As part of my desire to find a good use for the rear wave, I've been looking at transmission line theory from the bottom upwards. Actually I've been looking at the physics behind loudspeakers, as opposed to the number juggling of Thiele-Small parameters and enclosure alignments.
Anyway, I worked out what kind of pressurisation is produced by a cone at maximum excursion in a sealed box of appropriate size to get Qtc to 0.707. I was using the TS parameters of the Volt RV3143 (as used by PMC in their second largest TL monitor). As you might guess, this is a fairly large number, about 6304 Pascals.
Anyway, the end result is that to get the equivalent acoustic resistance to maximum excursion from an unstuffed TL, I needed a line CSA about 1/10th Sd
The numbers tally up for any extension, since there is only one variable, the cone excursion.
Now, either everyone has been building totally underdamped transmission lines, or I've got my maths for the confinement of the port wrong (about a 50/50 chance of that).
What seems mathematically obvious to me is that if you set the line CSA equal to the Sd of the driver, it behaves as if it was in free space, except that the rear wave is now in phase with the front wave, increasing acoustic output.
This is ignoring flow effects of course, it's likely if you wanted dipole style bass from a TL you'd need a bigger than Sd line.
Anyway, I worked out what kind of pressurisation is produced by a cone at maximum excursion in a sealed box of appropriate size to get Qtc to 0.707. I was using the TS parameters of the Volt RV3143 (as used by PMC in their second largest TL monitor). As you might guess, this is a fairly large number, about 6304 Pascals.
Anyway, the end result is that to get the equivalent acoustic resistance to maximum excursion from an unstuffed TL, I needed a line CSA about 1/10th Sd
The numbers tally up for any extension, since there is only one variable, the cone excursion.
Now, either everyone has been building totally underdamped transmission lines, or I've got my maths for the confinement of the port wrong (about a 50/50 chance of that).
What seems mathematically obvious to me is that if you set the line CSA equal to the Sd of the driver, it behaves as if it was in free space, except that the rear wave is now in phase with the front wave, increasing acoustic output.
This is ignoring flow effects of course, it's likely if you wanted dipole style bass from a TL you'd need a bigger than Sd line.
Hi Mark,
I have to admit that I am having trouble following your logic and arriving at the conclusion you have drawn. My experience simulating, building, and testing a few TLs does not seem to lead me down the path you are following. Could you provide a few more details on how you think a TL works so I can understand what you are concluding.
Thanks in advance,
I have to admit that I am having trouble following your logic and arriving at the conclusion you have drawn. My experience simulating, building, and testing a few TLs does not seem to lead me down the path you are following. Could you provide a few more details on how you think a TL works so I can understand what you are concluding.
Thanks in advance,
Martin,
My results are from an unstuffed line, effectively a straight continuous line of a fixed CSA.
Anyway, you have the standard transmission line behaviour which is well explained. Then you have the behaviour in the throat of the line. If the line csa is above the Sd of the driver then there is no restorative force on the driver, as in an open baffle loudspeaker.
If you reduce the csa to below the Sd of the driver, then some work must be done on the air in the throat of the line, in order to force it down the line. As a result of this there would be an opposing force on the driver, analogous to a sealed box.
Using this restorative force to control driver motion, as in an acoustic suspension design, requires a value of Sline much lower than anyone seems to use. It's a tradeoff for someone who greatly prefers the high quality of sealed box bass to the loose flabby stuff you get from a conventional ported box. Anyway my results with a Sline below Sd follow the behaviour of a normal TL quite well, that is they have Qts (for the driver) values (and those I've heard sound like) a sealed box of very low Qts (0.4-0.6).
Have you ever built a TL with such a low Sline?
My results are from an unstuffed line, effectively a straight continuous line of a fixed CSA.
Anyway, you have the standard transmission line behaviour which is well explained. Then you have the behaviour in the throat of the line. If the line csa is above the Sd of the driver then there is no restorative force on the driver, as in an open baffle loudspeaker.
If you reduce the csa to below the Sd of the driver, then some work must be done on the air in the throat of the line, in order to force it down the line. As a result of this there would be an opposing force on the driver, analogous to a sealed box.
Using this restorative force to control driver motion, as in an acoustic suspension design, requires a value of Sline much lower than anyone seems to use. It's a tradeoff for someone who greatly prefers the high quality of sealed box bass to the loose flabby stuff you get from a conventional ported box. Anyway my results with a Sline below Sd follow the behaviour of a normal TL quite well, that is they have Qts (for the driver) values (and those I've heard sound like) a sealed box of very low Qts (0.4-0.6).
Have you ever built a TL with such a low Sline?
Hi Mark,
No I have never built a low cross-sectional area TL. I have found that the bigger the cross-sectional area the better the low bass performance up to some point at which the returns become small for additional area. Typically for a straight constant area line my designs approach 3 x Sd.
No I have never built a low cross-sectional area TL. I have found that the bigger the cross-sectional area the better the low bass performance up to some point at which the returns become small for additional area. Typically for a straight constant area line my designs approach 3 x Sd.
Hmm, I use T/S because they work quite well. You are right though, if you use sealed 0.707 as a reference Vb, then for a 1/4WL pipe, its cross sectional area will be considerably < Sd in most cases, but Vas, Qts will vary it quite a bit.
Yes, TLs are underdamped to start with, then are stuffed to lower it to somewhat < 0.707 normally.
Don't know about the math, but no way, no how does a 1/4WL pipe allow the driver to perform as if in free space with CSA = Sd. This will require the pipe Vb to be 4-10x Vas depending on the driver's specs, so this is the range that CSA should be derived from. Normally though, the Vb of a T/S max flat for the desired Fb works well enough as a balance between LF extension, gain, and ripple in the passband.
WRT adding a filter chamber to the Sline, this is what was once called an acoustic labrynith and now a Daline, i.e. a bandpass with a very long, well damped vent.
GM
You are right though, if you use sealed 0.707 as a reference Vb, then for a 1/4WL pipe, its cross sectional area will be considerably < Sd in most cases, but Vas, Qts will vary it quite a bit. Yes, TLs are underdamped to start with, then are stuffed to lower it to somewhat < 0.707 normally.
Don't know about the math, but no way, no how does a 1/4WL pipe allow the driver to perform as if in free space with CSA = Sd. This will require the pipe Vb to be 4-10x Vas depending on the driver's specs, so this is the range that CSA should be derived from. Normally though, the Vb of a T/S max flat for the desired Fb works well enough as a balance between LF extension, gain, and ripple in the passband.
WRT adding a filter chamber to the Sline, this is what was once called an acoustic labrynith and now a Daline, i.e. a bandpass with a very long, well damped vent.
GM
Exactly what physical effect do you think causes Vline to have any relation to Vas? If you build a 100m line with the appropriate CSA, then it will have the same Vline as one of 4xSd, but I guarrantee that the behaviour of the driver will be somewhat different.
Vline is irrelevant, there are two parameters, one is the restorative force on a driver, which is a function of the impedance of the line, which is harder to calculate when the line is stuffed and the other is the frequency of the 1st standing wave in the line.
If the flow impedance of the stuffed line is 40x that of the empty line, then of course the CSA of the line should be 4x Sd, if the line impedance, as determined by the TS parameters (by a rather complex set of equations as yet) requires an unstuffed line of CSA 1/10 Sd.
Vline is irrelevant, there are two parameters, one is the restorative force on a driver, which is a function of the impedance of the line, which is harder to calculate when the line is stuffed and the other is the frequency of the 1st standing wave in the line.
If the flow impedance of the stuffed line is 40x that of the empty line, then of course the CSA of the line should be 4x Sd, if the line impedance, as determined by the TS parameters (by a rather complex set of equations as yet) requires an unstuffed line of CSA 1/10 Sd.
The less you load the driver with it's own rear wave, the lower the resonant frequency of the driver and consequently the more output you will get at low frequencies for the correct line length.
Once you unload the driver completely, it's resonant frequency becomes Fs and any gains from this point on will be minimal.
Sd is the surface area of the driver.
Once you unload the driver completely, it's resonant frequency becomes Fs and any gains from this point on will be minimal.
Sd is the surface area of the driver.
>Exactly what physical effect do you think causes Vline to have any relation to Vas? If you build a 100m line with the appropriate CSA, then it will have the same Vline as one of 4xSd, but I guarrantee that the behaviour of the driver will be somewhat different.
>Vline is irrelevant, there are two parameters, one is the restorative force on a driver, which is a function of the impedance of the line, which is harder to calculate when the line is stuffed and the other is the frequency of the 1st standing wave in the line.
>If the flow impedance of the stuffed line is 40x that of the empty line, then of course the CSA of the line should be 4x Sd, if the line impedance, as determined by the TS parameters (by a rather complex set of equations as yet) requires an unstuffed line of CSA 1/10 Sd.
====
Being a resonant device, a driver wants to 'feel' a certain amount of compliance, which is defined by its Vas. For it to 'feel' a ~equal amount of acoustic mass loading on both sides of it ('free space') requires the rear cab, be it sealed, vented, or pipe, to have a Vb of 4-10x Vas to be 'close enough' fo a typical HIFI app, not CSA = 1/10, or Sd, even if you make up the difference in Vb by increasing its length beyond that required to damp its Fs impedance spike.
Sd, not Vas, is totally irrelevant WRT CSA until the CSA = <Sd. Some of the newer sub drivers have such a low Vas and Fs that the pipe is too small to fit the driver without an adapter. Otherwise, Sd is only relevant as being one of the components that defines Vas.
MJK chose to use Sd as a convenient way to input the CSA in his worksheets, but it has caused much confusion for many folks who don't understand the basics of the various resonant devices used in speaker design.
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>so, for any finished strait TL design, if you increase the cross sectional area it will improve the low end response?? Will that change the length of the line or the amount of stuffing?
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Yes, though once the line's Vb exceeds ~10x Vas, any gains are tiny, just like when comparing a 10x Vas sealed cab to a true IB.
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>The less you load the driver with it's own rear wave, the lower the resonant frequency of the driver and consequently the more output you will get at low frequencies for the correct line length.
Once you unload the driver completely, it's resonant frequency becomes Fs and any gains from this point on will be minimal.
====
The driver's Fs doesn't change, only the amount the line damps its impedance peak changes. Once the line's Vb is large enough that no damping of its impedance peak occurs, then there will be no more gains.
GM
>Vline is irrelevant, there are two parameters, one is the restorative force on a driver, which is a function of the impedance of the line, which is harder to calculate when the line is stuffed and the other is the frequency of the 1st standing wave in the line.
>If the flow impedance of the stuffed line is 40x that of the empty line, then of course the CSA of the line should be 4x Sd, if the line impedance, as determined by the TS parameters (by a rather complex set of equations as yet) requires an unstuffed line of CSA 1/10 Sd.
====
Being a resonant device, a driver wants to 'feel' a certain amount of compliance, which is defined by its Vas. For it to 'feel' a ~equal amount of acoustic mass loading on both sides of it ('free space') requires the rear cab, be it sealed, vented, or pipe, to have a Vb of 4-10x Vas to be 'close enough' fo a typical HIFI app, not CSA = 1/10, or Sd, even if you make up the difference in Vb by increasing its length beyond that required to damp its Fs impedance spike.
Sd, not Vas, is totally irrelevant WRT CSA until the CSA = <Sd. Some of the newer sub drivers have such a low Vas and Fs that the pipe is too small to fit the driver without an adapter. Otherwise, Sd is only relevant as being one of the components that defines Vas.
MJK chose to use Sd as a convenient way to input the CSA in his worksheets, but it has caused much confusion for many folks who don't understand the basics of the various resonant devices used in speaker design.
====
>so, for any finished strait TL design, if you increase the cross sectional area it will improve the low end response?? Will that change the length of the line or the amount of stuffing?
====
Yes, though once the line's Vb exceeds ~10x Vas, any gains are tiny, just like when comparing a 10x Vas sealed cab to a true IB.
====
>The less you load the driver with it's own rear wave, the lower the resonant frequency of the driver and consequently the more output you will get at low frequencies for the correct line length.
Once you unload the driver completely, it's resonant frequency becomes Fs and any gains from this point on will be minimal.
====
The driver's Fs doesn't change, only the amount the line damps its impedance peak changes. Once the line's Vb is large enough that no damping of its impedance peak occurs, then there will be no more gains.
GM
Um, I hate to point this out, but for an open ended line, you are not loading the driver with a fixed volume of space, you are driving the rear wave through a wave guide so that it emerges in-phase with the front wave off the driver.
A transmission line is not a Helmholtz resonator. If you build a TL that behaves like one, you have failed miserably. Of course the line has a resonant behaviour, but the wave in the line is created at the fixed end, therefore for a standing wave to develop, it would have to be the front wave of the driver entering the open end of the line and combining with the rear wave.
Compliance is the mechanical restorative force as generated by the suspension, which can also be expressed as a volume. It has units of N/m. In a sealed box system, compressing Vb by Vd (where Vd is Sd times the displacement of the cone in metres) produces a change in pressure between the inside and the outside of the box, which in turn exerts a restorative force on the driver, which is a function of the pressure multiplied by the cone area, (where the pressure is a function of the displacement), so cancelling out common terms you derive an enclosure compliance. Enclosure compliance is how we adjust Qts to get Qtc.
Since there is no theoretical difference between compressing a finite volume of air, and trying to force too much air into a narrow pipe, a transmission line speaker behaves in much the same was a sealed box loudspeaker, except that at the resonant frequency of the line the front and rear waves constructively interfere to produce much greater output. This is why TLs have the slowest roll off of all and the driver doesn't suddenly unload and bottom out at high SPL when it hits the resonant frequency of the line.
The only reasons that a driver mounted in a line of CSA = Sd would not behave as if in free space are if the end of the line is loaded against a wall or the walls of the line are not perfectly smooth. Since both conditions are ever present, it is necessary to approximate their effects, especially in the case of a stuffed TL, where the resistande of the damping material to airflow must be considered when trying to determine what the Qtc is and what the target line length should be.
A transmission line is not a Helmholtz resonator. If you build a TL that behaves like one, you have failed miserably. Of course the line has a resonant behaviour, but the wave in the line is created at the fixed end, therefore for a standing wave to develop, it would have to be the front wave of the driver entering the open end of the line and combining with the rear wave.
Compliance is the mechanical restorative force as generated by the suspension, which can also be expressed as a volume. It has units of N/m. In a sealed box system, compressing Vb by Vd (where Vd is Sd times the displacement of the cone in metres) produces a change in pressure between the inside and the outside of the box, which in turn exerts a restorative force on the driver, which is a function of the pressure multiplied by the cone area, (where the pressure is a function of the displacement), so cancelling out common terms you derive an enclosure compliance. Enclosure compliance is how we adjust Qts to get Qtc.
Since there is no theoretical difference between compressing a finite volume of air, and trying to force too much air into a narrow pipe, a transmission line speaker behaves in much the same was a sealed box loudspeaker, except that at the resonant frequency of the line the front and rear waves constructively interfere to produce much greater output. This is why TLs have the slowest roll off of all and the driver doesn't suddenly unload and bottom out at high SPL when it hits the resonant frequency of the line.
The only reasons that a driver mounted in a line of CSA = Sd would not behave as if in free space are if the end of the line is loaded against a wall or the walls of the line are not perfectly smooth. Since both conditions are ever present, it is necessary to approximate their effects, especially in the case of a stuffed TL, where the resistande of the damping material to airflow must be considered when trying to determine what the Qtc is and what the target line length should be.
>Um, I hate to point this out, but for an open ended line, you are not loading the driver with a fixed volume of space, you are driving the rear wave through a wave guide so that it emerges in-phase with the front wave off the driver.
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Ah, but that's exactly what a closed pipe (plane wave tube) does in effect. It's a standing wave generator of 'x' Vb that drives a very thin acoustic 'membrane' (for lack of a better description) at its terminus where its length plus an end correction defines its resonant characteristics and its cross sectional area its displacement amplitude (gain).
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>A transmission line is not a Helmholtz resonator. If you build a TL that behaves like one, you have failed miserably.
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A ML-TL (TL with a vent) can be a 'beautiful thing' sonically if properly designed/implemented, so I definitely disagree with you, and judging by how popular they have become recently thanks to MJK's worksheet, so do many others.
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>Of course the line has a resonant behaviour, but the wave in the line is created at the fixed end, therefore for a standing wave to develop, it would have to be the front wave of the driver entering the open end of the line and combining with the rear wave.
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Nope, doesn't work this way. If it did, a sealed back driven PWT or horn wouldn't work.
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>Since there is no theoretical difference between compressing a finite volume of air, and trying to force too much air into a narrow pipe, a transmission line speaker behaves in much the same was a sealed box loudspeaker, except that at the resonant frequency of the line the front and rear waves constructively interfere to produce much greater output.
====
Sorry, but comparing a sealed system to a resonant one is an apples n' oranges one.
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>This is why TLs have the slowest roll off of all and the driver doesn't suddenly unload and bottom out at high SPL when it hits the resonant frequency of the line.
====
Well, they can if their Vb is quite small and are heavily stuffed, but F3 shifts up so high that I can't imagine anyone actually having a need for it in a HIFI app.. Indeed, unstuffed their roll off slope can be > a BR's/ML-TL's 24dB/octave if it has a very large Vb. Stuffed, it will ~match its IB equivalent, so for HIFI apps I have to disagree with your assertion.
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>The only reasons that a driver mounted in a line of CSA = Sd would not behave as if in free space are if the end of the line is loaded against a wall or the walls of the line are not perfectly smooth.
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Sorry, but this is just plain ridiculous. It's obvious we're poles apart, so I see no point in spending any more time on audio TL design theory until you have a better understanding of resonant air columns and how they mesh with T/S theory.
GM
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Ah, but that's exactly what a closed pipe (plane wave tube) does in effect. It's a standing wave generator of 'x' Vb that drives a very thin acoustic 'membrane' (for lack of a better description) at its terminus where its length plus an end correction defines its resonant characteristics and its cross sectional area its displacement amplitude (gain).
====
>A transmission line is not a Helmholtz resonator. If you build a TL that behaves like one, you have failed miserably.
====
A ML-TL (TL with a vent) can be a 'beautiful thing' sonically if properly designed/implemented, so I definitely disagree with you, and judging by how popular they have become recently thanks to MJK's worksheet, so do many others.
====
>Of course the line has a resonant behaviour, but the wave in the line is created at the fixed end, therefore for a standing wave to develop, it would have to be the front wave of the driver entering the open end of the line and combining with the rear wave.
====
Nope, doesn't work this way. If it did, a sealed back driven PWT or horn wouldn't work.
====
>Since there is no theoretical difference between compressing a finite volume of air, and trying to force too much air into a narrow pipe, a transmission line speaker behaves in much the same was a sealed box loudspeaker, except that at the resonant frequency of the line the front and rear waves constructively interfere to produce much greater output.
====
Sorry, but comparing a sealed system to a resonant one is an apples n' oranges one.
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>This is why TLs have the slowest roll off of all and the driver doesn't suddenly unload and bottom out at high SPL when it hits the resonant frequency of the line.
====
Well, they can if their Vb is quite small and are heavily stuffed, but F3 shifts up so high that I can't imagine anyone actually having a need for it in a HIFI app.. Indeed, unstuffed their roll off slope can be > a BR's/ML-TL's 24dB/octave if it has a very large Vb. Stuffed, it will ~match its IB equivalent, so for HIFI apps I have to disagree with your assertion.
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>The only reasons that a driver mounted in a line of CSA = Sd would not behave as if in free space are if the end of the line is loaded against a wall or the walls of the line are not perfectly smooth.
====
Sorry, but this is just plain ridiculous. It's obvious we're poles apart, so I see no point in spending any more time on audio TL design theory until you have a better understanding of resonant air columns and how they mesh with T/S theory.
GM
Exactly what don't I understand about resonant air columns? Especially as it applies to TL theory.GM said:
Now, I can see a few different physical models for the operation of the line.
One, the terminus of the line is the acoustic centre of the driver and the open end is just that, the open end. Now if the line is one contiguous unit, then system would behave as if there were two wave sources at either end of the line and when they constructively interferred, that would be the resonance of the system.
Two, the terminus of the line is fixed, and the driver is mounted somewhere in the middle. The driver creates two waves, with opposing vectors of propagation. When the wave that propagates towards the terminus encounters the terminus, it is reflected and inverted. When this wave constructively interferes with the other wave, that would be a resonance of the system.
Three, as in the first model, except that there is a choke point somewhere in the line. When the backwave from the driver encounters the choke point, it is reflected. When the reflections destructively interfere with the backwave, the driver unloads, and this is a resonance of the system.
I'm all too aware of the theory of a Helmholtz resonator, and thereby well aware of the problems such things cause, when accurate reproduction of recorded sound is the goal. If you honestly wish to listen to the reproduction of musical instruments through a device which behaves in much the same way, then that is your sacred right and I would not deny you that right.
My goal is a critically damped bass system that does not exhibit the unnatural resonances, phase errors and group delay of traditional vented systems. I've not done a proper calculation of the Helmoltzian behaviour of such a system, but a quick look over the sizes of the quantities involved leads me to believe that the resonant frequency of it's behaviour as a Helmoltz resonator is very low, below the useful bandwidth of the system in fact.
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