How Much Amplifier Power Do I Need

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How Much Amplifier Power Do I Need?
I'm playing folk music in a coffee shop. How much amplifier power do I need? Our rock group will be playing in a 2000-seat concert hall. How many watts will we need? I just bought some PA speakers. I want to play them as loud as they can get without blowing them up. Which amplifier should I get? At Crown, we often are asked similar questions, and this article will provide some answers. First, define your goal. Do you want to power some loudspeakers so they play as loud as possible without burning out? If so, all you need to read is the section below. Do you want to achieve a certain loudness in a certain venue? If so, skip to the section called Power vs. Application.

How much power can my speakers handle?
You can determine this by looking at the speaker's data sheet. Look for the Nominal Impedance spec. Typically it will be 2, 4, 8 or 16 ohms. Next, look for the loudspeaker specification called Continuous Power Handling or Continuous Power Rating. It might be called IEC rating or Power capacity. If you can prevent the power amp from clipping (by using a limiter), use a power amp that supplies 2 to 4 times the speaker’s continuous power rating per channel. This allows 3 to 6 dB of headroom for peaks in the audio signal. Speakers 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 power should equal the speaker’s continuous power rating. That way the speaker wont be damaged if the amp clips by overdriving its input. In this case there is no headroom for peaks, so youll have to drive the speaker at less than its full rated power if you want to avoid distortion. If you are mainly doing light dance music or voice, we 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 speaker 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 much more power, you are likely to damage the speaker by forcing the speaker cone to its limits. If you use much less power, youll probably turn up the amp until it clips, trying to make the speaker loud enough. Clipping can damage speakers due to overheating. So stay with 1.6 to 2.5 times the speaker's continuous power rating.

Power vs. 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 total 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, we made the following assumptions: • Typical loudspeaker sensitivity is 85 dB SPL/W/m for home stereos, 95 dB SPL/W/m for small PA speakers, 100-105 dB for medium PA speakers, and 110 dB for large PA speakers. • The recommended power allows for signal peaks of 10 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. • According to Crown's chief amplifier engineer, Gerald Stanley, 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.

Total amplifier power 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 speaker 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 speaker 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 speaker 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 speakers 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 1000 watts to achieve the desired average loudness, but your speakers 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 speaker 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 speakers, their total impedance is halved. For example, two 8-ohm speakers in parallel have an impedance of 4 ohms. In that case, each speaker would receive half of the amplifier's 4-ohm power.

Power Calculator
On the Crown website is a calculator that determines the amplifier power required to achieve the desired SPL at a certain distance. It also accounts for the number of dB of amplifier headroom needed for audio peaks. Text accompanying the calculator gives the equations used. Click on the following link to go to Crown's power calculator: Calculator

To use that calculator, you need to know the loudspeaker sensitivity, peak headroom, listener distance, and the desired SPL. Let's examine each factor. Sensitivity The sensitivity spec can be found in the loudspeaker's data sheet. Typical sensitivity for a PA loudspeaker is 95 to 110 dB-SPL/watt/meter. Bigger speakers generally have higher sensitivity than smaller speakers, and high-frequency drivers have higher sensitivity than low-frequency drivers. Peak headroom Because music has transient peaks that are 6 to 25 dB above the average level, the power amplifier needs to produce enough power to handle those peaks without distortion. For example, if you need 100 watts continuous power to achieve the desired average SPL, you need 1,000 watts continuous to handle 10 dB peaks, 3,162 watts to handle 15 dB peaks, and 10,000 watts to handle 20 dB peaks. Clearly, the peaks require far more power than the average levels. In the calculator's Peak Headroom field, enter 6 dB for rock music that is compressed or limited, or enter 20 to 25 dB for uncompressed live music. If you can live with some short-term clipping which may be inaudible, enter 10 to 15 dB. 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 speakers 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) 2000-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) Desired SPL 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.

Other Considerations

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 1000 watts for peaks, and your speaker's continuous power handling is 250 watts. A speaker's peak power handling is typically 4 times its continuous power handling. So the speaker can probably handle 1000 watts peak. That means you can use a 1000 watt amplifier to drive that speaker -- as long as you use that power for peaks, and do not drive the speaker continuously with 1000 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 3-way system. Determine the power separately for the subs, midrange 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 speaker clusters on delays every 100 feet, or a set of ceilingmounted speakers. Apply the calculator to each nearby speaker cluster or speaker.

Crown Amplifier Selection Guide (rated by total power)
Once you know how much power you need, you can select a Crown amplifier from this list. There is some overlap in this list because each power amplifier produces different amounts of power depending on the load impedance. 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! Total power (both channels combined) 25-50 W: D-45 50-100 W: 180A, 180MA, D-75A 100-200 W: 280A, 280MA, CP660 200-400 W: 1160A, 1160MA, CP660, CTs 600, XLS 202 400-800 W: CE 1000, CE 2000, CH1, CL1, CTs 600, CTs 1200, K1, MA-602, MA-1202, SR II, XLS 202, XLS 402, XLS 602 800-1,000 W: CE 1000, CE 2000, CH1, CH2, CL2, CTs 4200, K1, MA-1202, SR II, XLS 402, XLS 602, Xs500, Xs700 1,000-1,500 W: CE 1000, CE 2000TX, CE 4000, CH2, CH4, CL1, CL2, CL4, CTs 1200, CTs 2000, CTs 3000, CTs 4200, CTs 8200, K1, K2, MA-1202, MA-2402, SR II, XLS 402, XLS 602, Xs500, Xs700, Xs900, Xs1200 1,500-5,000 W: CE 4000, CH4, CL2, CL4, CTs 2000, CTs 3000, CTs 8200, I-T4000, I-T6000, K2, MA-3600VZ, MA-5002VZ, SR I, XLS 602, Xs700, Xs900, Xs1200 4,000-8,000 W: I-T6000, I-T8000, MA-5002VZ With the tools and advice in this article, you should be able to purchase or recommend a power amplifier with the right amount of wattage for the style of music and venue.

References:

Bradford Benn, Business Development Manager at Crown International. Don & Carolyn Davis, Sound System Engineering, second edition. Howard W. Sams & Co., 1987, pp. 273-275. John Eargle, JBL Professional Sound System Design Manual 1999 Edition (from www.jblpro.com) David L. Glass, Tech Support Specialist at Crown International. JBL, Speaker Power Requirements. From www.jblpro.com. Chuck McGregor, How Big an Amplifier Do I Need for a Loudspeaker?, www.liveaudio.com/studyhall/watts.html. Brad Nelson, Six and a Half Steps to Proper Amplifier Size, Syn Aud Con Newsletter (Vol. 27, No. 1, Winter 1999). In that same issue, Pat Brown wrote an article on amplifier power calculation. Brad Nelsons article was republished as The Right Call in the Sept 2000 Sound & Video Contractor magazine. Gerald Stanley, Senior Vice President of Research & Development at Crown International. Syn Aud Con mail list. Special thanks to Pat Brown and Brad Nelson. Chris Vice, calculator Javascript programming

Power Amplifier: Buying Guide

The right amount of power, and the right features, that's what marks the right power amp for your live PA system. This Sweetwater Buying Guide includes information that can help you choose a Power Amp for your needs. Since there's so much to consider when purchasing a Power Amp, don't hesitate to call us at 1-800-222-4700 for more information.

Matching Amps to Speakers
When you're matching a Power Amp to a PA Speaker, a good rule of thumb is to pick an amplifier that can deliver power equal to twice the speaker's continuous IEC power rating. This means that a speaker with a "nominal impedance" of 8 Ohms and a continuous IEC power rating of 350 watts will require an amplifier that can produce 700 watts into an 8 Ohm load. For a stereo pair of speakers, the amplifier should be rated at 700 watts per channel into 8 Ohms. A quality professional loudspeaker can handle transient peaks in excess of its rated power if the amplifier can deliver those peaks without distortion. Using an amp with some extra "headroom" will help assure that only clean, undistorted power gets to your speakers. Some professional amplifiers are designed so they have additional headroom. These amps can cleanly reproduce transient peaks that exceed their rated power. In this case select a model with an output power rating equal to the continuous IEC power rating of the speaker. Consult the amplifier manufacturer or owner's manual to learn more. In some applications, such as critical listening in a studio environment, it is important to maintain peak transient capability. For these applications, use an amplifier that can deliver 6db (or four times as much) more power than the continuous IEC power rating. If budget restraints or legacy equipment force you to use an amplifier with less power, extreme care should be taken to see that the amplifier is not driven into clipping. It may surprise you to learn that low power can result in damage to your speaker or system.

Damping Factor De-Mystified
Loudspeakers have a mind of their own. You send them a signal and they add their own twist to it. They keep on vibrating after the signal has stopped, due to inertia. That ’s called "ringing" or "time smearing." In other words, the speaker produces sound waves that are not part of the original signal. Suppose the incoming signal is a "tight" kick drum with a short attack and decay in its signal envelope. When the kick-drum signal stops, the speaker continues to vibrate. The cone bounces back and forth in its suspension. So that nice, snappy kick drum turns into a booming throb. Fortunately, a power amplifier can exert control over the loudspeaker and reduce ringing. Damping is the ability of a power amplifier to control loudspeaker motion. It’s measured in Damping Factor, which is load impedance divided by amplifier output impedance. Let’s explain. If the speaker impedance is 8 Ohms, and the amplifier output impedance is 0.01 Ohms, the damping factor is 800. That’s a simplification. Since the speaker impedance and amplifier output impedance vary with frequency, so does the damping factor. Also, the impedance of the speaker cable affects damping. Thick cables (with low AWG) allow more damping than thin cables with (high AWG). The lower the amplifier’s output impedance, the higher the damping factor, and the tighter the sound is. A damping factor of 1000 or greater is considered high. As you might suspect, damping factor is most important at low frequencies, say 10 Hz to 400Hz. High damping factor equals tight bass.

- How It Works
How does an amplifier control speaker motion? When the loudspeaker cone vibrates, it acts like

a microphone, generating a signal from its voice coil. This signal generated by the speaker is called back EMF (back Electro Motive Force). It creates a current, which travels through the speaker cable back into the amplifier output, then returns to the speaker. Since back EMF is in opposite polarity with the speaker’s motion, back EMF impedes or damps the speaker’s ringing. The smaller the amplifier output impedance, the greater is the effect of back EMF on the speaker’s motion. An amplifier with low output impedance short-circuits the back EMF, so the back EMF drives the loudspeaker with a relatively strong current that works against the speaker’s motion. When the speaker cone moves out, the back EMF pulls the speaker in, and vice versa In short, the loudspeaker damps itself through the amplifier output circuitry. The lower the impedance of that output circuitry, the more the back EMF can control the speaker’s ringing.

It’s All in the Ohms
Ohms, is a measure of resistance. Audio amplifiers are commonly designed to work with 4, 8 or 16 Ohms of resistance, and optimum system performance will be obtained if the total resistive load (or impedance) of the loudspeaker or set of speakers is exactly correct for the amplifier. If the total loudspeaker impedance is too high, the power delivered to the loudspeakers will be reduced. If the total loudspeaker impedance is too low, the power delivered to the loudspeakers will be increased, which can result in speaker overload and damage to the amplifier. You can connect any amount of speakers to one amplifier provided that they are correctly wired and do not collectively fall below the specified output impedance of the amp. Multiples of loudspeakers can be connected together by three different methods, termed Series, Parallel, and a combination of the two, Series/Parallel. In the case of PA sound, calculating parallel loads is an important capability for two main reasons; first, because dual speaker connections whether on an amplifier, a mixer/amplifier or a speaker enclosure are all wired in parallel. Some people think that if you run separate speaker cables from each speaker output on the amp or mixer/amp to the enclosures you somehow "avoid" putting the speakers in a parallel circuit. Others think that if you run a speaker cable from one cabinet to another you put the cabinets in "series" and that just adds the two loads together (e.g., two 4-ohm speakers in series = 8 ohms). But the truth is that everything gets put in parallel. In fact it's quite difficult to put speaker enclosures in series you need a special wiring harness. The following equations help you match the impedance of PA Speakers to Power Amplifiers for optimized performance (avoiding overloads and other issues). Impedance (Z) is how much a device resists the flow of an AC signal, such as audio. Impedance is similar to resistance, which is how much a device resists the flow of a DC signal. Both impedance and resistance are measured in ohms

For ease of understanding, we’ll start with series calculations:
R = resistance (the ohm rating of your loudspeaker) t = total

Series:
THE FORMULA: Rt = R1 + R2 + R 3 etc.... If we have 4 speakers, each with a 4 Ohm rating, using the formula equation for our example gives: 4+4+4+4 = 16 Rt = 16 Ohms So in this case 16 Ohms of resistance is presented to the amp, or in other words, the output current of the amp would meet with 16 Ohms of resistance at the speaker. Parallel: To keep life as simple as possible, most people put enclosures of the same impedance in a parallel circuit. If you do this it's all just a matter of dividing that impedance by the number of speakers. If you connect speakers of different impedances, the power output will be greater to some, less to others, which means some will be louder than others. (In higher tech circles, we commonly refer to this condition as “very not good.”) THE FORMULA: 1/Rt = 1/R1 + 1/R2 + 1/R3 + etc. ("R" = ohms) Two 16R loads = 8R Two 8R loads = 4R Two 4R loads = 2R Three 16R loads = 5.33R Three 8R loads = 2.67 R Three 4R loads = 1.3R Four 16R loads = 4R Four 8R loads = 2R Four 4R loads = 1R. Example; four 16-ohm loads in parallel = 16/4 = 4 ohms. (Similarly, two 8-ohm loads in parallel = 8/2 = 4 ohms.) You can see that for the same number of speakers, the Ohm load presented to the power amp is significantly reduced. Use this formula to insure that the impedance of your total number of speakers matches the output impedance on the amp. The following is a quick reference listing of some commonly used parallel loads: (Avoid the ones that go lower than output impedance rating of your power amp.)

Slew Rate, Does it Really Matter?
Slew rate is a measure of an amplifier's ability to follow its input signal. The term is used to define the maximum rate of change of an amplifier's output voltage with respect to its input voltage. The unit of measure is volts per microsecond. To put it in more technical terms, Slew Rate is nothing more than a term used to describe how quickly the potential on a circuit node must change with respect to time. As far as slew rate having an effect on perceived sound, the real issue is slew rate limiting, which relates to an amplifier’s ability to pass complex waveforms without clipping them, resulting in an open musical sound. Slew rate is measured by feeding an input signal that is too fast for the amplifier to cope with. So slew rate is an overload condition, and it should not happen at all for an audio amplifier. Therefore, being proud of a slew rate is very strange indeed. In fact, the following is taken from a lab assignment at MIT and is the only reference to slew rate regarding the overall design and building of an audio amplifier:

6.101 Introductory Analog Electronics Laboratory No. 5 Objective: "Build a small audio power amp and play loud music to retaliate against the 6002 students!" Slew rate: No visible slewing allowable within the frequency range of 10 Hz to 20 kHz at full output into 100 Ω." Many mic amp specifications play a purely objective role. These include voltage gain (usually just called "gain"), input noise, common mode rejection, and so forth. Other objective specifications, such as THD, slewing, frequency response, and phase response curiously do not always translate into specific predictable sound quality. Specifications should be treated with respect, but your ears should be the final judge of any preamp’s performance.

How do I choose the right amplifier power for my speaker system? When it comes to choosing a power amplifier there are a number of factors to consider. Power Generally you should pick an amplifier that can deliver power equal to twice the speaker's continuous IEC power rating. This means that a speaker with a "nominal impedance" of 8 ohms and a continuous IEC power rating of 350 watts will require an amplifier that can produce 700 watts into an 8 ohm load. For a stereo pair of speakers, the amplifier should be rated at 700 watts per channel into 8 ohms. Headroom A quality professional loudspeaker can handle transient peaks in excess of its rated power if the amplifier can deliver those peaks without distortion. Using an amp with some extra "headroom" will help assure that only clean, undistorted power gets to your speakers. Some professional amplifiers are designed so they have additional headroom. These amps can cleanly reproduce transient peaks that exceed the amplifier's rated power. In this case select a model with an output power rating equal to the continuous IEC power rating of the speaker. Consult the amplifier manufacturer or owner's manual to learn more. Budget If budget restraints or legacy equipment force you to use an amplifier with less power, extreme care should be taken to see that the amplifier is not driven into clipping. It may surprise you to learn that low power can result in damage to your speaker or system, not to mention ear fatigue caused by the resultant distortion.

Secrets of Amplifier and Speaker Power Requirements Revealed
As audio/video hobbyists, most of us grew up thinking that if we have an amplifier with 50 watts of rated output power into 8-ohm speakers, and that combination produces reasonably clean and loud music, then by doubling the amplifier power to 100 watts per channel, the system would then play twice as loud. Many readers likely still believe that. Not so. Although it's not the easiest thing to comprehend, doubling the amplifier power does not double the loudness. In the above example, the sound from the speakers would not be "twice as loud"; it would only be "a little louder," an increase of 3 decibels. How loud is that? Hearing tests with large groups of people have revealed that a one-decibel (1 dB) change in loudness is approximately the smallest audible step that the average listener can detect, so an increase of 3 dB most listeners term "slightly louder." So why doesn't that 100-watt amplifier always sound twice as loud? Because the acoustic decibel--the decibel (dB) being the unit of measurement used worldwide to quantify the acoustic loudness of sound--has a peculiar relationship to amplifier power output measured in electrical watts. That relationship is called "logarithmic." If that word gives you an instant headache (nightmares of high-school math), then here's a simpler explanation: If a sound gets louder by 3 decibels or "slightly louder," it takes twice as much electrical power from your receiver or amp to produce that modest increase. Therefore, a 100-watt amplifier will produce sound only slightly louder than a 50-watt amplifier.
Incidentally, if you'd like a kind of immortality, be terribly clever and work out a system of measurement. It may be named after you. The "decibel," one tenth of a bel and named for Alexander Graham Bell, recognizes his contributions to the understanding of sound. Likewise, we have to thank James Watt, Georg Simon Ohm, and Heinrich Hertz for their contributions to the industry. And then there's the Lofft, a measurement of neighbors' tolerance to testing new speaker systems . . .

So far, so good. But what if it's party time, and you're listening to music "very loud," a level defined as about 90 dB Sound Pressure Level (SPL), and your speakers are gobbling up swings of 15 to 20 watts per channel on those musical peaks. Drink in hand, you advance to the volume control on your receiver thinking, "I'll just crank this up to make the music twice as loud," and you turn up the volume control until there's a 10 dB increase in the sound level. Now your party-time goal of "twice as loud" will make huge electrical demands on your nice little multi-channel receiver or power amp. The receiver must deliver ten times as much power to double the subjective loudness. Between 6 dB and 10 dB is double the volume level, where 6 dB is four times the power and 10 dB is 10 times the power. In the aforementioned example, the amp must produce 150 to 200 watts per channel for those peaks in loudness. Therefore, every 10-dB increase in acoustic loudness--from 80 dB to 90 dB, or 90 dB to 100 dB--requires ten times as much electrical power in watts. That's all very well if you have a monster amplifier or multi-channel A/V receiver with huge reserves of power output (most of us don't). If not, watch out. Your receiver or amp may "clip" or distort (or both), which will put a clamp on the output of the amp. When you push your amplifier into overload or "clipping," several things may happen. First, the top and bottom of the waveforms (representing the audio signals) are clipped off, generating distortion. Next, the amplifier's protection circuits are activated, removing those portions of the signal that are causing the overload, generating distortion. And finally, the amplifier's power supply may fluctuate according to the demands of the music signals.

Not everyone is affected by this scenario, of course. Some people (increasingly few, it seems) don't listen to loud music. They like background levels, and with average speakers, background levels demand 1 watt or less of amplifier power. Or they may have very efficient speakers (Klipsch, Cerwin-Vega, Tannoy, and the like) that will play extremely loud using modest amplifiers, the trade-off being a very large degradation in tonal accuracy, a definite harshness, and a complete loss of off-axis performance that accompanies horn-loaded designs. But in many situations, speakers will be damaged and distorted sound will offend many ears. No discussion of decibels, acoustic loudness, and electrical watts is complete without an explanation of loudspeaker "sensitivity." (Another way to define a speaker's sensitivity is to look at how efficiently the speaker converts electrical power, in watts, to acoustic sound output in decibels.) Let it be said in a general way that speakers are not very efficient or sensitive devices. They need a lot of electrical power input to produce relatively little acoustic output. Nevertheless, speakers do vary quite a bit in sensitivity. To determine a speaker's sensitivity, we feed the speaker with 1 watt of amplifier power, using a test signal of pink noise, and measure in decibels how loud the sound is at a distance of 1 meter (about 3 feet). A lot of domestic hi-fi speakers measure in at about 89 or 90 dB SPL at 1 meter. Larger speakers, with bigger woofers and more drivers, typically produce greater acoustic output; smaller bookshelf models have to work harder, and their output is typically less, often between 86 and 88 dB SPL at 1 meter. Placing the speaker in a room helps (the walls, ceiling, and floor reflect and reinforce the speaker's sound), adding about 4 dB to its output. For example, a speaker like Axiom's M80ti has a measured sensitivity in an anechoic chamber of 91 dB SPL at 1 watt at 1 meter. But putting the M80ti in a room raises its sensitivity rating to 95 dB SPL at 1 watt, 1 meter. A 95-dB sound level happens to be "very loud," as most of us would subjectively describe it. And it is--from 3 feet (1 meter) in front of the speaker. But let's move our listening seat back twice as far, to 6 feet. Guess what happens? We instinctively know that sound gets weaker as the distance from the source is increased, but by how much? A formula called the "inverse square law" tells us that when the distance from the source is doubled, the sound pressure weakens by 6 dB. Among sound engineers, there's a common saying: "6 dB per distance double." So at a 6-ft. distance, the M80ti is now producing 89 dB. Now let's double that distance again to 12 feet, a fairly common listening distance. The speaker now produces 83 dB, which isn't all that loud at all. And if you sat 24 feet away, a not uncommon distance in big rooms, the speaker would produce 77 dB SPL. But what about stereo, I hear you shout. Here's another oddity of loudness and the decibel. When one speaker is producing a level of 90 dB, adding a second speaker playing at the same level only increases the overall loudness by 3 dB! (The loudness does not double!). So the two speakers in stereo produce a loudness level of 93 dB. So adding a second M80ti will raise the loudness at 12 feet from 83 dB to 86 dB. And don't forget we're still using 1 watt of amplifier power output into Axiom's most sensitive speaker. But how loud are real-life instruments, orchestras and rock bands? Now, while 86 dB SPL is "fairly loud," it's not nearly as loud as what you might hear from a good seat at an actual rock concert or from an orchestra or pianist in a concert hall. A solo grand piano can reach peak levels of 109 dB SPL, a full orchestra and chorus in a concert hall will measure 106 dB, and a rock group, 120 dB SPL. Now let's try and get our peak speaker sound levels to 96 dB, "twice as loud" as our 86-dB listening level. That isn't that difficult because right now we're only using 1 watt per channel to drive the M80ti's to 86 dB. So we'll need ten times as much power, or 10 watts, to reach 96 dB. Big deal. We've got lots more. But things begin to change, and rather dramatically. Let's push the M80ti's to what we might experience from a solo grand piano, 109 dB. We're at 96 dB with 10 watts per channel. Let's go to 106 dB. So that requires 10 x 10, or 100 watts. Close, but not quite there yet. Just 3 dB more. Remember, we have to double the power for a 3-dB increase in sound level. So 100

watts becomes 200 watts. Yikes! Our receiver has only 110 watts maximum output! We've run out of amplifier power! And what about the rock concert? Let's lower our expectations and aim for 119 dB. Going from 109 dB SPL, which needs 200 watts per channel, to 119 dB SPL (get out your ear plugs) is another 10-dB jump and--you do the math--that requires 10 x 200, or 2,000 watts per channel! From all this you can see the huge power requirements inherent in reproducing reallife acoustic sound levels in average or big rooms. The M80ti's are tested to levels of 1,200 watts of input power so they come very close. But the truth is that if we are seeking real-life acoustic sound levels in our listening rooms, there's a very persuasive argument for very large, powerful amplifiers. And if your speakers are less sensitive (and many are), then the power demands rise even more dramatically. Sizeable rooms and greater listening distances will also increase power demands tremendously. And what many of us don't realize until we hear it, is that clean undistorted loud sound often does not sound that "loud." The key here is that in most or our home listening, there are small amounts of distortion caused by a lack of dynamic headroom (but more on that next month). It's the distortion that makes it sound "loud" in a domestic setting. To remove those distortions and increase dynamic headroom relates to even more power. We've become accustomed to accepting some distortion with our reproduced music, because all amplifier's distortion ratings gradually increase as they approach their output limits or slightly clip the audio signals. When that happens, we turn down the volume, because distortion starts to intrude on our listening pleasure, and it sounds "too loud." The lesson in all this is that you can never have too much power, and that big amplifiers rarely damage speakers. Little amplifiers driven into clipping burn out speakers. In the scheme of high fidelity, that last barrier to realism is having enough power and being able to approximate real-life loudness levels.

Amplifier Output Power: How Much Power is Enough?
Amplifier output power is one of the most important considerations in choosing a stereo receiver. Power is measured in watts per channel and the decision about how much power you need should be based on your selection of loudspeakers, the size and acoustic characteristics of your listening room, and how loud you like to listen. It is always best to match the power requirements of the speakers with the output power of the receiver. Some speakers require more or less power, expressed as loudspeaker sensitivity (in decibels , dB), which is a measure of how much sound output is produced with a specified amount of amplifier power. A speaker with lower sensitivity of 88dB-93dB (also known as speaker efficiency) will require more amplifier power than a speaker with a higher sensitivity (94dB to 100dB or more) to play at the same volume level. Power output and speaker volume is not a linear relationship.For example, a receiver with 100 watts per channel will not play twice as loud as a receiver with 50 watts per channel using the same speakers – the difference in maximum loudness would be barely discernable, only 3 decibels (dB). Rather, more amplifier power will allow the system to more easily handle musical peaks without straining, which results in better sound clarity. When comparing the power output of different amplifiers, it is important to know how the power is measured. The most accurate measure of power is RMS (Root Mean Square, a mathematical formula), as opposed to peak amplifier power, a less accurate specification. Some manufacturers inflate specifications by measuring power at a single frequency, say 1kHz, instead of the frequency entire range, 20Hz-20kHz. When comparing receivers with different power outputs, always make sure they are measured the same way.

Speaker Box Design Example
Note, this sample speaker box makes use of many of the calculators found on the menu on the left. You should also review the Speaker Building FAQ for help with this example. For this example, I picked 3 Scan Speak drivers for a 3-way speaker - the same 3 used on the Crossover Example. Note: This example old and the characteristics of these drivers have since changed. These 3 drivers might be smaller than what is expected of a typical 3-way system. The mid is 4" and the woofer is 6.5" in size, but this system is still capable of producing deep frequencies at 35Hz. The drivers I chose for this example are: Driver Equivalent Volume Resonance Free Air Model Frequency Range Imped Sensitivity Total Q (Qts) (Vas) (Fs) 8 ohms 90 db SPL 8 ohms 88 db SPL 8 ohms 89 db SPL 3 liters 49 liters 1000Hz 77Hz 30Hz 0.32 0.22

Tweeter D2008/8512 2k-30k Hz Mid 13M/8636 200-4k Hz Woofer 18W/8543 35-3.2k Hz

A sealed chamber will be used for the mid and a ported enclosure for the woofer. Calculating box volume for a sealed box requires Vas, Fs, Qts, & Qtc. The drivers above don't specify Qtc, so the standard .707 value will be used. Calculating box volume and port size for a ported enclosure requires Vas, Fs, Qts, D, & optionally Fb which is not provided.. The tweeter itself is sealed and doesn't need an enlosure. To calculate the speaker box volumn, we will use the Speaker Box Calculator. Remember to change to metric units - all ScanSpeak nubmbers are in mm & liters. on the sealed box midrange driver gives us:

.03 cubic feet is an extremely small space for a speaker. The speaker itself is only 4" round. If we go with a minimum 4" x 4" box (the smallest the speaker will allow), then the box can only be about 3" deep - 4in x 4in x 3in = 4/12ft x 4/12ft x 3/12ft = .027 ft^3. But I am of course ignoring the space taken up by the speaker itself. This driver is small and only half of it will stick out the back of the

front baffle, but we will do the calculation anyway. ScanSpeak doesn't provide a specific number for the volume of the driver, so we will approximate it using some of their drawings.

The 51.5mm depth and 90mm diameter look like the best numbers to use. Converting to inches. 51.5mm / 25.4 = 2.03" & 90mm / 25.4 = 3.54". To calculate the volume of a cylinder, we need height * pi * r^2. Our cylinder diameter = 3.54", so the radius is half that = 1.77". Our cylinder height = 2.03". So 2.03 * 3.14 * 1.77 * 1.77 = 20 cubic inches. The metal basket housing on the speaker isn't solid like the magnet, so to be safe we will assume 80% of this volume is accurate. 20in^3 * 0.08 = 16in^3. We will be flush mounting this driver with the front of our speaker box, so not all of this 16in^3 is inside the chamber. Assuming 3/4" MDF is used, we need to calculate the size of another cylinder. .75" * 3.14 * 1.77 * 1.77 = 7.38in^3. With this small driver, almost half if its volume is in the wooden baffle. 16in^3 - 7.38in^3 = 8.62in^3. This is the number that we use to increase the size of our enclosure. Converting cubic inches to cubic feet, 8.62in^3 / (12*12*12) = .005ft^3. Not a very large number, but this was a small enclosure to begin with. 03ft^3 (original calculated enclosure size) + .005ft^3 = .035ft^3 which is the size of our midrange driver enclosure. Now for the woofer. When using the ported speaker box calculator, the driver size (Effective Cone Diameter - D) is only used to determine port width. Using the Speaker Box Calculator for the ported box for the woofer gives us:

Our calculator gives us a .23ft^3 enclosure with a 1" wide circular x 2.15" long port (5.47cm / 2.54 = 2.15"). Again, we don't have the driver displacement. This time we will skip the exercise of trying to calculate it ourselves and simply assume that an additional .03ft^3 box volume needs to be added to the .23ft^3 from our box calculator for a total of 0.26ft^3. Instead of calculating these values, you can usually contact the manufacturer through email or their web page, or check online for projects using similar drivers and see what box sizes they used.

The next step is to decide on the general size and shape of the speaker box. Some possible options are shown below. The box volume for these drivers allow for a bookshelf style speaker, but for this example a floor standing speaker will be used instead. Note It is not required to use the entire speaker box for the driver enclosure, so the outer dimensions of the speaker itself can be as large as desired.

From left to right: A bookshelf speaker • A floor standing speaker • The side view of the same floor standing speaker. Note: the woofer will be ported in all • of these design options, even when it isn't shown. Notice that the chamber for the midrange driver isn't the full depth of the speaker. Side view of an alternate design where the speaker is angled back. In an ideal speaker • configuration, the back of each speaker cone lines up vertically. When flush mounted to a vertical piece of wood, the woofer will be a couple of inches behind the mid & tweeter. Another side view alternate configuration. In this design, only the front board is angled. • The math in calculating chamber volume gets a little more complicated, but the build may get simpler with having only one angled side. There are also less balance problems. This design also leverages the fact that the top chambers are smaller (our midrange chamber needs to be small) so that the mid chamber can extend to the full depth of the speaker. In the final configuration there are two 6.5" woofers. Two woofers could be used to help • with the fact that the woofers have lower power handling than the other drivers in this system and two woofers will also help in the low end frequencies. Adding a second driver doesn't simply mean you should double the box and port sizes. It might be a good starting point, but experimentation would be required to achieve the desired result. Without adequate testing equipment, you would be better off sticking to a simpler system unless you were following the published design from someone else. Some other thinks to consider:

The box depth must be at least the port length + the port diameter - not really a • problem for this system. Account for the size of the internal bracing when determining the size of each chamber. • Account for the size of the crossover when determining the size of each chamber. Since • this speaker has an unused chamber at the bottom the crossover will go there. This allows for changing/repairing the crossover without taking the speaker apart.

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