We will have to disagree on this one. When modeling them one does not use two different approaches, just one for all frequencies.
The acoustic centers of the two sources is coincident with the tweeter if it is between them.
Lobbing is an effect that happens due to the finite size of the source. There are "lobes" that circumscribe the source - all the way around it.
When there are two non-coincident sources the cancellations only occur at discrete points in space, a null or nulls depending on wavelength. These cancellations do not circumscribe the sources. These two effects are really quite different but you are treating them as the same. I don't see it that way.
It does so by following simple laws of electronics. I have problems following the intent of your very generic question.
His sim is based on a different L-C circuit which has a higher resonance but otherwise it's the same thing going on.
Note that this all has nothing to do with Class-D itself, it's just the effect of an simple LC filter damped by an unknown (the speaker) and you will get the exact same results when you hook up a standard linear amplifier at the input of the filter.
Here is simplified theory (with cardioid point sources) how much and where power & DI errors are located when M-M = 240 mm and X/O=4 kHz LR4.
An externally hosted image should be here but it was not working when we last tested it.
M-M lobing makes max 2 dB power & DI error which can be compensated by horizontal directivity, or just axial response if DI error is ignored. Full compensation may be too much.
MM-T and LR4 is totally ~1.5 dB which may disappear with some luck in driver selection.
Errors are more significant in practice if vertical reflections are much stronger than horizontal.
Well if that one model takes into account the driver separation and then shows lobes in the vertical off axis towards high frequencies then there is no need for two separate approaches.
Yes but only if you are directly on axis with the tweeter and if not, only if the devices are crossed low enough. Lobing occurs when you go off axis and this is what I was talking about. Lobing, of the same type, does not occur with the true coaxial as the path differences between the tweeter and mid remain identical regardless of the vertical off axis angle.
And of course the directivity and primary listening lobe will narrow as the speaker goes from being omnidirectional towards not being, or goes towards being constant directivity.
Of course this happens, I wasn't saying that it wasn't.
The mechanism might be different, but the end result is the same. They both end up creating 'lobes' that detail how a loudspeaker performs on and off axis.
The non coincident variety is the one that most people focus on mainly because directivity is largely ignored in most loudspeaker designs. The only issue that people usually contend with is the wide-narrow-wide aspect in making sure that the xover frequency is low enough, so that the narrowing is kept to a minimum. People then show horizontal off axis plots to detail how bad or good the narrowing of their design is and then show vertical polar plots to detail the primary listening lobe, ie how far up and down you can go before you run into trouble. Then of course to show if the lobing pattern is symmetrical or not indicating how the two drivers are specifically integrated about the xover frequency.
I would say that the lobing pattern of the loudspeaker, in association with it's inherent off axis behaviour, due to the inherent directionality of the drivers is pretty much ignored. This is mainly because nothing special (apart from using a low enough xover point) is done to control directivity in the vast majority if designs. It's just how a standard dome tweeter beams, which is really neither use nor ornament to anyone particularly.
In your case though, and in the way that you design loudspeakers, I can see that the lobing pattern, created by non coincident drivers, takes a bit of a back seat. This is one caveat of wave guide loudspeakers in that the C2C spacing is usually quite large relative to the wave length at the crossover frequency. You're not designing for it in particular though, you're focus is obviously on getting the lobing pattern, created by the off axis nature of the individual drivers, as close to how you'd want it to be, as you can.
Edit - I suppose as a question, do you actually pay attention to the vertical off axis response of your loudspeakers, or do you just take it for granted that you're going to have problems in that area?
And as another question, that ties in with the 1-4kHz issue. Your loudspeakers typically crossover quite low, this doesn't change the fact that they are going to experience vertical lobing from the non coincident nature of the wave guide and the mid bass. But do you think that having the crossover frequency down at say 700Hz lessens the impact from the lobing created than if it were at say 2kHz?
This would in effect be rather beneficial, because even though you've got a rather large separation between the wave guide and the mid bass, crossing so low would, again, help to reduce the degree to which the vertical off axis issues could impinge on the sound.
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But only where the lobing exists, which is only at the crossover point. Hardly "limiting", I should think.
That depends on how you want to use the loudspeakers. If you use them in different positions and at different listening heights then it is a bit of a problem.
5th element - this is one area where I don't think that you have it right.
This is not correct. If the sources are in the same baffle plane then the acoustic centers of the two LF drivers is always at the same point as the tweeter off axis or not. It is a point and if it is coincident then it is coincident everywhere.
The fact is that my software package SPEAK, from way back in 1990's, was able to model the situation that you are talking about. The techniques used are in my book as well. The "null" from non-coincident sources is a point not a "lobe".
There will always be a null with non-coincident drivers at some vertical angle. At very low crossover frequencies this null can be beyond 180 degrees. As the crossover frequency goes up this null will move forward in angle and in fact more nulls can begin to appear. Hence the lower the crossover the less of an effect this hole is likely to be.
Yes, I pay a lot of attention to these nulls, but I do accept that they will never go away. Lowering the crossover helps, that's one of the reasons that I try and push it lower. Another factor is the acoustic phase angle between the two drivers which will determine if the nulls are symmetrical WRT the axis. One must carefully tweak the crossover components to get this just right. (With an active crossover one can move the nulls up and down with delay.) I have software that lets me do this and over the years I have found that it is accurate enough that I don't need to double check it. But over the years I have checked the vertical response several times but I always find that it is as expected - two nulls, one up and one down, usually not symmetric because the system is not symmetric in the vertical plane. They are located about 20 degrees up and a little more down.
So yes, I do and have paid a great deal of attention to this effect and have for many years now. That said, the horizontal is far more important, which we should not forget in these discussions.
This is not correct. If the sources are in the same baffle plane then the acoustic centers of the two LF drivers is always at the same point as the tweeter off axis or not. It is a point and if it is coincident then it is coincident everywhere.
The fact is that my software package SPEAK, from way back in 1990's, was able to model the situation that you are talking about. The techniques used are in my book as well. The "null" from non-coincident sources is a point not a "lobe".
There will always be a null with non-coincident drivers at some vertical angle. At very low crossover frequencies this null can be beyond 180 degrees. As the crossover frequency goes up this null will move forward in angle and in fact more nulls can begin to appear. Hence the lower the crossover the less of an effect this hole is likely to be.
Yes, I pay a lot of attention to these nulls, but I do accept that they will never go away. Lowering the crossover helps, that's one of the reasons that I try and push it lower. Another factor is the acoustic phase angle between the two drivers which will determine if the nulls are symmetrical WRT the axis. One must carefully tweak the crossover components to get this just right. (With an active crossover one can move the nulls up and down with delay.) I have software that lets me do this and over the years I have found that it is accurate enough that I don't need to double check it. But over the years I have checked the vertical response several times but I always find that it is as expected - two nulls, one up and one down, usually not symmetric because the system is not symmetric in the vertical plane. They are located about 20 degrees up and a little more down.
So yes, I do and have paid a great deal of attention to this effect and have for many years now. That said, the horizontal is far more important, which we should not forget in these discussions.
Let me explain something that may not be well understood - maybe my explanation won't make it any better 
There is a theorem in acoustics that says that if a source can be represented as two sources superimposed, such as two point sources separated by some distance and a piston - which represents the configuration that we are talking about - then the directivity of the combination will be the product of the directivities of the two separate sources. In our case we would multiply the polar response of a 6.5" piston by the polar response of two point sources separated by 8 inches.
So the vertical "nulls" are caused by the separated point sources, but the "lobbing" would be caused by the finite size of the individual drivers.
This theorem is very powerful as it allows for extremely complex situations to be analyzed in a very simple manner. We know the directivity of a piston and the directivity of two point sources is quite easy, so just multiply the two together and you have a situation that would be very hard to analyze as a full system.
In case you are wondering, this theorem comes from the fact that the directivity of a source is the Fourier Transform of its velocity profile. Two variables that are convolutions in one domain are simply products in the other domain. Time and frequency for example, ka*sin (theta) and velocity are another.
There is a theorem in acoustics that says that if a source can be represented as two sources superimposed, such as two point sources separated by some distance and a piston - which represents the configuration that we are talking about - then the directivity of the combination will be the product of the directivities of the two separate sources. In our case we would multiply the polar response of a 6.5" piston by the polar response of two point sources separated by 8 inches.
So the vertical "nulls" are caused by the separated point sources, but the "lobbing" would be caused by the finite size of the individual drivers.
This theorem is very powerful as it allows for extremely complex situations to be analyzed in a very simple manner. We know the directivity of a piston and the directivity of two point sources is quite easy, so just multiply the two together and you have a situation that would be very hard to analyze as a full system.
In case you are wondering, this theorem comes from the fact that the directivity of a source is the Fourier Transform of its velocity profile. Two variables that are convolutions in one domain are simply products in the other domain. Time and frequency for example, ka*sin (theta) and velocity are another.
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But only if the wavelengths you are looking at are reasonably larger than the path separation between the drivers used. If the wavelengths are shorter then the drivers do not act as one coincident source.
I am only talking about the vertical plane here though.
Obviously in the horizontal plane, if the baffle is flat and the acoustic centres are aligned, then going off axis wont change the phase relationship between the drivers.
Yes, but this is only if the xover frequency itself is lowered and everything else about the loudspeaker remains the same (ie driver separation etc). This is not what I was talking about.
What I was meaning is that your loudspeakers are pretty much designed around specific physical dimensions. That is a wave guide of a certain design and diameter (lets say it's 6" here) will have a certain range of controlled directivity. If you pair this wave guide with a mid bass then the mid bass will be of a similar diameter and you will end up crossing them at a specific frequency. The frequency chose,n to get a good directivity match between the two, is also related directly to the size of the radiators used. Obviously the design will have it's own lobing pattern within the vertical axis.
Now if you were to take this design and scale it up by a factor of two, ie the wave guide is now 12" in diameter, then the range of controlled directivity would drop by roughly an octave, the driver to driver spacing would double as you now need a 12" mid bass too, but the xover frequency required would also drop by an octave.
If one were to take a polar plot and look at the lobing pattern of the larger design it would look pretty much identical to the smaller one, except that the frequency at which the lobing occurs would be an octave below the smaller one.
This is what I was asking.
If the vertical lobing pattern between two loudspeakers is identical, except that one loudspeaker exhibits the lobes at 2000Hz, whereas another exhibits them at 1000Hz. Will the ones at 1000Hz be less subjectively offensive?
This is most certainly not how the term is used in everything I've ever read about loudspeaker design. Everyone I've ever encountered always uses the term 'lobe' to refer to the vertical off axis pattern, around the xover point, to describe the window over which you can shift your listening height and not have the sound too affected. Ie a wide primary or narrow primary lobe.
As an example.
The green line around the 0 degree axis would be called the primary listening lobe. Presumably because it looks just like a 'lobe' on a polar plot. I have never heard the word 'point' used to describe this.
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Yes, but apart from the theoretical side of why these things are occurring (ie interference vs off axis beaming), the end result, from a measured perspective, is exactly the same. You have a polar plot with regions of high intensity and low intensity. A lobe is a region of high intensity, whereas a null is the reverse.
Indeed, a lobe can be present in any direction of measurement, in radio antenna the polar plots can be in 3 dimensions.
Your simulation suggests there are deviations of 7.5dB whereas xrk971's data suggests the error is <1dB. So I guess my questions is which of these numbers is realistic for real class D implementations? Are there any amplifiers on the market that have even lower magnitude distortion?
This is not distortion that I simulated - it is the effect of the LC filter used by the tpa3116 on gain and phase when tied to various resistive loads. The class D amp such as the 3116 has a feedback loop before the LC filter so it will try to maintain a constant voltage (proportional to audio signal) leading to the LC portion. That is, what the LC filter does to the gain after, the feedback loop cannot correct. However this effect is probably less than 1dB is what am trying to show. Some class D amps (more expensive and bigger discrete components typically) have feedback tied to point after LC filter.
The harmonic distortion is available in the factory data sheet as function of different parameters. For the 3116, THD is typically less than 0.1% for a 19v supply driving a 4ohm load at less than 40watts output.
There are class D amps that have very low HD, such as the IRS2091 types with external discrete MOSFET and heatsinks and variable switching freq - they need dual rail supplies though. However they can get very high power up to 1kW+.
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I would certainly expect the lower one to be less of a problem.
I understand that, but the loose usage leads to misunderstandings like the one we are having now.
Your example only looks like a "lobe" because it is one dimensional - angle off axis - only in one plane. If you were to look at it as a polar map showing two angles - off axis and around the axis - you would see that the 30 degree "hole" goes away in different planes. If this plot were due to a finite sized piston then the null would be a circle and not be different in different planes. Using the term "lobe" for both effects leads one to believe that they represent the same kind of effect when in fact they don't. Use the term "lobe" if you like, it can usually be determined from the context which effect you are talking about, but I will continue to understand them as two different effects because the results are quite different.
And the answer is . . . yes . . . both of them. If you are talking "black box amplifier" connected to "black box speaker, with badly designed crossover" then the response deviation at 20kHz can be considerable, and may even extend audibly down to 10kHz or even below. It is a toss up, however, even where the response deviation is audible, whether the result is "good" or "bad". If the speaker is "hot" on the high end and the filter interaction rolls that off a bit (the result the one time I encountered it) you might count it as a benefit . . .
If you're DIYing it, and using the Class D amp after an active crossover, then it's not an issue at all. The effect is inaudible, and as a practical matter unmeasurable, with most class D amps driving the woofer or midrange, and it simply becomes a part of the device response curve if you are using the amp to drive a tweeter . . . you design for the combination.
The effect is not the same as what you get with a high output impedance tube amp . . . in that case the result is broadband, interacting with the bad (passive) crossover at all frequencies. With class D designs the filter's effect is limited to a possible response deviation at the high end only, and the result may, as noted, be either good or bad, depending . . .
Here is yet another way to look at lobing/combing of a single source vs. two sources, both 220mm edge to edge. Two 60mm drivers simulated in the worst direction (along the line) in The Edge. As we have seen in previous examples, the lobing/combing gets even worse at larger off-axis angle. Low and steep xo helps to minimize these problems.
This worst direction of a loudspeaker is usually vertical. A clever MTM has driver diameter, separation and xo selected so that horizontal and vertical "valleys and hills" compensate each other. However, a cleverly designed coaxial maintains smooth response both vertically and horizontally.
This worst direction of a loudspeaker is usually vertical. A clever MTM has driver diameter, separation and xo selected so that horizontal and vertical "valleys and hills" compensate each other. However, a cleverly designed coaxial maintains smooth response both vertically and horizontally.
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To ear is human...
I've found it's easy to optimize crossover points in an actively filtered system.
I've returned to small open baffle speakers (neo 10+ neo 3), and a topless h frame podium pp183 woofer fed from a plate amp with a 2nd order filter built in.
The mids and tweeters are 4th order filtered. The active crossovers are continuously variable, I chose to work from the midrange out.
The cross over points are far different from what loaded my room best from boxed drivers.
Got close within a 1/2 hour, and am satisfied after a week of small adjustments not to tweak further. I've settled on 80 hz roll off on the plate amp, ramping up its volume to meet the neo 10's filtered highpass at 250 hertz,which cross to the neo 3's at 3700 hertz.
I have the left/right points slightly different to lock in the centre image, I'm not certain if this is a mis calibration of the inexpensive pro crossovers, driver mismatches, or room placement. After several years of mucking about with hundreds of crossovers, I'm glad to have sold the testing clutter, and be unconcerned with endless calculations and mods.
I can't make it sound like unamplified live music; but it sounds convincing of amplified live music.
Ran a bluray player into the DAC ; movies are more convincing with 2.1 than the 7.1 Tannoy fronts plus Kef effects channels.
Using test tones to start with, then familiar voices, tweaking until bass lines may be easily followed evenly, until the strike points on a ride cymbal may be placed, or a paiste be easily differentiated from a ziljean cymbal,
It can be done by ear, just not in a day.
I've found it's easy to optimize crossover points in an actively filtered system.
I've returned to small open baffle speakers (neo 10+ neo 3), and a topless h frame podium pp183 woofer fed from a plate amp with a 2nd order filter built in.
The mids and tweeters are 4th order filtered. The active crossovers are continuously variable, I chose to work from the midrange out.
The cross over points are far different from what loaded my room best from boxed drivers.
Got close within a 1/2 hour, and am satisfied after a week of small adjustments not to tweak further. I've settled on 80 hz roll off on the plate amp, ramping up its volume to meet the neo 10's filtered highpass at 250 hertz,which cross to the neo 3's at 3700 hertz.
I have the left/right points slightly different to lock in the centre image, I'm not certain if this is a mis calibration of the inexpensive pro crossovers, driver mismatches, or room placement. After several years of mucking about with hundreds of crossovers, I'm glad to have sold the testing clutter, and be unconcerned with endless calculations and mods.
I can't make it sound like unamplified live music; but it sounds convincing of amplified live music.
Ran a bluray player into the DAC ; movies are more convincing with 2.1 than the 7.1 Tannoy fronts plus Kef effects channels.
Using test tones to start with, then familiar voices, tweaking until bass lines may be easily followed evenly, until the strike points on a ride cymbal may be placed, or a paiste be easily differentiated from a ziljean cymbal,
It can be done by ear, just not in a day.
Any change on the input signal is distortion. Sorry if I'm using the term too strict. Nevertheless my question is, are those number posted by you and KSTR a real depiction of real amps connected to real speakers?
If I'm reading your post right then the error in real world applications is <1dB and therefore a non-issue?
Well what I showed is a SPICE circuit sim, which is, I think, generally good enough or this kind of a circuit simulation of an LC filter. It does accurately depict what happens for an AC signal with a fixed resistive load. If you want to add the effect of a reactive load such as a speaker driver, we can do that by representing the T/S parameters as lumped RLC elements in the circuit. Here is a typical driver with a 4.6ohm DCR. The simulation, now accounting for how the reactive components of a driver interact with the LC filter in the TPA3116D2, actually provides a much nicer gain and phase error response. Working together as a 'System', the gain error is now under 0.5dB at 20kHz and phase error is under 3 deg.
Here is the schematic including a reactive driver (magenta line):
Here is the resulting predicted gain and phase response for this driver interacting with this LC filter (magenta line):
So you can see that for all intents and practical purposes, the class D amp LC filter is flat in gain and phase for a typical driver. Thus, if you do your XO actively before the amp, it is a non-issue. The LC filter essentially presents no distortion in amplitude or phase is used as an active XO amp.
As Dewardh said above,
- I agree.
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