There are two goals: Power the loudspeakers so they play as loudly as possible without burning out; achieve a certain loudness in a certain venue. Here's an exhaustive overview covering both topics and much more.
February 21, 2011, by Bruce Bartlett
Determining which power amplifier is appropriate for a specific application is not as easy as one may think. To fully understand what needs to be considered, three specific case studies will be outlined:
• A client wants to play folk music in a coffee shop. How much amplifier power do they need?
• A rock group will be playing in a 2,000-seat concert hall. How many watts will you need to provide?
• A jazz-fusion group bought some PA loudspeakers. They want to play the loudspeakers as loud as they can get without blowing them up. Which amplifier should you recommend?
Questions such as these arise in any sound system design. To help you specify an optimum amount of amplifier power for a system, I’ll explain the relevant audio concepts here.
There are two goals:
1) Power the loudspeakers so they play as loudly as possible without burning out. In other words, determine the optimum powering for the chosen loudspeakers.
2) Achieve a certain loudness in a certain venue.
We’ll cover both topics.
First let’s review the concept of average levels and peak levels.
As shown in Figure 1 (below), a musical signal changes in level (voltage) continuously as it plays. Imagine a musical passage with a low-level synth pad, but with high-level drum hits. The average level or volume of the passage is low, but the transient peak levels are high.
Peak levels may be up to 24 dB above average levels depending on the type of signal. Percussive sounds have much higher peaks than continuous sounds do (synth pads, organ, flute) – even if the two signals have similar average levels.
The peak-to-average ratio of the signal is called the crest factor or peak factor. In other words, crest factor is the difference in dB between the peak levels and the average level of the signal. Percussive sounds have a high crest factor.
Flutes, organs and violins have a low crest factor. The crest factor of speech is about 12 dB. Highly compressed rock music has a crest factor of about 6 dB: the peaks are about 6 dB higher than the average level.
See Figure 2 (below). It is a graph of signal level versus time when the amp is fed a typical musical signal. The average level corresponds to the signal’s loudness. The peak level is 6 to 24 dB above the average level, depending on the type of signal. In other words, the signal crest factor is 6 to 24 dB.
The bottom of Figure 2 shows an example of amplifier power output versus time when the amp is fed a musical signal. The amplifier is rated at 800 W continuous power. That’s the maximum power it can produce at rated distortion.
However, in this example the amplifier is putting out 50W on the average, so that occasional peaks of 12 dB don’t exceed the amp’s 800 W capability. Also, there is a little headroom so that the peaks don’t clip.
In Figure 2, headroom is the difference in dB between the signal peak levels and the amplifier’s clipping level. Normally you want to allow at least 3 dB of headroom so that signal peaks don’t accidentally clip.
This term, coined by Syn-Aud-Con instructor Pat Brown, is crest factor plus headroom. Peakroom indicates how many decibels that peaks can be above the average level without clipping.
Power Amplifier Specifications
Now that we understand signal levels, let’s see how they relate to power amp specifications.
Continuous Average Power
The power specification of most amplifiers is continuous average power. That’s the maximum power in watts that the amplifier can produce at rated distortion, at a certain load impedance, when playing a continuous sine wave. That sine wave signal is either a 1 kHz tone or is a range of tones from 20 Hz to 20 kHz.
For example, one amplifier puts out 1,800 W per channel into 4 ohms in stereo mode at 0.1% THD at 1 kHz. Another amp produces 8,000 W into 8 ohms in bridge-mono mode at 0.35% THD from 20 Hz to 20 kHz.
Many loudspeakers are also rated in continuous or average power handling. If the loudspeaker’s continuous power handling is 500 W, that means it can handle 500 watts of pink noise continuously without mechanical or thermal damage.
To generate that power-handling spec, the loudspeaker is usually fed “AES pink noise”, which is pink noise that is clipped so that its crest factor is 6 dB. Normally pink noise has a crest factor of 12 dB. The AES loudspeaker test signal IEC 268-5 specifies band-limited pink noise with a crest factor of 6 dB.
I recommend that the amplifier’s continuous power be twice the loudspeaker’s continuous power handling (within 80% to 125%). If the amp’s continuous power is higher than 125%, you risk damaging the loudspeaker with too much power in the event of feedback. If the amp’s continuous power is lower than 80%, you will probably clip the signal in an attempt to get enough volume out of the loudspeaker. Clipping a signal produces strong high frequencies which can burn out tweeters.
For example, suppose a loudspeaker has 200 W continuous power handling. The amplifier’s continuous average power should be twice that, or 400 watts (within 80% to 125%, or 320 watts to 500 watts).
Some loudspeakers are rated in program power (music power), which is usually twice the continuous average power. A suitable amplifier should have a continuous average power that matches the loudspeaker’s program power (within 80% to 125%). For example, if a loudspeaker is rated at 400 W program, the amp should provide 400 W continuous (x 80% to 125%).
This is the power, in watts, that an amplifier can produce during short peaks or transients. Typically, peak power is 1 to 3 dB higher than the continuous power. Peak power depends on the amplifier’s power reserves (energy storage). If the amplifier’s power supply has a bank of large filter capacitors, they can store energy that can be released during short peaks.
Many loudspeakers are rated in the peak power they can handle. Ideally, the power amplifier’s peak power should not exceed the loudspeaker’s peak power rating. If the power amp does not have a peak power spec, just make sure that the amp’s continuous power is twice that of the loudspeaker (within 80% to 125%).
Creating Headroom For Signal Peaks
In practice, you don’t run the amp at full continuous power because that does not allow extra power for signal peaks, which might be 6 to 24 dB above the average level. Instead, the amp’s average power is typically 6 to 24 dB below clipping to allow for undistorted signal peaks.
For example, you might turn the amp down so it puts out 1/16th of its rated continuous power on the average. Occasional peaks will make the amp produce its rated continuous power during those peaks.
Suppose an amp is rated at 800 W continuous average power. You might run it at 50W on the average so that occasional peaks can reach 800W without clipping.
In other words, you allow 12 dB for signal peaks (Figure 2, bottom). Actually, peaks can be a bit higher than that because an amplifier’s peak power is typically 1 to 3 dB higher than its continuous power.
In this case, crest factor (dB) = 10 * log (800/50) = 12 dB.
The power specs below are continuous average power:
• An 800 W amp run at 400 W allows for 3 dB peaks above the average level. In this case, the only undistorted signal you could play would be a sine wave or square wave.
• An 800 W amp run at 200 W allows for 6 dB peaks above the average level. This is adequate for highly compressed rock music or a rock broadcast.
• An 800 W amp run at 100 W allows for 9 dB peaks above the average level.
• An 800 W amp run at 50 W allows for 12 dB peaks above the average level. This is adequate for speech.
Many power amplifiers include an output limiter to prevent clipping. If you drive that limiter hard enough, it will reduce the signal peaks frequently, letting you bring up the average level to increase loudness. I don’t recommend that practice because it will make the amp and loudspeaker run hotter and may cause shutdown.
If you can prevent the power amp from clipping (by using a limiter), use a power amp that supplies two to four times the loudspeaker’s continuous power rating per channel. This allows 3 to 6 dB of headroom for peaks in the audio signal. Loudspeakers are built to handle those short-term peaks.
If you can’t keep the power amp from clipping (say, you have no limiter and the system is overdriven or goes into feedback) the amplifier’s maximum power should equal the loudspeaker’s continuous power rating. That way the loudspeaker won’t be damaged if the amp clips when you overdrive its input.
If you are mainly doing light dance music or voice, I recommend that the amplifier power be 1.6 times the Continuous Power rating per channel. If you are doing heavy metal/grunge, try 2.5 times the Continuous Power rating per channel. The amplifier power must be rated for the impedance of the loudspeaker (2, 4, 8 or 16 ohms).
Here’s an example. Suppose the impedance of your loudspeaker is 4 ohms, and its Continuous Power Handling is 100 W. If you are playing light dance music, the amplifier’s 4-ohm power should be 1.6 x 100 W or 160 W continuous per channel. To handle heavy metal/grunge, the amplifier’s 4-ohm power should be 2.5 x 100 W or 250 W continuous per channel.
If you use two loudspeakers in parallel per channel, each loudspeaker receives half of the amplifier’s power output. So the amplifier power per channel should be 4 times one loudspeaker’s continuous power rating instead of 2 times. If both speakers are 8 ohms, refer to the amp’s 4-ohm power spec (because the paralleled impedance is 4 ohms).
Two 8-ohm loudspeakers are wired in parallel to one amplifier channel. Each loudspeaker is rated at 300 W program. The amplifier should provide 600 W into 4 ohms per channel. That’s 4X one loudspeaker’s continuous power rating and half the loudspeaker’s impedance.
Two 8-ohm loudspeakers are wired in parallel to an amplifier in bridge mono mode. Each loudspeaker is rated at 300 W program. The amplifier should provide 600 W continuous (300 W per loudspeaker) into 4 ohms in bridge-mono mode.
• Amplifier continuous power should equal 2X the loudspeaker’s continuous power handling (at the same impedance).
• Amplifier continuous power should equal the loudspeaker’s program power handling (at the same impedance).
• If two loudspeakers are wired in parallel, amplifier continuous power should equal 4X one loudspeaker’s continuous power handling (at one half of the loudspeaker’s impedance).
Multiply the amp’s power by 80% to 125% to get a range of acceptable power levels.
Power Versus Application
This section will suggest how big a power amplifier you need to fill a venue with loud, clear sound. Basically, the louder the sound system and the bigger the room, the more power is required. Loudspeakers with high sensitivity need less power than loudspeakers with low sensitivity.
The list below recommends the amplifier power needed for several applications. Each application has a range of power based on the desired loudness and the typical loudspeaker sensitivity.
In compiling this list, I made the following assumptions:
• Typical loudspeaker sensitivity is 85 dB SPL/W/m for home stereos, 95 dB SPL/W/m for small PA loudspeakers, 100-105 dB for medium PA loudspeakers, and 110 dB for large PA loudspeakers.
• The recommended power allows for signal peaks of 10 to 15 dB for folk, jazz and pop music. Actually the peaks might be as high as 25 dB, but we’re allowing for some inaudible short-term clipping.
• The recommended power allows for signal peaks of 6 dB for rock music that is highly limited or compressed.
• Amplifier continuous power and amplifier peak power are nearly the same. Typically, peak power is only 1 dB higher than continuous power, and depends on peak duration.
Continuous amplifier power per channel required in various applications:
• Nearfield monitoring: 25 W for 85 dB SPL average (with 15 dB peaks), 250 W for 95 dB SPL average (with 15 dB peaks)
• Home stereo: 150 W for 85 dB SPL average (with 15 dB peaks), 1,500 W for 95 dB SPL average (with 15 dB peaks)
• Folk music in a coffee shop with 50 seats: 25 to 250 W
• Folk music in a medium-size auditorium, club or house of worship with 150 to 250 seats: 95 to 250 W
• Folk music at a small outdoor festival (50 feet from loudspeaker to audience): 250 W
• Pop or jazz music in a medium-size auditorium, club or house of worship with 150 to 250 seats: 250 to 750 W
• Pop or jazz music in a 2000-seat concert hall: 400 to 1,200 W
• Rock music in a medium-size auditorium, club or house of worship with 150 to 250 seats: At least 1,500 W
• Rock music at a small outdoor festival (50 feet from loudspeaker to audience): At least 1,000 to 3,000 W
• Rock or heavy metal music in a stadium, arena or ampitheater (100 to 300 feet from loudspeaker to audience): At least 4,000 to 15,000 W
Although a rock concert in an arena could be powered by 15,000 watts (allowing only 6 dB of headroom for peaks,) you’ll often see large touring sound companies using 80,000 to 400,000 watts total. That much power is needed to handle 20-to-24 dB peaks without any clipping, and to power extra loudspeakers for even coverage of a large area.
If one loudspeaker won’t handle the total power required, you need to divide the total power among multiple loudspeakers and multiple amplifier channels.
For example, suppose you need 1,000 watts to achieve the desired average loudness, but your loudspeakers power handling is 250 watts continuous. You could use a power amplifier of 500 watts per channel. Connect two loudspeakers in parallel on each channel. That way, each loudspeaker will receive 250 watts (not considering the change in amplifier power at different impedances, and not considering cable losses).
Note that if you parallel two loudspeakers, their total impedance is halved. For example, two 8-ohm loudspeakers in parallel have an impedance of 4 ohms. In that case, each loudspeaker would receive half of the amplifier’s 4-ohm power.
Some websites provide a calculator that determines the amplifier power required to achieve the desired SPL at a certain distance. The Crown calculators on ProSoundWeb, for example, also account for the number of dB of amplifier headroom needed for audio peaks. Text accompanying the calculator gives the equations used.
You input the desired SPL, the listener’s distance from the loudspeaker, the loudspeaker’s sensitivity rating (SPL/1W/1m), and the desired headroom. “Headroom” in the Crown calculator is actually crest factor. So in the Crown calculator, entering 12 dB of headroom allows for peaks 12 dB above average power without clipping.
The calculator tells you how many watts of continuous average power you need to get that average SPL, plus “headroom dB” of peaks, at that distance.
Listener distance from source: 15 meters (49 feet).
Desired level at listener distance: 85 dB SPL average (fairly loud).
Loudspeaker sensitivity rating: 98 dB SPL/1W/1m.
Amplifier headroom: 12 dB (this crest factor is adequate for speech).
Calculation results: 179 watts.
So you specify an amplifier that provides 179 watts continuous average power per channel (at the impedance of the loudspeaker). The amplifier will reach 179 watts only on short peaks. Most of the time its signal will be 12 dB lower, or 11 watts average.
It’s a good idea to have a few dB of headroom above those peaks as well so that occasional peaks don’t accidentally clip. If you want 3 dB of headroom above those 12 dB peaks, the amplifier should provide 358 watts continuous average power. That’s if the loudspeaker is used outdoors.
If you use it indoors, you usually get about 3 dB of room gain due to sound reflections off the room surfaces. So indoors a power amp of 179 watts would probably be sufficient.
Some of the calculator parameters need a detailed explanation:
Listener Distance From Source
This is the distance from the loudspeaker to the farthest listener. If you are using several loudspeakers that extend into the audience, this distance is from the nearest loudspeaker. For example, if the audience is 100 feet deep, and you have loudspeakers at 0 feet and 50 feet, the listener distance is 50 feet.
If you don’t know this distance, you can make a rough estimate from the typical values below. Be sure to enter the distance in meters (m).
Coffee house: 16 to 32 feet (4.8 to 9.8 m)
Small club or auditorium: 32 feet (9.8 m)
Medium club, auditorium or house of worship: 45 feet (13.7 m)
2,000-seat concert hall: 110 feet (33.5 m)
Small outdoor festival: 50 feet (15.2 m)
Stadium or arena: 100 to 300 feet (30.5 to 91.4 m)
Listed below are typical sound pressure levels (SPLs) for various types of music. The SPL meter was set to C-weighting, slow response. You might want your system to be at least 10 dB above the background noise level to achieve a good signal-to-noise ratio.
New age: 60-70 dB
Folk: 75-90 dB
Jazz: 80-95 dB
Classical: 100 dB
Pop: 90-95 dB
Rock: 95-110 dB
Heavy metal: 110 dB.
The calculations discussed here apply to anechoic or outdoor conditions. If the sound system is inside a venue, the room reverberation will increase the SPL typically by 6 dB. You can use this room gain as extra headroom.
Suppose you need to supply 1,000 watts for peaks, and your loudspeaker’s continuous power handling is 250 watts. A loudspeaker’s peak power handling is typically four times its continuous power handling. So the loudspeaker can probably handle 1,000 watts peak. This means you can use a 1,000-watt amplifier to drive that loudspeaker – as long as you use that power for peaks, and do not drive the loudspeaker continuously with 1,000 watts. In other words, don’t turn up the amp so high that it clips.
What if your sound system uses an active crossover and a separate power amp channel for each driver? Apply the calculator to each driver type. Say you have a three-way system. Determine the power separately for the subs, mid-range drivers and high-frequency drivers. All three types of driver should produce the same SPL at the same distance. Note that horn-loaded drivers tend to have much higher sensitivity than subwoofers, so the horns need less power to produce the same SPL as the subs.
Suppose your sound system has multiple loudspeakers that extend into the audience area. For example: an outdoor festival with loudspeaker clusters on delays every 100 feet, or a set of ceiling-mounted loudspeakers. Apply the calculator to each nearby loudspeaker cluster or loudspeaker.
Once you know how much power you need, you can select an amplifier from manufacturers’ websites or datasheets. Look for the per-channel power specs, at the appropriate load impedance, and dual or bridge-mono mode.
You might want to choose an amplifier that has more power than you need in case you expand your applications. Also, it’s wise to specify a little more power than you need. You can always turn down a power amp if the system is too loud, but you can’t turn up a power amp past maximum if the system is too quiet.
Power Amplifier Notes
Creating Headroom For Peaks
• Run an amp at 1/2 its maximum power to allow for 3 dB peaks
• Run an amp at 1/4 power for 6 dB peaks
• Run an amp at 1/8 power for 9 dB peaks
• Run an amp at 1/16 power for 12 dB peaks
Crest Factors (Peak Factors)
• Live music and percussion: up to 24 dB
• Speech: 12 dB
• AES pink noise for speaker power testing: 6 dB
• Highly compressed rock, synth pads, flute: 6 dB
Continuous average power of an amplilfier: long-term maximum power output from an amp at rated THD, sine wave signal.
Power handling of a loudspeaker (recommended power): continuous average power of AES pink noise, or short-term peak power, that a loudspeaker can handle.
Program power (music power) rating of a loudspeaker: 2X continuous average power rating.
Peak power of an amp: 1 to 3 dB above its continuous average power
Peak power rating of a loudspeaker: Maximum short-term power that the speaker can handle
Maximum Recommended Amplifier Power vs. Loudspeaker Power Handling
In general, the recommended amplifier Continuous Average Power (CAP) = 2X the loudspeaker’s continuous power rating (within 80 to 125%).
Suggestions for special cases:
• Use 1X the loudspeaker’s CAP power handling if the system is not limited or is not controlled by an operator.
If the system can be limited to prevent clipping,
• Use 1.6X the loudspeaker’s CAP power handling for light dance music or speech
• Use 2.5X for heavy metal or grunge
• Use 4X to allow for 6 dB peaks. Run the amp at 1/4 of its maximum power output on the average.
AES and Syn Aud Con member Bruce Bartlett is a recording engineer, audio journalist and microphone engineer. His latest books are “Practical Recording Techniques 5th Ed.” and “Recordng Music On Location.”