier Output Power Recommendations

From our experience, the below recommendation can be used to get an estimate of amplifier power for a given speaker efficiency. This assumes that the amplifier performs well playing audio content near its rated output power.

If possible, we suggest you review your current amplifier power specifications (and how much of the power you use) and speaker efficiency to get a baseline in your room.