Why Lower Crossover Frequency Does Not Always Improve Loudspeaker Directivity

[Ditonica]

Introduction

Crossover frequency is one of the most important aspects of loudspeaker design, significantly impacting overall performance. Among other factors, a smooth transition of directivity between drivers is crucial for sound quality. However, the common opinion that lower crossover frequency results in smoother directivity of the system is not always correct, and reviewers often misinterpret the reasons for directivity errors in some loudspeakers. In fact, in many cases, speakers can benefit from a higher crossover frequency. In this article, I will describe the directivity pattern of drivers in rectangular cabinets and suggest a rule of thumb that can be useful for both professional and enthusiast speaker builders.

The driver's directivity is just a part of the picture

A popular explanation for directivity index problems in loudspeakers is that the transition between drivers happens where the woofer is narrow and the tweeter is wide. In reality, the difference between a 5-inch or a 6.5-inch woofer and a non-waveguided tweeter is not that significant, and using a 2nd order crossover at frequencies between 2000-3000 Hz on an infinite baffle, it is possible to achieve quite a stable transition in the horizontal plane. What makes it problematic to achieve a smooth overall directivity index in a typical rectangular cabinet and non-coaxial design loudspeakers is edge diffractions and vertical lobing.

The cabinet is a waveguide

Edge diffraction is not only something that might change the on-axis frequency response of the speaker, but also the off-axis response. The amount of sound power the driver radiates remains stable, and the peaks and dips observed on-axis are often a result of the sound power distribution from off-axis directions. Let's look at some interesting examples.

The graph below shows the normalized horizontal directivity of a 3-way speaker. The midrange driver crossover frequencies are 380 and 2850 Hz; its location is at the center of a 350 mm width baffle. The distance between the center of the driver and the edge of the speaker cabinet is 175 mm, which is equal to the wavelength of 1960 Hz; the half of this frequency is 980 Hz. That is the place where the directivity dip appears, after which a dramatic rise happens.

Another similar example of a loudspeaker that has a midrange driver operating in the 550-2500 Hz range on a 300 mm-wide baffle.

These examples illustrate the pattern of loudspeaker driver directivity in rectangular cabinets, where the crossover frequencies are far from the problematic region. Once the cabinet width is smaller, it becomes more complicated to distinguish this baffle effect from directivity changes due to driver transition. In the case of a centred driver position in a 200 mm-wide baffle, the directivity dip is concentrated around 1720 Hz, while the directivity peak is around 3000 Hz (x1.5-2 from initial frequency).

When two problems compensate for each other

Another significant factor affecting overall speaker directivity, aside from the drivers themselves, is vertical lobing. The dips in vertical directivity index are usually significant around the crossover frequency between a typical midbass/midrange driver and tweeter, even below 2000 Hz. When we summarize horizontal and vertical directivity in overall directivity indexes, these lobing dips may appear at the same frequency as diffraction dips; as a result, a massive drop in overall directivity appears, followed by a sharp rise. The example below shows a 2-way loudspeaker (6.5-inch woofer + non-waveguided tweeter) with a width of 216 mm and crossover frequency 1600 Hz. The lobing amplifies the diffraction effect.

On the other hand, lobing around x1.5-2 from the initial baffle frequency may help smooth out the directivity rise caused by diffraction. Another example is a 2-way 231 mm-wide bookshelf loudspeaker (6.5-inch woofer + non-waveguided tweeter) with a crossover frequency of 2600 Hz. Here, the lobing levels out the diffraction effect.

Conclusions

An obvious solution is to use full-range / coaxial drivers in rounded/beveled cabinets to eliminate both problems. However, there are not many coaxial drivers with stable on and off-axis behaviour on the market available for small manufacturers or DIY enthusiasts. At the same time, cabinets with significantly rounded or beveled edges require additional material thickness, equipment, costs, and external design compromises.

An additional option is to displace speaker drivers from the baffle center. This way, the diffraction effect from the left and right edges can be divided into different frequencies. To implement this approach, the diameter of the midbass/midrange and tweeter drivers must be significantly smaller than their baffle width.

The tweeter's waveguide may help eliminate the directivity rise after the crossover frequency. Although if the problem of the directivity dip remains the same, the overall directivity index will have an obvious step, which creates a sound power dip in the midrange.

An effective way to achieve smooth directivity in typical simple design loudspeakers is to choose the crossover frequency far enough from the diffraction directivity dip. Even better if this crossover frequency lobing compensates the rising directivity after diffraction frequency, which happens at around x1.5-2 of the baffle width frequency. For example, for a 5-inch woofer and 2-way design speaker with a 0.174 m baffle width, this diffraction directivity dip will appear at 0.5*343/(0.174*0.5)= 1971 Hz. An optimum crossover frequency lies between approximately 3000 and 3500 Hz. This simple rule of thumb may help professionals and enthusiasts prepare more suitable baffle dimensions before building a speaker prototype, or to achieve smoother directivity without making polar measurements.

I would be interested to hear about the reader's personal experience or approach. I am aware that there are some counterarguments; for example, a higher crossover frequency narrows the vertical listening window. So feel free to express your opinion.

 

[Arindal]

Crossover frequency is one of the most important aspects of loudspeaker design, significantly impacting overall performance. Among other factors, a smooth transition of directivity between drivers is crucial for sound quality.

I agree on the importance of crossover frequency, problematic edge diffraction phenomena and importance of directivity in general. But directivity should not only be viewed from the point of smooth transition or steady behavior in terms of increasing or decreasing. It is also important to look at specific windows which are shaping tonality of different phenomena of reflections, like side-wall, floor reflections or late diffuse reverb. And I would say tonal balance between several broad frequency bands (one octave or more) is even more important than just the transition.

In reality, the difference between a 5-inch or a 6.5-inch woofer and a non-waveguided tweeter is not that significant, and using a 2nd order crossover at frequencies between 2000-3000 Hz on an infinite baffle, it is possible to achieve quite a stable transition in the horizontal plane.

It is significant enough in my understanding to create a disbalance between the highest octave the woofer is playing alone, the transitional band, and the lowest octave of the tweeter. With a non-waveguided tweeter, I would personally always opt for smaller midrange cones to have a smooth transition and balance between broader bands alike.

On the other hand, lobing around x1.5-2 from the initial baffle frequency may help smooth out the directivity rise caused by diffraction.

The main problem with lobing is that it is not only affecting the overall d.i., but leading to significant dips in frequency response of the ceiling and floor/desk/console reflections, which is pretty important both for perceived tonality and imaging, while leaving the important side-wall reflections, responsible for localization issues, untouched. A constant d.i. is in general a reasonable goal in my understanding, but not should be achieved by balancing out dips in different windows.

An obvious solution is to use full-range / coaxial drivers in rounded/beveled cabinets to eliminate both problems.

Fullrange drivers in my experience cause more directivity issues than they solve. Even with very small and SPL-limited specimen, directivity index will either skyrocket above a certain frequency threshold, or broader directivity is achieved by non-pistonic movement which on the other hand causes lobing, cancellation and ´phaseyness´ issues. If anyone can name a good compact fullrange driver, it is appreciated.

A coaxial in a non-edged baffle would in theory be ideal, I agree. In the real world, it seems to be pretty difficult to balance competing goals like smooth directivity transition, absence of resonance/cancellation issues and constant directivity at the same time. Many coaxials which look fine on the isobaric graph, tend to narrow down dispersion pretty steeply which I would avoid under any condition. A small (in the region of 4") and shallow midrange coaxial should in theory solve this issue.

So where does this leave us? Anyways, driver diameters and baffle geometry should be always first in my understanding. It is still a mystery to me why so many big midwoofers and non-waveguided tweeters are around, as well as many coaxials with narrowing dispersion or waveguided concepts with severe lobing. A simple combination of 8" + 3" + 1" goes a long way, if done right:

If you want higher directivity index, a smart combination of different strategies to achieve this, seems to be the best strategy. Cardioids seem to be the most popular concept at the moment, but they are far from the only one.

 

[Waveform Fidelity]

Just a bit of anecdotal information from some of my measurements with the KEF UniQ Coaxial driver and selecting crossover frequencies and slopes.

I measured the horizontal beam-widths of both tweeter and mid range unit in the far field and outside in practically free field conditions over a wide frequency range for the frequency range (MLS signal) at 5 degree increments up to +/-85 degree off-axis.

I found 2800-2900Hz is the band where the beam-widths are a close match which coincides with KEF selected crossover range of 2900Hz - they use gradual crossover slopes.

Going lower in frequency the THD of the Tweeter climbs quickly and going higher doesn’t “fully” suppress the MF cone break up (the beam shape collapse at the breakup region too) - these are two additional constraints on the selection of a crossover frequency.

The objective with picking the slopes is to smoothly integrate the overall directivity of the MF/Tweeter. With passive crossovers the constraints are creating the drive signals so that the vector sum of the SPLs from each driver gives a reasonably flat amplitude response and best group delay. Sorry nothing new here.

However, after multiple experiments, using FIR/IIR filters, I found the best solution was to use a LR -48dB/Oct acoustic target and equalize the phase on both drivers to zero (or +-180) phase. With that I got a semaless transition in SPL and zero group delay.

Just a bit of anecdotal info^^ for anyone interested.

BTW with 3D printers its possible for DIY’s to design and create a diffraction ring - using the principle KEF uses in their shadow flare, to direct energy away from sharp cabinet edges.

 

[charlielaub]

I would be interested to hear about the reader's personal experience or approach. I am aware that there are some counterarguments; for example, a higher crossover frequency narrows the vertical listening window. So feel free to express your opinion.

IMO a great way to control directivity is to build a loudspeaker with a dipole radiation characteristic. I have been building some nude dipole projects for this purpose during the last 10 years. Apart from SPL challenges in the low bass I find that a 3-way design can sound excellent and has nearly constant directivity over most of the audio band, without any problematic cabinet diffraction or panel resonances. As it's a multi way design the vertical pattern at the crossover points can break down a bit but I use relatively steep crossover filters to limit the frequency extent of these issues. Because the pattern of each driver alone is a dipole and is not changing with frequency like with boxed systems the overall pattern can be smoother and DI remains more constant. I'm very happy to continue building systems around the nude dipole concept and feel that the imaging can be very impressive over a wide range of listening axes.

 

[Digital_Thor]

Just a bit of anecdotal information from some of my measurements with the KEF UniQ Coaxial driver and selecting crossover frequencies and slopes. Going lower in frequency the THD of the Tweeter climbs quickly and going higher doesn’t “fully” suppress the MF cone break up (the beam shape collapse at the breakup region too) - these are two additional constraints on the selection of a crossover frequency.

Just use the Meta version

 

[Waveform Fidelity]

Where did you obtain those?

 

[Digital_Thor]

Where did you obtain those?

Bought the R3 Meta and took them out...

 

[Digital_Thor]

One is the KEF R3 Meta - vanilla/passive. And the other is my active DIY with the same driver - guess which is which...
The measurements are both gated and going from "on" to "off" axis - 0 to around 80 degrees

 

[Waveform Fidelity]

Do you happen to know the difference in actual performance between meta and non-meta? Ive read all the KEF stuff, but I have never seen yet the raw responses of meta and non-meta comapred - SPLY and phase for example?

 

[Waveform Fidelity]

View attachment 517168
View attachment 517169
One is the KEF R3 Meta - vanilla/passive. And the other is my active DIY with the same driver - guess which is which...
The measurements are both gated and going from "on" to "off" axis - 0 to around 80 degrees

Yep these driver are amazing

 

[Digital_Thor]

Do you happen to know the difference in actual performance between meta and non-meta? Ive read all the KEF stuff, but I have never seen yet the raw responses of meta and non-meta comapred - SPLY and phase for example?

This is the same speaker, same filter and same everything, just Meta vs non-Meta

I could hardly measure an spl difference, but when we blind-tested it, the Meta got picked every time for its superior clarity, which I think is mostly because of the lower distortion and generally just a better and optimized design of the driver.
Though, I would agree a lot with KEF, that a normal R3 non-Meta coax - 2018 version - made active, is a very good sounding driver. Which I've had with great pleasure for more than 2 years... Before I went all Meta.

 

[Waveform Fidelity]

Yes, these steady state, stationary, single amplitude test signals rarely tell the story. Music waveforms contain time varying AM/FM - they have non-stationary stats and a complex electroacoustic device reacts differently to that type of signal. I am not talking about non-linearities per se, but rather the test waveform itself. Many people think of a transfer function of a device as fixed, but, for example, in communications engineering, we treat the transfer function as simply the output response over the input response, and for different inputs different outputs occur.

Anyway, looking at the traces above, my guess is that the Meta version is the blue trace - because the orange impulse response has little ripples (reflections) which meta are claimed to absorb, but I cant be sure those are reflections because the time axis is not shown. I would expect round trip delay to the rear of the tweeter assembly and back to be just 3-6 cm at most so around 10 usec ish from the main impulse. Well thats my off-the cuff reasoning…. I don’t have much insight in to the design which is not public.

So which is the meta trace?

 

[Arindal]

One is the KEF R3 Meta - vanilla/passive. And the other is my active DIY with the same driver - guess which is which...
The measurements are both gated and going from "on" to "off" axis - 0 to around 80 degrees

Thanks, very interesting. Although it is only covering an angle of +-80deg, it shows exemplarily the problem with well-designed coaxials I have been mentioning. They have successfully eliminated cancellation and lobing issues (which usually can be found at higher frequencies in such a coaxial) and achieved a very smooth transition, but almost completely sacrificed constant directivity over several broad frequency bands. Your 80deg measurements show the exemplary steps up in directivity, around 2.2K and 7K.The baffle step as a third one is relevant here as well, and if you take the windows above 90deg into account, this in many cases results in a severely colorated indirect sound field lacking brilliance and treble while being heavy on lower midrange.

In my understanding this is a textbook example of what to avoid in terms of ideal directivity, regardless the crossover frequency.

 

[Digital_Thor]

Yes, these steady state, stationary, single amplitude test signals rarely tell the story. Music waveforms contain time varying AM/FM - they have non-stationary stats and a complex electroacoustic device reacts differently to that type of signal. I am not talking about non-linearities per se, but rather the test waveform itself. Many people think of a transfer function of a device as fixed, but, for example, in communications engineering, we treat the transfer function as simply the output response over the input response, and for different inputs different outputs occur.

Anyway, looking at the traces above, my guess is that the Meta version is the blue trace - because the orange impulse response has little ripples (reflections) which meta are claimed to absorb, but I cant be sure those are reflections because the time axis is not shown. I would expect round trip delay to the rear of the tweeter assembly and back to be just 3-6 cm at most so around 10 usec ish from the main impulse. Well thats my off-the cuff reasoning…. I don’t have much insight in to the design which is not public.

So which is the meta trace?

The orange is the Meta - the peak at 38kHz is even lower. I agree with the developers at KEF, that when you lower distortion, you no longer feel the same need to turn down like before, because the sound is clearer and sounds better.

 

[Digital_Thor]

Thanks, very interesting. Although it is only covering an angle of +-80deg, it shows exemplarily the problem with well-designed coaxials I have been mentioning. They have successfully eliminated cancellation and lobing issues (which usually can be found at higher frequencies in such a coaxial) and achieved a very smooth transition, but almost completely sacrificed constant directivity over several broad frequency bands. Your 80deg measurements show the exemplary steps up in directivity, around 2.2K and 7K.The baffle step as a third one is relevant here as well, and if you take the windows above 90deg into account, this in many cases results in a severely colorated indirect sound field lacking brilliance and treble while being heavy on lower midrange.

In my understanding this is a textbook example of what to avoid in terms of ideal directivity, regardless the crossover frequency.

I did it quickly, mostly to ensure that levels were matched, before I did a blind test with a friend, to see if we could actually identify the Meta each time - we could.
Usually when there's added detail and clearer sound, it's just a higher level - essentially cheating myself. But here, there's no added sibilance, harshness or anything like these classical hifi-terms. Just played "Just a friend of mine" by Vaya con dios, and the "space" or "air" is very clearly there + her voice is just there... very crisp and clear - yet never "aggressive" - It just sounds darn good!
Actually, I just aim for the - not perfect - but smooth performer, and I think I love this one

 

[Penelinfi]

Fullrange drivers in my experience cause more directivity issues than they solve. Even with very small and SPL-limited specimen, directivity index will either skyrocket above a certain frequency threshold, or broader directivity is achieved by non-pistonic movement which on the other hand causes lobing, cancellation and ´phaseyness´ issues. If anyone can name a good compact fullrange driver, it is appreciated.

Mark Audio has some interesting drivers, eg Alpair 7ms . Still rolls of from around 5khz though would be less than many other drivers.

Another option would be to use a "full range" driver that can play high and low enough so that you only need more dedicated woofer and simple tweeter.

 

[Waveform Fidelity]

The orange is the Meta - the peak at 38kHz is even lower. I agree with the developers at KEF, that when you lower distortion, you no longer feel the same need to turn down like before, because the sound is clearer and sounds better.

Oh, the orange trace surprising! Well it was a 50/50 guess.
I have considered swapping out the SP1632 with a later UNIQ version, but I can’t find any detailed drawing/measurements to see if newer versions of the UNIQ have the same baffle opening and driver depth etc. The later versions also have the shadow flare ring.

If i gave you the dimensions of my SP1632, would you mind measuring your R3 Meta driver flange and bolt pattern for me?

Current my speakers are wired with an 6 pol cam switch which allows me to select OEM passive or Active connection through the Neutrik connector you can see in the photo. So the meta driver might not play well with the OEM passive crossover, but I could live with that, if the response change is not too large.

 

[Waveform Fidelity]

Thanks, very interesting. Although it is only covering an angle of +-80deg, it shows exemplarily the problem with well-designed coaxials I have been mentioning. They have successfully eliminated cancellation and lobing issues (which usually can be found at higher frequencies in such a coaxial) and achieved a very smooth transition, but almost completely sacrificed constant directivity over several broad frequency bands. Your 80deg measurements show the exemplary steps up in directivity, around 2.2K and 7K.The baffle step as a third one is relevant here as well, and if you take the windows above 90deg into account, this in many cases results in a severely colorated indirect sound field lacking brilliance and treble while being heavy on lower midrange.

In my understanding this is a textbook example of what to avoid in terms of ideal directivity, regardless the crossover frequency.

Hi Arindal,

I guess I am missing something here, but the theory for a rigid piston is that D/lambda sets the beam-width, so higher frequencies the beam width shrinks. KEF developed the tangerine waveguide (aka phase plug) along with the MF cone shape to broaden the beam width at higher frequencies. The directive index figures published provide evidence that this goal has been achieved in practice. Not perfect, but very good, in my opinion

How would one theoretically reach a constant directivity from a diaphragm driver, without crossing over to a super tweeter (smaller d)

Many thanks

 

[Digital_Thor]

If i gave you the dimensions of my SP1632, would you mind measuring your R3 Meta driver flange and bolt pattern for me?

Sure, we can also make a dedicated thread and share measuremens if you want, I'm game

 

[Waveform Fidelity]

Thank you, I’ll do that tomorrow - its late evening here in San Diego