Hi Overkill
I think how a simple driver like a woofer can be explained but for you to understand it, you will have to accept several principals some of which are not intuitive.
The woofer consists of several separate elements, each of which should be considered as separate components each with their own impact.
Let’s start with the “DC motor” a coil of wire in a magnetic gap. It produces force when current is passed through it, the direction set by the input polarity. The force is proportional and given by the “BL” factor, B being the magnetic field strength in Tesla (10kg) and L being the length of wire in that gap.
Alternately, that same BL factor can also be interpreted into Newton’s of force (not the little cookies) per Amp of current. Many mistakenly think of BL as an indicator of motor strength but it is not, just the force factor. A proper figure of merit includes the Rdc of the motor so that either of these formula’s are more suitable for comparing motors. Fm=BL^2 / Rdc or BL / sqr root of Rdc.
The stronger you make the magnetic field (or longer wire), the greater the force per Amp is produced. Locked directly to that Current to force conversion and always proportional to it is the generator constant or Back EMF.
While many think of back EMF as a problem, it is simply a property of an electrodynamic motor like this, when you move it, it generates voltage, the greater the BL, the more Voltage it produces at a given Velocity.
Simple permanent magnet motors, even a brush commutated slot car motor follows the same rules on this except in a rotary motor, the force per amp is expressed as a torque constant, expressed as torque per amp (kt) and the generator effect in volts per thousand RPM etc.
So with this simple motor in mind imagine you add a flywheel to the motor, one that has several times the inertia of the motor alone. Also, we will put a resistance in series as well between it and the battery supply. Now, what happens when you connect the battery?
The motor is not turning but as soon as the toque is applied it begins to accelerate. Initially, when the battery was first connected, the voltage across the motor was zero and so the current flowing was set by the battery voltage across the series resistance, that current limited he torque force hat was being applied, making the acceleration slow.
As the speed increases, the voltage produced by the generator constant or back emf rises proportionally with speed and so this Voltage being in series reduces the voltage across the series resistor (the total available being set by the battery) and so the current falls off and then the rate of acceleration slows.
If you wait a while, the motor will be going as fast as it is going to go and then one finds only a small current is flowing, that current is what is required to overcome the motor’s static friction and internal wind resistance and any other losses..
Now, you can imagine that if one made the series resistance smaller, that at any given point, more current will flow and so the time it takes to get to that full speed is shorter.
Also, if while running at full speed, you add a load by say putting your foot against the flywheel, you will see the current increase and the speed fall. If you could get rid of he remaining internal resistance, then the motor speed would not fall regardless of load, the back emf forces the proper current to flow for the torque required to make the load go that speed.
Again, a voice coil is the same thing except it has limited motion and driven with an AC signal.
Actually you can produce sound with a rotary motor in fact. In the 80’s and 90’s I worked for a NASA contractor that let me start and run a small speaker division around a Servomotor driven subwoofer invention I had. These were mostly used for special effects in las Vegas and Disney and a bunch of concert tours (Michael Jackson, U-2, Garth Brooks, Def leopard etc).
Live Sound International | Real World Gear: Making Better Bass
The smallest one we made as a product was at the time unimaginably “way too much” for home use at the time but eventually one got reviewed before the company went under (due to the shuttle disaster the main business was cut off), the Contrabass here.
Way Down Deep II ServoDrive Contrabass | Home Theater
Anyway so picture the motor spinning away and now you short the terminals as some as suggested here with the speaker. The “battery” is now gone and replaced with a short, all the voltage the back emf is producing is applied across the series resistance and the current that this introduces, produces a torque which opposes the motor and what one sees is that the faster the motor is going, the more Voltage is produced and so the more current is flowing and the greater the breaking force.
Fwiw, many railroad locomotives use the traction motors on the wheels as electrodynamic brakes, when slowing or breaking on a down grade, the motor is generating a voltage and this is put across the series resistance and due to the scale, there are often fans and radiators on the upper sides of the locomotive which disperse the heat the resistors dissipate.
Point being, the motor will come to a stop like the brakes were on.
Now picture what happens with an AC signal, go back to the batter idea but now you make a pretend square wave, after the motor is nearly up to speed you play a funny joke on the motor, you flip the battery instantly.
Now, one has the reversed battery voltage, which causes the back emf AND battery voltage to be across the series resistance. For a short time, more current will flow than is possible even if you clamped the motor motionless because of the back emf being added to the supply Voltage.
All that current will be acting to slow and reverse the motor direction.
If you do this with a square wave, you have a visually simple signal that requires about a factor of 10 in well behaved magnitude and near zero acoustic phase both above and below the square wave frequency, to look good great on an oscilloscope. When the driver produces a sine wave, it has the most gradual acceleration and deceleration possible in that period and with loudspeaker drivers, getting them to ONLY produce the input signal is part of the list of problems. Also, when you want the speaker to change very quickly, one finds the motor also has a series inductance and this limits how fast the current can build up. In a speaker, this acts like a low pass filter, either irrelevant or a show stopper depending on the driver and what your trying to do with it.
Why all the concern about acceleration?
Like speaker Dave said, over most of the range the woofer is an acceleration controlled device but why?
Examine the “impedance match to air” curve at the bottom of the page here
Loudspeakers
This represents the “load” that a given radiator faces when producing sound. Note that when the radiator is small compared to the wavelength, one is on a slope. This IS where one is when you have a woofer or subwoofer (consider the bottom annotation).
So, in order to make a nice flat response in light of that curve, a roll off must be applied to the radiator velocity or the response will rise accordingly.
This is done by placing the mass in parallel with a spring (suspension and box compliance sum into a stiffer spring). When the mass reactance and spring reactance are equal but opposite, the cancel each other out and one has the Fs or Fb in a box. Above that point, the mass dominates and if our world were Velocity based, we would see that when the woofers pressure response is flat, it’s Velocity is falling as the frequency increases.
Thus, anywhere on that slope, should one glue a lead ring to the woofer voice coil, one finds it has NO impact on the speaker speed of response or any measure one would connect to speed.
Fwiw, notice how that curve also has a flat part when the radiator is large? An object of a full size horn is to connect a very small driver to the radiation resistance an enormous radiator would feel, allowing a very high efficiency.
Another cool thing, about the closest thing to a free lunch there is in audio. Take one subwoofer, it has a sensitivity and it handles X power before sound bad therefore produces a maximum usable loudness of X-SPL. Take a second identical subwoofer and amplifier and put it next to the first one. Now one has two amplifiers so you have twice he power (+3dB) but what you measure when hey are close is you can get 6dB (4X) louder.
The reason is also in that curve, doubling the power is easy to picture but doubling the radiator area, bumps you up on that curve and so your efficiency also goes up 3dB.
Hope this makes sense, got to tend dinner now it’s in the final stage.
Best,
Tom Danley
Danley Sound Labs
I think how a simple driver like a woofer can be explained but for you to understand it, you will have to accept several principals some of which are not intuitive.
The woofer consists of several separate elements, each of which should be considered as separate components each with their own impact.
Let’s start with the “DC motor” a coil of wire in a magnetic gap. It produces force when current is passed through it, the direction set by the input polarity. The force is proportional and given by the “BL” factor, B being the magnetic field strength in Tesla (10kg) and L being the length of wire in that gap.
Alternately, that same BL factor can also be interpreted into Newton’s of force (not the little cookies) per Amp of current. Many mistakenly think of BL as an indicator of motor strength but it is not, just the force factor. A proper figure of merit includes the Rdc of the motor so that either of these formula’s are more suitable for comparing motors. Fm=BL^2 / Rdc or BL / sqr root of Rdc.
The stronger you make the magnetic field (or longer wire), the greater the force per Amp is produced. Locked directly to that Current to force conversion and always proportional to it is the generator constant or Back EMF.
While many think of back EMF as a problem, it is simply a property of an electrodynamic motor like this, when you move it, it generates voltage, the greater the BL, the more Voltage it produces at a given Velocity.
Simple permanent magnet motors, even a brush commutated slot car motor follows the same rules on this except in a rotary motor, the force per amp is expressed as a torque constant, expressed as torque per amp (kt) and the generator effect in volts per thousand RPM etc.
So with this simple motor in mind imagine you add a flywheel to the motor, one that has several times the inertia of the motor alone. Also, we will put a resistance in series as well between it and the battery supply. Now, what happens when you connect the battery?
The motor is not turning but as soon as the toque is applied it begins to accelerate. Initially, when the battery was first connected, the voltage across the motor was zero and so the current flowing was set by the battery voltage across the series resistance, that current limited he torque force hat was being applied, making the acceleration slow.
As the speed increases, the voltage produced by the generator constant or back emf rises proportionally with speed and so this Voltage being in series reduces the voltage across the series resistor (the total available being set by the battery) and so the current falls off and then the rate of acceleration slows.
If you wait a while, the motor will be going as fast as it is going to go and then one finds only a small current is flowing, that current is what is required to overcome the motor’s static friction and internal wind resistance and any other losses..
Now, you can imagine that if one made the series resistance smaller, that at any given point, more current will flow and so the time it takes to get to that full speed is shorter.
Also, if while running at full speed, you add a load by say putting your foot against the flywheel, you will see the current increase and the speed fall. If you could get rid of he remaining internal resistance, then the motor speed would not fall regardless of load, the back emf forces the proper current to flow for the torque required to make the load go that speed.
Again, a voice coil is the same thing except it has limited motion and driven with an AC signal.
Actually you can produce sound with a rotary motor in fact. In the 80’s and 90’s I worked for a NASA contractor that let me start and run a small speaker division around a Servomotor driven subwoofer invention I had. These were mostly used for special effects in las Vegas and Disney and a bunch of concert tours (Michael Jackson, U-2, Garth Brooks, Def leopard etc).
Live Sound International | Real World Gear: Making Better Bass
The smallest one we made as a product was at the time unimaginably “way too much” for home use at the time but eventually one got reviewed before the company went under (due to the shuttle disaster the main business was cut off), the Contrabass here.
Way Down Deep II ServoDrive Contrabass | Home Theater
Anyway so picture the motor spinning away and now you short the terminals as some as suggested here with the speaker. The “battery” is now gone and replaced with a short, all the voltage the back emf is producing is applied across the series resistance and the current that this introduces, produces a torque which opposes the motor and what one sees is that the faster the motor is going, the more Voltage is produced and so the more current is flowing and the greater the breaking force.
Fwiw, many railroad locomotives use the traction motors on the wheels as electrodynamic brakes, when slowing or breaking on a down grade, the motor is generating a voltage and this is put across the series resistance and due to the scale, there are often fans and radiators on the upper sides of the locomotive which disperse the heat the resistors dissipate.
Point being, the motor will come to a stop like the brakes were on.
Now picture what happens with an AC signal, go back to the batter idea but now you make a pretend square wave, after the motor is nearly up to speed you play a funny joke on the motor, you flip the battery instantly.
Now, one has the reversed battery voltage, which causes the back emf AND battery voltage to be across the series resistance. For a short time, more current will flow than is possible even if you clamped the motor motionless because of the back emf being added to the supply Voltage.
All that current will be acting to slow and reverse the motor direction.
If you do this with a square wave, you have a visually simple signal that requires about a factor of 10 in well behaved magnitude and near zero acoustic phase both above and below the square wave frequency, to look good great on an oscilloscope. When the driver produces a sine wave, it has the most gradual acceleration and deceleration possible in that period and with loudspeaker drivers, getting them to ONLY produce the input signal is part of the list of problems. Also, when you want the speaker to change very quickly, one finds the motor also has a series inductance and this limits how fast the current can build up. In a speaker, this acts like a low pass filter, either irrelevant or a show stopper depending on the driver and what your trying to do with it.
Why all the concern about acceleration?
Like speaker Dave said, over most of the range the woofer is an acceleration controlled device but why?
Examine the “impedance match to air” curve at the bottom of the page here
Loudspeakers
This represents the “load” that a given radiator faces when producing sound. Note that when the radiator is small compared to the wavelength, one is on a slope. This IS where one is when you have a woofer or subwoofer (consider the bottom annotation).
So, in order to make a nice flat response in light of that curve, a roll off must be applied to the radiator velocity or the response will rise accordingly.
This is done by placing the mass in parallel with a spring (suspension and box compliance sum into a stiffer spring). When the mass reactance and spring reactance are equal but opposite, the cancel each other out and one has the Fs or Fb in a box. Above that point, the mass dominates and if our world were Velocity based, we would see that when the woofers pressure response is flat, it’s Velocity is falling as the frequency increases.
Thus, anywhere on that slope, should one glue a lead ring to the woofer voice coil, one finds it has NO impact on the speaker speed of response or any measure one would connect to speed.
Fwiw, notice how that curve also has a flat part when the radiator is large? An object of a full size horn is to connect a very small driver to the radiation resistance an enormous radiator would feel, allowing a very high efficiency.
Another cool thing, about the closest thing to a free lunch there is in audio. Take one subwoofer, it has a sensitivity and it handles X power before sound bad therefore produces a maximum usable loudness of X-SPL. Take a second identical subwoofer and amplifier and put it next to the first one. Now one has two amplifiers so you have twice he power (+3dB) but what you measure when hey are close is you can get 6dB (4X) louder.
The reason is also in that curve, doubling the power is easy to picture but doubling the radiator area, bumps you up on that curve and so your efficiency also goes up 3dB.
Hope this makes sense, got to tend dinner now it’s in the final stage.
Best,
Tom Danley
Danley Sound Labs
The opposite of acceleration is braking. The speaker motor is both an accelerator and brake. I'll get back to this.
Braking is resistance to movement, not the opposite of acceleration.
The spring of the driver suspension has no breaking effect.
It accumulates energy to restore it later.
It's a quite often forgotten fact that there are always two forces which conjugate (vectorally add) to determine the acceleration of the diaphragm.
For a given signal, when the diaphram is just leaving its maximal excursion to come back to its rest position, the motor force is only slightly weaker than the spring force of the suspension, and not suddenly null as it seems to have been suggested.
Braking is resistance to movement, not the opposite of acceleration.
The spring of the driver suspension has no breaking effect.
It accumulates energy to restore it later.
It's a quite often forgotten fact that there are always two forces which conjugate (vectorally add) to determine the acceleration of the diaphragm.
For a given signal, when the diaphram is just leaving its maximal excursion to come back to its rest position, the motor force is only slightly weaker than the spring force of the suspension, and not suddenly null as it seems to have been suggested.
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Actually, we need to look at the phase of the impedance curve to say anything about the force direction vs. displacement. At frequencies well below resonance force and position are well in phase and coil force is always trying to push the unit out of the mid point against susension force. At and then above resonance the phase angle of driver current changes and this is no longer the case.
This is one reason why jump phenomonon (DC offset) happens just above resonance. Excursion is high and the phase angle between force and displacement is favorable.
David S.
This is one reason why jump phenomonon (DC offset) happens just above resonance. Excursion is high and the phase angle between force and displacement is favorable.
David S.
I don't have a copy in my hands (I do at home) but there was a great paper by T.H. Wiik of SEAS back in the 80s. Look through the AES preprints and it should be clear which one this was. He showed that, due to the changing phase angle, that you would have a situation where the woofer was coming out of the gap, hence Bl was dropping from the B field falloff, and force back into the gap was needed but not available. He was able to prove that a progressive spider with the right nonlinearity would actually reduce distortion.
Good paper.
David S.
Good paper.
David S.
DC offset and jump phenomonon are petty obscure topics that only the hardcore driver types are aware of (usually in pro audio or high output subwoofers). They can be real issues at high drive level, though.
David
(added) does Klippel cover the topic? I thought he goes over DC point "wander"
David
(added) does Klippel cover the topic? I thought he goes over DC point "wander"
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Quality and volume of info...Superb!
Hi Tom,( and others here)
Thanks for your time and advice, I am completely open to accepting your ideas even although they may be counter intuitive and even counter to my own ideas... That’s the only way for me learn!
Its worth saying here that this DIY forum is just fab... I would have to pay around £100 to £ 200 PER HOUR consulting fees to get this level of technical support and advice... The fact that you are willing to give this openly and for free speaks volumes about your characters and generosity...Also total confidence and belief in your own commercial products…Unlike some others who grudgingly give little or nothing except that which promotes their own products “ USP’s”.
You guys are “ High End Gentlemen”!!
I am travelling for two days but I will read, think and reply soon.
Thanks again.
Derek.
Hi Tom,( and others here)
Thanks for your time and advice, I am completely open to accepting your ideas even although they may be counter intuitive and even counter to my own ideas... That’s the only way for me learn!
Its worth saying here that this DIY forum is just fab... I would have to pay around £100 to £ 200 PER HOUR consulting fees to get this level of technical support and advice... The fact that you are willing to give this openly and for free speaks volumes about your characters and generosity...Also total confidence and belief in your own commercial products…Unlike some others who grudgingly give little or nothing except that which promotes their own products “ USP’s”.
You guys are “ High End Gentlemen”!!
I am travelling for two days but I will read, think and reply soon.
Thanks again.
Derek.
Also called "Dynamic offset" or "oilcanning" It is analogous to a motor running faster when the stator current is reduced.
Electrical damping of loudspeakers, paraticularly woofers is akin to dynamic braking in rotary motors. In this application a shunt is connected to a motor's armature windings after it is disconnected from a source.The motor acts as a generator and all inertial energy in the motor itself and any load that acts as a flywheel is dissipated as heat in the shunt. In an amplifier/speaker combination the source impedance of the output stage of the amplifier is the shunt. The impedance of the speaker wire is in series and can reduce the effect. The application of reverse EMF to the amplifier tends to displace the quiescent operating point of active devices. The faster and more efficiently and the more overbuilt the amplifier the more stable it will be in the face of what is clearly not a passive load. This points out one defect in the method used to measure and compare audio amplifiers. Seemingly identical performance on a lab test bench doesn't always translate into identical performance driving a loudspeaker system. The problem is clearly complex and will not yield to just a few simple numbers.
One factor often overlooked is the tendency of drivers to "break up." This means that the cone or other vibrating element does not maintain its shape and move as a unit. instead it flexes and different parts of it are traveling in opposite directions. This is due to the cone's inability to withstand forces imposed on it.
For a woofer there is the driving force appied at the center by the voice coil and former. then there is the inner spider and the outer suspension. In most drivers the mechanical restoring force in the principal force acting to return the cone to its neutral position. Differences in the force from one point to another translate into a force gradient. There are at least two types. Differences between the inner and outer force along any radial line will tend to shear the cone across its thickness. This is like two people holding opposite ends of a sheet of cardboard and one waving it up and down. The other variable is differences between force applied to the cone at different points around its circumference both on the inside and outside. This circumferential force gradient tends to twist or flex the cone. Stronger cone material and more uniformly manufactured surrounds help reduce this effect.
One advanage of the acoustic suspension principle for woofers is that most of the restoring force is applied by differences in air pressure between the inside and outside of the box as the cone compresses and rarifies the air inside. This uniform application of force results in no pressure gradients from one point on the cone to another. For this reason acoustic suspension speakers are less prone to breakup and resulting harmonic distortion than other designs if all other things are equal.
For a woofer there is the driving force appied at the center by the voice coil and former. then there is the inner spider and the outer suspension. In most drivers the mechanical restoring force in the principal force acting to return the cone to its neutral position. Differences in the force from one point to another translate into a force gradient. There are at least two types. Differences between the inner and outer force along any radial line will tend to shear the cone across its thickness. This is like two people holding opposite ends of a sheet of cardboard and one waving it up and down. The other variable is differences between force applied to the cone at different points around its circumference both on the inside and outside. This circumferential force gradient tends to twist or flex the cone. Stronger cone material and more uniformly manufactured surrounds help reduce this effect.
One advanage of the acoustic suspension principle for woofers is that most of the restoring force is applied by differences in air pressure between the inside and outside of the box as the cone compresses and rarifies the air inside. This uniform application of force results in no pressure gradients from one point on the cone to another. For this reason acoustic suspension speakers are less prone to breakup and resulting harmonic distortion than other designs if all other things are equal.
Neither do I. Reads almost word for word the same as claims made in another thread which I remember debunking a month or so ago... 😉
Braking is the applied force that decelerates a moving mass. One critical but often overlooked parameter in Newton's second law is viscosity (B), the velocity related frictional drag coefficient. In the the tuning of a mass spring dashpot system or its LCR equivalent, the size of this paramter relative to the other two is reflected in system Q.
In the link the comparison between the mass spring dashpot and LCR circuits can be seen.
Harmonic oscillator - Wikipedia, the free encyclopedia
The respective resonance frequencies for the undamped systems is 1/2TT*(sq rt K/M) and 1/2TT*(sq rt 1/LC)
In this link you can see the straightforward approximate solution where damping factor is included;
http://www.calpoly.edu/~rbrown/Oscillations.pdf
The basic equation is;
f(t) = m d squared x/dt squared + b dx/dt + kx.
And the solution for the resonant frequency is;
f = 1/2TT* sq rt[k/m-(b/2m)squared]
The optimal Q for a speaker is 0.707 which gives the most extended FR without a peak. In a sealed AS enclosure the stuffing creates the aerodynamic drag force b where the speaker must push and pull air between the fibers. Therefore the precise number, size, shape, nature and packing of the fibers is critical to tuning the system. While Villchur believed that the loss could be explained thermodynamically and it's true that this drag coefficient causes minute heating of the fibers, it is not a useful model to use to explain what is happening. (Villchur was neither an engineer nor scientist but his background was as an educator. He got the right answer for the wrong reason, not uncommon but it was still right which is all that matters.) Typically the system is tuned by experimention (empirically) through trial and error. It should be noted that as the sealed enclosure is filled with stuffing it will tend to increase B but it also increases K by displacing air at the same time. The less air trapped in the box the tighter (higher) its spring constant k.
How does this all relate to two things:
- baffle area vs. frequency response
- IB "enclosures" where the air on both sides of the driver is essentially identical, so there is no enclosure to "add", yet the usable LF point now becomes lower than in a box, and at Fs.
_-_-bear
_-_-
Whether IB or OB there is no air trapped on one side of the cone to add to k and no external factor adding to b. All mechanical restoring force and mechanical damping must be inherent in the design of the driver itself. As can be seen from the last equation in my previous post, the resonant frequency is related to k and b so this would tend to lower system F3 all other things being equal. Dayton claims to be the only manufacturer in the US to build drivers specifically for IB designs. They would probably be good candidates for OB designs as well.
In my way of thinking at the moment, your two things are really the one above.
Response on a baffle will have a lower Fs than response in free air because the baffle loads the driver differently. T/S theory assumes that the box is less than wavelength divided by 6 at all frequencies of interest.
Many T/S programs assume that the loading on the driver is approximately that of a piston at the end of a long tube, not a large baffle.
By the way, the whole point of my "tap test" was to show the OP that there is a lot more damping happening in a speaker than s/he thinks.
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