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No, a square wave isn't 3X the power of a sine wave. The average power of a sine wave is half the peak power. The average power of a square wave is its peak power. The RMS value of a sine wave is 0.707 x peak. 0.707 is -3dB, which is half power.



It doesnt depend at all.

Leaving out drivers deteriorating from being in the elements.. Overexcursion by too low of a crossover for given applied power, and too much power in general (not to be mistaken for RMS power) is purely what destroys speakers. overexcursion will destroy the driver by bottoming out the coil and/or tearing the surround/spider. too much power will melt or deform the coil.

before anyone replies to this and says "BuT wHaT aBoUt cLiPpInG bRo"... a square wave is equal to 3x the applied power (heat) over a given cycle than a sine wave is. If a speaker can thermally handle 100 watts, and you use a 25 watt rms amplifier and send that driver a signal that is clipped to the moon and back, its still not going to blow, since that will heat the coil as if it were being powered with an unclipped 75 watt signal
 

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No, a square wave isn't 3X the power of a sine wave. The average power of a sine wave is half the peak power. The average power of a square wave is its peak power. The RMS value of a sine wave is 0.707 x peak. 0.707 is -3dB, which is half power.
Weird, because this is a quote DIRECTLY from you on Facebook a couple months back..

Sent from my SM-G975U using Tapatalk
 

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And why are you quoting me without attribution? LOL
I will definitely be sure to quote you in the future with screenshots :)
 

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I'm happy to be corrected if I make a mistake. Regarding the flipping of scripts--I make new information available as I learn. Sometimes what I learn means that what I thought I knew before wasn't entirely correct. Because that's what happens when we learn.
 

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Nevertheless, multiplying by .707 isn't one of those feats of strength that should be commemorated during Festivus. It's simple arithmetic.
 

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Discussion Starter #28
Article from Zed audio:
http://www.zedaudiocorp.com/techtalk/amplifierclipping.pdf

Clipping is the arch enemy of speakers, especially higher frequency drivers. It is probably the biggest cause of speaker failure. Looking at the diagram below which shows a clipped sinewave we see from the time axis that the waveform remains at a high amplitude (either positive or negative) for a period of time which is longer than the time it spends when the sinewave is not clipped.

287340


The result of the speaker cone “spending” too much time at one end of its travel will cause voice coil overheating, deformity of the cone/spider assembly. Another effect of amplifier clipping is that harmonics are generated from the fundamental. Assume a 100Hz wave is being clipped. Harmonics at 200Hz, 300Hz, 400Hz, etc are generated. As the harmonic number increases, its amplitude decreases. The amplitude of these higher frequency harmonics is determined by how hard the amplifier clips at the fundamental frequency.

Because high frequency drivers are fragile as compared to high power low frequency and midrange drivers, they are more susceptible to damage. These high frequency harmonics do not generally damage low frequency drivers but this is not always 100% true.

Let us use a 200 watt amplifier as our example and let it be clipping at say +6dB worth of overdrive. +6dB of overdrive in power terms is calculated from the formula [dB=10 x log to the base 10 x power ratio]. Putting the numbers in the formula yields an answer of 4 times power. So the 200 watt amplifier will “attempt” to put out 800 watts. When an amplifier is hard clipped it puts out essentially a square wave which looks like this:

287341


The area under the squarewave represents power and if one compares this with a sinewave at the same frequency, then it is obvious that the area under a sinewave is much less than the square wave.

Music is not constant in its peak amplitude. The ratio of average power to peak power is in the order of 10-20dB. (10dB = 10 times power and 20dB = 100 times power). I would imagine that modern rock and roll/rap music the value is closer to 10dB. This means that with typical music the average power when using a 200w/ch amplifier is in the order of 20 watts per channel with the peaks rising to 200 watts. Anything higher than the 20 watt average will most certainly push the amplifier into clipping. With this scenario the tweeter in a typical bi-amplified system or one with passive crossovers will receive about 10-15% of the power. So the tweeter’s power is about 20-35 watts with our 200 watt amplifier. This is a lot of power for any single tweeter. But let us assume it is OK with this.

When the amplifier clips the energy into the tweeter is many times greater than with unclipped signals. (Of course the amount depends on the degree of clipping but it has been found that people will listen up to 10dB of clipping ). When this happens the compressed wave (now very close to a square wave) is absorbed by the tweeter (and do not forget about all the harmonics) and at this stage the tweeter goes to “the pie in the sky”.

Low frequency drivers are more tolerant of clipping simply because of their more robust construction. I have however seen many a woofer damaged through been overloaded on a continuous basis.

The above discussions have assumed that the waveform is symmetrical about the zero line. Unfortunately music is not like this. The positive half of the wave may not be the same as the negative half. As an example let us assume that this is so and that the positive part of the wave at time zero is larger in amplitude than the negative half. When the amplifier clips, the area under the positive half is more than the negative half and because square waves are being generated by the amplifier the DC component on the speaker rail will not be zero – as it should be.

Remember one fact. DC is a constant voltage. 10 volts positive DC (ref zero) is just that. If our amplifier was flat to DC and we put in a DC signal the amplifier would simply do it’s job – amplify and the output at the speaker rail would be a larger replica of the input. AC on the other hand is just varying DC. A sinewave begins at 0 volts. It rises at a particular rate (determined by the frequency) to its peak value and then declines to zero and repeats the same thing below the zero ref line. BUT at any given time during the single cycle of the sinewave it has an absolute value. The average is zero. A square wave (clipping!!!!) is similar but not the same. The square wave starts at zero, rises very rapidly to it’s peak value, stays there for a time (determined by the frequency) and then returns to zero and the other half of the cycle is below the zero line. The average of course is zero ONLY if the positive half of the square wave is equal to the negative half.

With music and clipped amplifier the average is not zero and in our example above the speaker rail will tend to move positive DC for the period of that non symmetrical clipped wave. DC on a speaker for a sustained period of time (Constant amplifier clipping) will sustain damage.
 

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Article from Zed audio:
http://www.zedaudiocorp.com/techtalk/amplifierclipping.pdf

Clipping is the arch enemy of speakers, especially higher frequency drivers. It is probably the biggest cause of speaker failure. Looking at the diagram below which shows a clipped sinewave we see from the time axis that the waveform remains at a high amplitude (either positive or negative) for a period of time which is longer than the time it spends when the sinewave is not clipped.

View attachment 287340

The result of the speaker cone “spending” too much time at one end of its travel will cause voice coil overheating, deformity of the cone/spider assembly. Another effect of amplifier clipping is that harmonics are generated from the fundamental. Assume a 100Hz wave is being clipped. Harmonics at 200Hz, 300Hz, 400Hz, etc are generated. As the harmonic number increases, its amplitude decreases. The amplitude of these higher frequency harmonics is determined by how hard the amplifier clips at the fundamental frequency.

Because high frequency drivers are fragile as compared to high power low frequency and midrange drivers, they are more susceptible to damage. These high frequency harmonics do not generally damage low frequency drivers but this is not always 100% true.

Let us use a 200 watt amplifier as our example and let it be clipping at say +6dB worth of overdrive. +6dB of overdrive in power terms is calculated from the formula [dB=10 x log to the base 10 x power ratio]. Putting the numbers in the formula yields an answer of 4 times power. So the 200 watt amplifier will “attempt” to put out 800 watts. When an amplifier is hard clipped it puts out essentially a square wave which looks like this:

View attachment 287341

The area under the squarewave represents power and if one compares this with a sinewave at the same frequency, then it is obvious that the area under a sinewave is much less than the square wave.

Music is not constant in its peak amplitude. The ratio of average power to peak power is in the order of 10-20dB. (10dB = 10 times power and 20dB = 100 times power). I would imagine that modern rock and roll/rap music the value is closer to 10dB. This means that with typical music the average power when using a 200w/ch amplifier is in the order of 20 watts per channel with the peaks rising to 200 watts. Anything higher than the 20 watt average will most certainly push the amplifier into clipping. With this scenario the tweeter in a typical bi-amplified system or one with passive crossovers will receive about 10-15% of the power. So the tweeter’s power is about 20-35 watts with our 200 watt amplifier. This is a lot of power for any single tweeter. But let us assume it is OK with this.

When the amplifier clips the energy into the tweeter is many times greater than with unclipped signals. (Of course the amount depends on the degree of clipping but it has been found that people will listen up to 10dB of clipping ). When this happens the compressed wave (now very close to a square wave) is absorbed by the tweeter (and do not forget about all the harmonics) and at this stage the tweeter goes to “the pie in the sky”.

Low frequency drivers are more tolerant of clipping simply because of their more robust construction. I have however seen many a woofer damaged through been overloaded on a continuous basis.

The above discussions have assumed that the waveform is symmetrical about the zero line. Unfortunately music is not like this. The positive half of the wave may not be the same as the negative half. As an example let us assume that this is so and that the positive part of the wave at time zero is larger in amplitude than the negative half. When the amplifier clips, the area under the positive half is more than the negative half and because square waves are being generated by the amplifier the DC component on the speaker rail will not be zero – as it should be.

Remember one fact. DC is a constant voltage. 10 volts positive DC (ref zero) is just that. If our amplifier was flat to DC and we put in a DC signal the amplifier would simply do it’s job – amplify and the output at the speaker rail would be a larger replica of the input. AC on the other hand is just varying DC. A sinewave begins at 0 volts. It rises at a particular rate (determined by the frequency) to its peak value and then declines to zero and repeats the same thing below the zero ref line. BUT at any given time during the single cycle of the sinewave it has an absolute value. The average is zero. A square wave (clipping!!!!) is similar but not the same. The square wave starts at zero, rises very rapidly to it’s peak value, stays there for a time (determined by the frequency) and then returns to zero and the other half of the cycle is below the zero line. The average of course is zero ONLY if the positive half of the square wave is equal to the negative half.

With music and clipped amplifier the average is not zero and in our example above the speaker rail will tend to move positive DC for the period of that non symmetrical clipped wave. DC on a speaker for a sustained period of time (Constant amplifier clipping) will sustain damage.

Right...sort of.

The additional power in the square wave IS high frequency content. So, any driver to which this additional high frequency content is applied gets hotter--woofer, midrange or tweeter. The additional POWER at high frequencies is what burns up the tweeter.

It isn't the waveform. It's the power in excess of the continuous average power rating of the speaker that does the damage.
 

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Discussion Starter #30
Rewrite of an old JBL tech paper recommending using an amp rated for twice the RMS power of the speaker, and in a critical listening environment four times the power for headroom. I would define a critical listening environment as a home audio/theatre system or a car audio application designed more for SQ than SPL (not saying you can't have SQL), but using four times the rated power while playing test tones to impress people may lead to issues :) .

The article describes what happens when a low powered amplifier is clipped for extended periods of time and discusses the nature of music. One challenge is music such as Dub Step, some rap and bass music as there are extended runs of low frequency tones - not that a well built speaker can't handle this but it does stress a system.

New Insights into the Dangers of Using Power Amplifiers That Are Too Small –

In general, the recommendation is that you should pick an amplifier that can deliver power equal to twice the speaker’s continuous average power rating. This means that a speaker with a nominal impedance of 8 ohms and a continuous average power rating of 300 watts, for example, would require an amplifier that can produce 600 watts into an 8 ohm load.

Too Little Amplifier Power Can Produce “Too Much”
We occasionally hear of loudspeaker owners who damage the high frequency components of their loudspeaker systems using amplifiers that are rated at less – rather than more – power output than recommended. Understandably, they may wonder how it is that such an amplifier can actually burn out components when the loudspeaker system is rated to handle larger amounts of power. The loudspeaker’s specifications are true, provided the amplifier is not overdriven. But that’s a very important caveat – not overdriving the amplifier. Driving an amplifier too hard in order to get higher sound level from it (whether perceived or real) can damage some components, especially the high frequency components.

The Nature of Amplifier Power
The power output specification of an amplifier is not absolute. Under certain operating conditions – such as when the volume control is set too high or when the input signal is too great or for shorter periods of time – the amplifier can exceed its published output. The power output of an amplifier is rated with reference to a given level of total harmonic distortion (THD). If required to produce more power, the amplifier will try to do so, but at considerably greater distortion levels. Between the fact that the amplifier is trying to produce more output power and the fact that people perceive distortion as being higher output, it may be natural for some users to do this at times – it sounds louder.

For example (using round numbers), an amplifier rated at 100 watts at no more than 0.5% THD could be overdriven to produce 200 watts of output power to the loudspeakers. Under these same adverse conditions, an amplifier rated at 200 watts could deliver 400 watts to the loudspeakers; a 300 watt amplifier could deliver 600 watts, and a 600 watt amplifier could be overdriven to deliver 1200 watts.

Here’s What the Signal Looks Like
When a sine wave test signal (a signal consisting of a fundamental frequency without overtones or harmonics) is looked at, its top and bottom extremes will exhibit normally rounded contours. Average output power is one-half the peak output power.

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Typical Sine Wave. Average output of a sine wave is one-half of the peak output.

But when an amplifier is overdriven, the contours of the wave are “clipped” off, producing a near square wave, having flat areas at the top and bottom limits.

The average power approaches the peak power. When this occurs, up to twice the amplifier’s rated output can be delivered, and much of that extra power is from harmonic distortion, which get routed by the loudspeaker’s crossover network to the high frequency driver(s), which may not be capable of handling the abnormally high level of power.

287519

In a clipped Sine Wave the average output approaches the peak output.
287520



What Can the User Do?
Matching the Amplifier to the Speaker(s) Purchase an amplifier that will provide more power than you will need and then never run the amplifier into clipping. Remember, a loudspeaker can require up to ten times the average power level for those instantaneous bursts of sonic power known as transients, so having an amplifier that’s capable of cleanly driving short-term peaks – without distortion – is important. If the amplifier has enough reserve power, transients will be clear and crisp. If not, the transients will be muddy or dull. When an amplifier runs out of undistorted power, it is forced to exceed its design capabilities, producing dangerous power levels rich in high frequency distortion. As a general rule-of-thumb, when possible, the ideal situation is to use an amplifier that’s rated at double the loudspeaker’s 2-hour average pink noise power rating. That will allow you to get all the sound level from the loudspeaker that it’s capable of producing.

Why Double? The recommendation of “double the power rating of the speaker” has to do with the fact that loudspeakers and amplifiers are tested, measured, and rated differently. Loudspeakers are tested with a signal – pink noise with 6 dB peaks (ie 6 dB “crest factor”) – where the peaks are 4 times (+6 dB above) the average power of the signal. By contrast, amplifiers are tested with a signal – sine wave – where the peaks are only two times (+3 dB) the average power of the signal. So in order to cleanly drive the peaks that the speakers are tested to be able to deliver, the amplifier has to have double (+ 3 dB) the power rating of the speaker. The amplifier’s +3 dB from being double the power rating is added to the +3 dB peak above its power rating, so that matches the + 6 dB (above its rated average pink noise power capability) that the loudspeaker is capable of producing. The amplifier is then able to cleanly drive the peaks that the loudspeaker is capable of reproducing. No clipping of the amplifier is necessary in order to get the peaks through cleanly to the loudspeaker.

Exception 1: Critical Listening – For critical listening situations such as in a studio environment, four times the speaker’s rating may be advisable to maintain peak transient capability.

Summary
We are not saying that any clipping of a power amplifier will blow your loudspeaker. But for passive (non-powered) speakers, if a small amplifier must be heavily overdriven to obtain the desired volume levels in the listening space, thus generating high power and distortion levels, the user would be better advised to purchase a larger amplifier capable of producing the required power with negligible distortion. In any case, the ideal situation is that an amplifier should be selected with an output power rating that is greater than the maximum power that will be used – the general recommendation is that the amplifier should be capable of delivering double the power rating of the loudspeaker. This margin of reserve power will ensure that the amplifier will not attempt to deliver more power than its design allows. The net result will be distortion-free sound reproduction and longer loudspeaker life.
 

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I don't believe it is so much under powering a speaker , and more that you are turning up the pre amp in your source unit, and distorting the signal that the amp now sends to the speakers.
 

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Yes, you can damage your speakers if you play them loud enough to use that much power. But that will be after your eardrums bursts, your house falls apart and your neighbors come with knifes at you for playing your speakers so loud. In reality, unless your room is the size of a cathedral, you wont use over about 30 watts from your amp unless you have very ineffecient speakers. the rest is for bursts and headroom.
 

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The result of the speaker cone “spending” too much time at one end of its travel will cause voice coil overheating, deformity of the cone/spider assembly. Another effect of amplifier clipping is that harmonics are generated from the fundamental. Assume a 100Hz wave is being clipped. Harmonics at 200Hz, 300Hz, 400Hz, etc are generated. As the harmonic number increases, its amplitude decreases. The amplitude of these higher frequency harmonics is determined by how hard the amplifier clips at the fundamental frequency.
...
Would a screen shot of clipping in the frequency domain be more useful than showing a time domain sketch?


...
Because high frequency drivers are fragile as compared to high power low frequency and midrange drivers, they are more susceptible to damage. These high frequency harmonics do not generally damage low frequency drivers but this is not always 100% true.
...
At some point we might talk about the tweeters in the 70s burning up in clipped systems with passive XOs, and how bi-amped speakers which run active cross overs sort of remove some of the woes of the past?
 

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Discussion Starter #34
I don't believe it is so much under powering a speaker , and more that you are turning up the pre amp in your source unit, and distorting the signal that the amp now sends to the speakers.
If you take a few moments and read through some of the articles linked in this post, you'll see that regardless of how dirty the signal is, it will never damage the speaker if it is below the rated power handling of that speaker. I call out in my first post that overdriving the preamp is how distortion is purposely created, and if a distorted preamp causes issues we could never listen to Hendrix.

An amplifier should increase whatever signal is presented at the preamp and amplify that signal. As long as the amplifier stays within operating parameters it will never damage a speaker with too little power. That's where it's important to know where clipping is occurring - if you overdrive your preamp it will sound terrible but won't cause damage, however if you overdrive your amplifier you run the risk of damaging your speakers.

-Eric
 
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