Understanding Directivity Error in the Measurements

[Trdat]

I would like to understand how to interpret a directivity error from the measurements and most importantly what exactly is a directivity error?

Am I right in understanding that its a mismatch between a conformed controlled dispersion between the two different frequency ranges at one point throuought the spectrum? Or particularly at the crossover region...?

Secondly, Amir points it out on the graph but what am I looking at exactly and is the measurment tellling me what the error is or I can only identify it...? To be honest, I do not even know what the bottom red line on the graph is.

 

[fluid]

The orange line at the bottom of the graph is the Sound Power Directivity index (SPDI) shown in db's with 0 being at 40dB on the graph and 10dB at 50dB. The blue dotted line is the Early Reflections DI (ERDI).

Explanation of the difference between the two from the standard
"Sound Power Directivity Index (SPDI) For the purposes of this standard the Sound Power Directivity Index is defined as the difference between the listening window curve and the sound power curve. An SPDI of 0 dB indicates omnidirectional radiation. The larger the SPDI, the more directional the loudspeaker is in the direction of the reference axis. Early Reflections Directivity Index (ERDI) The Early Reflections Directivity Index is defined as the difference between the listening window curve and the early reflections curve"

In the graph above the woofer is becoming more directional as frequency rises and the tweeter is becoming less directional from 3K down. The directivities do not match at the crossover point which is where the directivity error comes from. A peak in the DI shows as a dip in the off axis responses, matched directivity is nice but isn't easy to get in every form factor, the bump in DI being better than a dip where there will be an off axis peak.

 

[Trdat]

Your explanation was relatively simple I need to absorb it. But I will need a longer look at the difference in the standards.

A peak in the DI shows as a dip in the off axis responses,

I think this explains it well.

 

[TurtlePaul]

First thing you need to understand is the three lines up top. The black line, on-axis response, is relatively obvious. The blue line, the early reflections, is the predicted frequency characteristic of the sounds which are not direct sounds, but rather reflected to the listener in the first few miliseconds. This time component is important because our brain can clearly separate out sound which arrives in the first few milliseconds as the signal while later arriving echos are filtered out. Because we assume you are directly on axis, and most speakers have falling treble as you go off axis, the top blue line tends to fall over time. The top red dashed line is similar to the blue but is total sound power and not time gated.

The bottom 'directivity' lines are simply the on-axis response minus the listening window or sound power lines. The steeper they slope up, the narrower the directivity of the speaker and the steeper you would expect the in-room response line to be for a speaker which measures flat on-axis. If you EQ a speaker, you shift all three top lines up or down, but the bottom lines don't change - they are characteristic of the speaker.

 

[f1shb0n3]

I would suggest to check out Erin's videos explaining speaker measurements, directivity, etc. He has a talent for explaining complex topics in a simple way and has improved my understanding of the topic significantly.

 

[fluid]

The blue line, the early reflections, is the predicted frequency characteristic of the sounds which are not direct sounds, but rather reflected to the listener in the first few miliseconds. This time component is important because our brain can clearly separate out sound which arrives in the first few milliseconds as the signal while later arriving echos are filtered out.

The early reflections curve is meant to be representative of the first bounce reflections. The amount of time it takes for these to arrive depends entirely on the distance to the wall.

The top red dashed line is similar to the blue but is total sound power and not time gated.

There is no time gating involved.

The bottom 'directivity' lines are simply the on-axis response minus the listening window or sound power lines.

This is not quite right. In the CTA 2034 standard there are two basic DI curves SPDI and ERDI. Both use the listening window to represent the direct sound and either minus the sound power or early reflections curve from it to generate the DI.

Historically the DI was on axis minus sound power, but CTA2034 defines it differently as above.

A good general purpose spinorama explanation can also be found here from Sausolito Audio
https://www.sausalitoaudio.com/wp-content/uploads/2018/07/Interpreting-Spinorama-Charts.pdf

 

[Trdat]

First thing you need to understand is the three lines up top. The black line, on-axis response, is relatively obvious. The blue line, the early reflections, is the predicted frequency characteristic of the sounds which are not direct sounds,

Got the first two lines. Thanks.

but rather reflected to the listener in the first few miliseconds. This time component is important because our brain can clearly separate out sound which arrives in the first few milliseconds as the signal while later arriving echos are filtered out.

This is an interesting pshycoacoustic principal.

Because we assume you are directly on axis, and most speakers have falling treble as you go off axis, the top blue line tends to fall over time. The top red dashed line is similar to the blue but is total sound power and not time gated.

The top red line I still don't get 100% but it will come.

The bottom 'directivity' lines are simply the on-axis response minus the listening window or sound power lines. The steeper they slope up, the narrower the directivity of the speaker and the steeper you would expect the in-room response line to be for a speaker which measures flat on-axis. If you EQ a speaker, you shift all three top lines up or down, but the bottom lines don't change - they are characteristic of the speaker.

So the bottom directivity line pretty much needs to be consistently rising, any bump shows that the speaker has beamed or narrowed and then later widened again with its dispersion before narrowing again. The idea is to have smooth narrowing of the dispersion or a consistent rising line.

Im still baffled on why its so hard for major companies to achieve such a goal.

 

[Trdat]

The orange line at the bottom of the graph is the Sound Power Directivity index (SPDI) shown in db's with 0 being at 40dB on the graph and 10dB at 50dB. The blue dotted line is the Early Reflections DI (ERDI).

Explanation of the difference between the two from the standard
"Sound Power Directivity Index (SPDI) For the purposes of this standard the Sound Power Directivity Index is defined as the difference between the listening window curve and the sound power curve. An SPDI of 0 dB indicates omnidirectional radiation. The larger the SPDI, the more directional the loudspeaker is in the direction of the reference axis. Early Reflections Directivity Index (ERDI) The Early Reflections Directivity Index is defined as the difference between the listening window curve and the early reflections curve"

This explanation is actually quite good.

In the graph above the woofer is becoming more directional as frequency rises and the tweeter is becoming less directional from 3K down. The directivities do not match at the crossover point which is where the directivity error comes from. A peak in the DI shows as a dip in the off axis responses, matched directivity is nice but isn't easy to get in every form factor, the bump in DI being better than a dip where there will be an off axis peak.

Here I am just a little confused about how a dip in the off axis relates to a the bump in the directivity line? Firstly the above graph doesn't really have an off axis does it? The second line is the predicted in room reflection so are we looking at another graph?

 

[fluid]

Here I am just a little confused about how a dip in the off axis relates to a the bump in the directivity line? Firstly the above graph doesn't really have an off axis does it? The second line is the predicted in room reflection so are we looking at another graph?

When the DI rises the speaker is becoming more directional, that means there is less off axis energy at that point which is why there is a dip in the off axis responses at the same frequencies.

If you compare the on axis, listening window, early reflections and sound power lines they all dip down where the DI rises but as you move from on axis to sound power the dip gets wider and deeper as more off axis energy is included in the measurements as they move down.

There is no predicted in room response (PIR) in that graph in post #1 but it will resemble the early reflections curve with progressively more sound power as frequency goes down. The legend in the graph explains which line is which.

 

[Dennis Murphy]

So the bottom directivity line pretty much needs to be consistently rising, any bump shows that the speaker has beamed or narrowed and then later widened again with its dispersion before narrowing again. The idea is to have smooth narrowing of the dispersion or a consistent rising line.

Im still baffled on why its so hard for major companies to achieve such a goal.

Because, speaking as a very minor company, there can be a trade-off between carefully controlled directivity and dispersion, particularly in 2-ways. I personally prefer the sound of a speaker that combines a linear on-axis and listening window response with broad horizontal dispersion, even if that means living with a directivity mismatch at the crossover point that causes a dip in the reflected sound profile. Compared with a well-regarded 2-way wave-guide design that I tested a few months ago, the sound is more spacious and resolves upper midrange, lower treble detail better. Not everyone would agree, and the results will be dependent on the choice of program material, but I think the design approach I've taken with the Affordable Accuracy 2-way is defensible, and I have no desire to change it. With 3-ways, it's possible with the right choice of drivers and crossover points to achieve not only a smooth directivity plot, but also a nearly flat one, which in my experience is the best of both worlds.

 

[fluid]

This is an interesting pshycoacoustic principal.

6ms and 10ms are normally the figures quoted where reflections are heard as separate events that are perceived as room sound, and reflections below that are fused into the direct sound modifying the timbre of it.

The top red line I still don't get 100% but it will come.

The top red line is sound power which is every angle measured horizontally and vertically averaged together.

So the bottom directivity line pretty much needs to be consistently rising, any bump shows that the speaker has beamed or narrowed and then later widened again with its dispersion before narrowing again. The idea is to have smooth narrowing of the dispersion or a consistent rising line.

Im still baffled on why its so hard for major companies to achieve such a goal.

It is not quite that simple. CTA2034 includes the vertical and horizontal responses with equal weighting but it is the horizontal response that dominates perception particularly when the listening height is fixed. You have to be careful in looking at an overall DI change without considering the direction it came from. Lipshitz and Vanderkooy did research a long time ago that demonstrated that dips and holes in the power response were not very audible even up to 12dB but that a peak in the power response was heard very clearly.

There is argument as to whether the best directivity is flat or rising but the smoother it is the better as long as something else hasn't been traded away to get it that might be more audible as in Dennis's example.

Cost and size constraints are the reason why manufacturers struggle with the right balance.

 

[Trdat]

Because, speaking as a very minor company, there can be a trade-off between carefully controlled directivity and dispersion, particularly in 2-ways.

I get this, I suppose there is always trade-offs.

I personally prefer the sound of a speaker that combines a linear on-axis and listening window response with broad horizontal dispersion, even if that means living with a directivity mismatch at the crossover point that causes a dip in the reflected sound profile. Compared with a well-regarded 2-way wave-guide design that I tested a few months ago, the sound is more spacious and resolves upper midrange, lower treble detail better.

So your saying usually, the trade off in 2 ways or at least in this variable, is usually based between having controlled dispersion which will lack the broad horizontal dispersion and better on axis response vs the better on axis response and a wider dispersion which might have a mismatch in directivity around the crossover region? But isn't this basically waveguide or no waveguide...?

 

[TurtlePaul]

So your saying usually, the trade off in 2 ways or at least in this variable, is usually based between having controlled dispersion which will lack the broad horizontal dispersion and better on axis response vs the better on axis response and a wider dispersion which might have a mismatch in directivity around the crossover region? But isn't this basically waveguide or no waveguide...?

There is not necessarily a compromise in on-axis response. It is simply the trade for perfectly linear off-axis response vs. a wider response. The primary trade is that there are speakers which have"textbook" linear directivity but are narrow, which Dennis would not prefer for his designs. Other speakers which seem to follow Dennis' philosophy include Revel speakers. Note that both can have a waveguide. In addition to the depth of any waveguide, crossover frequency and woofer size also heavily influence this variable.

For example look at the directivity of the M106 vs. the Directiva. Dennis' philosophy would probably prefer the M106 which is wider than the directiva but with more directivity mismatch. The Directiva has 4-5 dB of early reflections directivity roll-off between 2-4 khz (where our hearing is very sensitive) while the M106 has 2-3 dB roll-off of early reflections, but with more directivity error, in the same range. The M106 doesn't approach 4 dB of early reflections roll-off until 10 kHz.

 

[Trdat]

6ms and 10ms are normally the figures quoted where reflections are heard as separate events that are perceived as room sound, and reflections below that are fused into the direct sound modifying the timbre of it

The top red line is sound power which is every angle measured horizontally and vertically averaged together.

There is argument as to whether the best directivity is flat or rising but the smoother it is the better as long as something else hasn't been traded away to get it that might be more audible as in Dennis's example.

Cost and size constraints are the reason why manufacturers struggle with the right balance.

Thanks for this, great info. The 6ms to 10 ms I have read into quite a bit and now see how it fits into the klippel graphs.

And now I get the red line.

 

[fineMen]

Thanks for this, great info. The 6ms to 10 ms I have read into quite a bit and now see how it fits into the klippel graphs.

I'm not sure if "the red line" relates to these time values. or how these are taken into account by the Klippel algorithms.
The so called Haas effect is described in detail, me hopes, there:

It's About Time... The Effective Haas Effect

To implement the Haas Effect, understanding the theory is a must. Dale Shirk explains the theory and ways to implement it.

www.prosoundtraining.com

I personally always had other values in mind.

 

[Trdat]

There is no compromise in on-axis response. It is simply the trade for perfectly linear off-axis response vs. a wider response. The primary trade is that there are speakers which have"textbook" linear directivity but are narrow, which Dennis would not prefer for his designs. Other speakers which seem to follow Dennis' philosophy include Revel speakers. Note that both can have a waveguide. In addition to the depth of any waveguide, crossover frequency and woofer size also heavily influence this variable.

My mistake when I said waveguide or no waveguide, you can technically have a wide dispersion speaker with a waveguide. But let me try and rephrase again to see if I understood this, a perfect linear off-axis response will usually equate to a narrower dispersion which is what Dennis doesn't prefer. While a wider reponse might trade for a mismatch in directivity for a wider horizontal coverage which is what Dennis prefers and the Revels although with a waveguide are an example of this?

For example look at the directivity of the M106 vs. the Directiva. Dennis' philosophy would probably prefer the M106 which is wider than the directiva but with more directivity mismatch. The Directiva has 4-5 dB of early reflections directivity roll-off between 2-4 khz while the M106 has 2-3 dB roll-off of early reflections, but with more directivity error, in the same range. The M106 doesn't approach 4 dB of early reflections roll-off until 10 kHz.

I can hazard a guess that Directiva has a narrower dispersion compared to the Revel but what on the graph depicts the wider dispersion? Sorry if the answer is somehwere above in the comments.

Also, does a mismatch in the directivity cause non linear behaviour in the off axis response or different things?

So the Revel for arguments sake, has traded off the perfect off axis response with a slight direcivity mismatch(or are both of these the same thing hence my question above) to get more horizontal dispersion and this is a preference compared to a more linear directivity which yields a narrower dispersion, I think I repeated myself but I got it right?

 

[fineMen]

... has traded off the perfect off axis response with a slight direcivity mismatch ...

... because of a trade off in production cost and development cost and time to market cost.

The technique for perfect (!!) dispersion is at hand, really. Don't be fooled by business men who want to sell You a cheap compromise.

 

[Dennis Murphy]

... because of a trade off in production cost and development cost and time to market cost.

The technique for perfect (!!) dispersion is at hand, really. Don't be fooled by business men who want to sell You a cheap compromise.

?

 

[fineMen]

... because of a trade off in production cost and development cost and time to market cost.

The technique for perfect (!!) dispersion is at hand, really. Don't be fooled by business men who want to sell You a cheap compromise.

?

Genelec 8351B Review (Studio Monitor)

This is a review and detailed measurements of the Genelec 8351B powered monitors (speakers). It was purchased used by a member and kindly drop shipped to me for testing. They cost US $3,995 each. The 8351 is a thee-way speakers with the bass drivers hidden beyond the front baffle...

www.audiosciencereview.com

 

[TurtlePaul]

Genelec 8351B Review (Studio Monitor)

This is a review and detailed measurements of the Genelec 8351B powered monitors (speakers). It was purchased used by a member and kindly drop shipped to me for testing. They cost US $3,995 each. The 8351 is a thee-way speakers with the bass drivers hidden beyond the front baffle...

www.audiosciencereview.com

It has already been established that 3-ways allow you to get the best of all worlds.

Making a 3-way isn't extra development cost or time to market. Making a 3-way is simply more expensive in BOM costs and has a size trade off (you need cabinet volume for a midrange chamber and space on the baffle for the drivers). There is a (large) market for speakers which aren't large enough or expensive enough to be true 3-ways.