Amplifier Power Requirements

How much power do you need for your speakers? How loud is loud? What’s with all the crazy amplifier rating systems out there? Here we will explore some different topics that help explain what’s going on.

To start, we need to give some background on what exactly loudness is and how we measure it. Loudness (Sound Pressure Level) is something we can measure with microphones and we represent that measurement in dB (deci-Bel). The raw measurement that a microphone would gather would be air pressure (technically, voltage of the recording diaphragm circuit). The range between quiet measurements and even moderately loud measurements is and exponentially growing difference and it becomes very hard to review in this state. The decibel scale is a logarithmic scale and this has some good advantages for us. The first advantage is it allows the exponential SPL data to be well displayed on standard graphs for analysis. Secondly, it allows us to make easy comparisons and use ratios to make power requirement calculations easier.

So how loud is loud on the dB scale? If you’re sitting in a quiet office or a quiet room at home, with no conversations going on, and only the furnace fan running, then it’s probably around 40 to 50dB in that room. With quiet conversation it would be in the 50-60dB range. With normal conversation it jumps into the 60-70dB range. 70-80dB would be a car passing by or a phone ringtone. 80-90dB is a busy street, loud traffic, or an alarm clock. 90-100dB would be loud industrial equipment or construction site with heavy equipment. 100-110dB is a train passing by at a close distance. At 120dB we enter the threshold of pain, where the sound will cause you actual discomfort. A Jet airplane taking off would be 130 to 140db, and the space shuttle was recorded at over 180dB.

As you can see, every 10dB change is a considerable jump in loudness, and in fact, 10dB higher SPL is what you would perceive as something being twice as loud, and 10dB lower SPL would be what you perceive as something half as loud. So that means a 70dB sound seems twice as loud as a 60dB sound. What are some of the other common ratios with the dB scale?

3dB = a 2x increase of power, or, what many people would perceive as one ‘click’ on a volume dial on a TV or Stereo. A noticeable change, but not particularly significant.

6dB = a 2x increase of Sound Pressure Level or a 4x increase of power

10dB = a 10x increase of power or a 2x perceived increase in loudness

20dB= a 100x increase of power, a 4x perceived increase in loudness, or a 10x increase in SPL

So based on the above information, if you had a single loudspeaker playing in a room being given 25 watts of power, for that same speaker to be twice as loud in the room, you would need to a 10x increase in power, or 250 watts. As you can see, the power requirements to be twice as loud can increase dramatically.

So how loud do you actually need to play your music? Unfortunately this isn’t well defined with music, but it’s very well defined by Dolby and DTS for movie soundtracks so we will start there. Dolby says audio should reach the listening position and be capable of un-clipped peaks of 105dBc when played back at reference volume. Reference volume is defined as the volume where pink noise played back at -20dB full scale (0dB full scale is the loudest sound the digital file can hold) reaches the listening position as 85dBc RMS. If you have an A/V receiver the volume scale on most units is set to reference this scale. So we have a target of 105dB peaks to calculate how large of an amplifier we need.

To consider the 105db peak pink noise value as something we can actually measure, we will need to convert it into dB RMS, or average.  For pink noise, there is no reliable conversion rate as the crest factor can be anywhere from 8 to 14db, depending on the source.  To be conservative we will consider a conversion rate of 6db.  So our 105db peak requirement is 99db RMS.

Even though we will be using two speakers for music, or many more for surround sound, we do not add these speakers together into our calculations.  Each channel must be independently capable of reaching the peaks we require.

Now we need to consider distance; because speaker efficiency is quoted from a reference distance of 1m.  We subtract 6dB for every doubling of distance.  It’s 6dB and not 3dB because we are dealing with the wave expanding into a larger area and thus the calculation is a square and 3db^2 = 6db. So if the listening position was 8ft away (2.4 meters) from the loudspeaker, that would be a -7.7dB decrease in loudness, or a 7.7db increase in our amplifier’s requirements (now 106.7dB).  In reality this 6dB decrease will be less because the expansion into the volume of the room is blocked by the walls, ceiling and floor of the room you’ve placed the speaker in.

Another complication is 8ohm vs 4ohm speakers.  8ohm speakers follow the rule above, but because of the nature of 4ohm speakers they’re usually rated 3db higher then they really are.  Most speakers you will come across are 8ohm  speakers, but note that if the speakers you are using are 4ohms you will need to investigate further how the efficiency was calculated.

At this point, we need to know the specific loudspeaker we intend to use. In this case we will we consider a Paradigm Monitor 7 loudspeaker, a fairly representative tower loudspeaker with an efficiency of 91dB 1watt/1meter. This means at 1 watt of input power, at a distance of 1 meter, the speaker will produce SPL of 91db. To calculate the final amplifier power required, in watts, we subtract the 91db efficiency from the 106.7db requirement to net 15.7db of additional power required. Thankfully with logarithmic scales we can break this up into parts, and consider a 10db increase, and then another ~6db increase for illustration purposes. So we need to multiply the power by 10x and then by 4x, so we actually need 40watts to drive a Monitor 7 speaker to clean peaks of 105db at a listening position 8ft away.

Peak Target – Crest factor = RMS Target  (105-6 = 99db)
(105-6 = 99db)
RMS Target + Distance – Efficiency = Gain
99+7.7-91 = 15.7db Gain

Gain

Now, a 91db efficient speaker is on the fairly high side of efficiency. Many loudspeakers will have efficiency in the 85 to 87db range. In our example decreasing from 91db efficiency to 88db, would mean an amplifier requirement of 80 watts. A further decrease to 85 would mean another doubling to 160 watts. If you have started to shop for amplifiers then you already know that a good 160watt amplifier is very expensive and fairly rare. Reviewing speaker efficiency can be the biggest budget saving decision you make in the entire system building process. 

Distance vs Efficiency
Amplifier Power Required (Watts RMS) for 105db peaks at the listening position

I put together the above chart as a quick reference for looking up required power to hit 105dB peaks at the listening position.  Look up your speaker efficiency on the LH side and cross reference to your distance away from the speaker along the top.  I’ve included speakers over 98dB efficiency for comparison purposes, but generally these are not used in home environments due to size.  The highlighted box in the middle shows the typical home environment with distances of 3 to 5 meters with speakers of 86 to 89dB efficiency.  The grey shaded areas are those power figures where typical consumer A/V receivers can cleanly provide, for reference purposes.  What this means is, for typical home set ups a basic receiver just will not cut it to provide clean power all the way up to 105dB with all channels playing.

Power vs Efficiency.PNG
dB SPL at listening position given a particular Efficiency and Power (2 Channels)

The above chart shows what the SPL would be, in dB at a listening position, for a given speaker efficiency.  The grey shaded area is those combinations that produce 102dB RMS (105db peaks) at the listening position per Dolby specifications for Movie soundtracks, which we are using as our reference for music playback.  Red is simply areas where hearing damage can occur quite quickly, and black are SPL levels that are particularly dangerous.

Copied from “Noise – Occupational Exposure Limits in Canada” the following chart lists the time required for hearing damage to occur at a particular noise level. Note that at sustained levels of 100 decibels, hearing damage can set in after 15 minutes.  Also note that every 3dB increase results in a halving of the allowed exposure time.

Table 1B
Noise Exposure Limits when Criterion Level = 85 dB(A)
3 dB(A) Exchange Rate Maximum Permitted
Daily Duration (hours)
5 dB(A) Exchange Rate
Allowable Level dB(A) Allowable Level dB(A)
85 8 85
88 4 90
91 2 95
94 1 100
97 0.5 105
100 0.25 110

What we have provided here is a method to solve the question ‘what size amplifier do I need’.  By using the 105db peak spec, we can clearly answer that question.  We are also not creating a situation where you will be subjected to 102db sound; music and movies generally have little content recorded this loudly and this capability just gives us the headroom to experience those strong peaks and transients exactly as the recording engineer intended.

Edit 2016-07-30: Added some clarifications from peer review.

 

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2 thoughts on “Amplifier Power Requirements

    1. For Party Loud you need efficient speakers and a decent amount of power. Generally Klipsch speakers are high efficiency and get surprisingly loud. They’re not the cheapest but they make a quality product. I would need more information such as Music Style, where the speakers are located, how many people you’re trying to cater to, etc, to give you better advice. Thanks.

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