Numerical Solving Techniques for Optimum Crossover Design

[thadman]

I've been contemplating an optimum method to achieve synergy between drivers in a loudspeaker. We obviously need crossovers to transition between drivers, but what techniques can we use to optimize the crossover filter so that radiated energy is as uniform as possible throughout the crossover region whilst simultaneously staying within the mechanical/thermal limits of the drivers used at the desire output levels?

A possible method I've deduced is first constructing the optimal enclosure(s) for each driver over its particular passband, followed by measuring each individual driver in its enclosure on the listening axis. We would then measure the radiated energy at specific intervals over its axis, 5* may be sufficient (the interval is arbitrary, Dr. Geddes measured the Summa's radiated energy in increments of 5*). We would do this in both the horizontal and vertical planes and once we reached a complete data set (360*) we would import this data into a computational software package such as matlab and connect all of the data points with a spline curve so that we achieve a function that attempts to describe the loudspeakers amplitude response vs angle.

Once this information has been gathered, a genetic algorithm may be implemented that uses this information.

http://en.wikipedia.org/wiki/Genetic_algorithm

The bandwidth (amplitude >-40dB) for each driver could be subdivided into individual values that represent amplitude at a particular frequency. Each of these individual values would represent a specific location on the chromosome of the genetic algorithm. To create the curve we would decompose the chromosome into its constituent values and once again connect these points with a spline curve.

To achieve the total loudspeaker response, we would sum all of the individual drivers and evaluate the performance of the chromosome based on how uniform the radiated energy was throughout the crossover region and place penalties on crossovers that imposed excess mechanical/thermal stress on the drivers.

Is this a good solution to the crossover optimization problem or are there better techniques?

Thanks,
Thadman

[fjhuerta]

That sounds interesting (although 90% flew over my head).

One question - shouldn't non-linear distortions be considered in order to arrive at the optimum answer, too?

[thadman]

That sounds interesting (although 90% flew over my head).

One question - shouldn't non-linear distortions be considered in order to arrive at the optimum answer, too?

non-linear distortion/compression/etc can be regarded as mechanical/thermal stress, where appropriate penalties can be placed as I had suggested.

[augerpro]

The hard part is defining what the ideal energy curve (or power response) looks like for a complete sphere of sound radiation. What do people like? The best answer I've seen so far is brief description in Toole's book about the standard developed by Sean Olive at Harman. I was *just* looking for some documentation from Olive about this, I hope it's not proprietary.

In that same vein not all angles of radiation are important to look at. How would you weight them?

Very interesting idea, not sure how this would end up differing from a typical optimizer, except for analyzing the driver limits maybe?

[JonMarsh]

I've been contemplating an optimum method to achieve synergy between drivers in a loudspeaker. We obviously need crossovers to transition between drivers, but what techniques can we use to optimize the crossover filter so that radiated energy is as uniform as possible throughout the crossover region whilst simultaneously staying within the mechanical/thermal limits of the drivers used at the desire output levels?


To achieve the total loudspeaker response, we would sum all of the individual drivers and evaluate the performance of the chromosome based on how uniform the radiated energy was throughout the crossover region and place penalties on crossovers that imposed excess mechanical/thermal stress on the drivers.

Is this a good solution to the crossover optimization problem or are there better techniques?

Thanks,
Thadman

These are all solid ideas, but may involve an unnecessarily complex approach to getting what is needed. And determining the best answer probably deserves two stages- one, analyzing ideal target transfer functions, and how well they meet these criteria, including the stress load on the drivers (which would usually tend to rule out running drivers in phase quadrature, something common in standard constant power networks, but somewhat out of favor with current all pass approaches- but very useful as Curt C will testify in optimizing the behavior of the Statements) and which is done to a certain degree even in the NeoD CC.

Then, there's the consideration of the driver selection, baffle type and size, etc, how that relates to the overall performance.

You see, if you follow the physics and let function dictate form, then speaker design tends to converge, for given types- for example, for three way dipole speakers with conventionally available drivers, an optimization for size and bandwidth will tend to seek out an optimized solution- so, for instance, they'll tend to look a lot like an Orion by the the time they're done, UNLESS an arbitrary decision is made in the process that then requires fitting to that anomaly.

Another comment, considering how circular drivers work, and how typical room layouts and listening positions are used, the same detail in vertical measurements as in horizontal are probably unnecessary.

Last, since you only have one feed to the drivers, there are simpler ways to get a good averaged data target to use for the target, as it's probably a fairly valid assumption that designing for the smoothest, mostly flat power response in the forward +/- 30 degree angle may give the best overall compromise; measuring and doing this is pretty straightforward, using my current tools and turntable test system.

And that's what I'm doing in my current projects.

~Jon

[thadman]

Another comment, considering how circular drivers work, and how typical room layouts and listening positions are used, the same detail in vertical measurements as in horizontal are probably unnecessary.


~Jon

This neglects the inclusion of non-cylindrical drivers, ie ribbons/planars.

[thadman]

Very interesting idea, not sure how this would end up differing from a typical optimizer, except for analyzing the driver limits maybe?

distortion/compression vs frequency measurements could also be taken at the desired output levels and incorporated into the genetic algorithm (we now have a multiobjective genetic algorithm). Penalties could corresponding be applied to those that violate our criteria.

For example, as long as distortion components/compression were appreciably low in level we would ignore that aspect of the design. For this discussion lets assume our criteria for distortion products is -40dB.

If a system whose distortion profile was below our -40dB criteria at our desired output level, radiation profile would solely be considered for ranking individuals in the population. However, if a system exceeded our distortion criteria, penalties could be implemented that gave favorable ranking to systems in the population that exhibited a good radiation profile whilst meeting our distortion criteria and unfavorable ranking to systems in the population that while exhibiting a good radiation profile, violated our distortion criteria. In this way our population would evolve by avoiding systems that place unnecessary mechanical/thermal stress on the constituent drivers.

[JonMarsh]

This neglects the inclusion of non-cylindrical drivers, ie ribbons/planars.

True, but that's a special case where you MUST make the driver the full height of the listening window, and in that case the driver output is rather consistent for the entire height anyway.

[Dennis H]

These are all solid ideas, but may involve an unnecessarily complex approach to getting what is needed.

Bingo! My experience in trying to use neural nets, etc. to analyze data in another field (predicting the stock market) is that they just aren't smart enough to figure out what to use and what to ignore. If you know enough to constrain the software to what's really important, you also know enough to figure it out without the fancy software and simpler tools work as well or better.

[---k---]

Bingo! My experience in trying to use neural nets, etc. to analyze data in another field (predicting the stock market) is that they just aren't smart enough to figure out what to use and what to ignore. If you know enough to constrain the software to what's really important, you also know enough to figure it out without the fancy software and simpler tools work as well or better.

A friend of mine in grad school, his PhD thesis was to be on using neural nets to predict traffic flow. Even with the resources of a powerful computer cluster and a top 10 engineering university, it was eventually abandoned due to the similar conclusions.

seams like a lot of mental masturbation.

[JoshK]

GAs are inherently more suited to such a problem then NNs. I am not a fan of NNs cause I've never seen an actual good use for them. Predicting the stock market with them has been done to death. It was particularly in fashion in the '80s and then abandoned by the majority of practitioners.

Still the idea of using a GA has some merits, but these procedures, IMO, are only as good as your constraints and heuristics. That is essentially what Jon Marsh and Dennis said. Without good constraints you'll get non-sensical answers. Once the constraints have been hammered out, you'll likely get an answer you didn't need the process to tell you.

[dwk]

While I'm intrigued by the geek factor of this idea, I have to agree with the consensus that given our current level of psychoacoustic understanding, it's a pretty low-value proposition. This should be evident even from the way thadman phrased his original post. He assumes that we already have
- a system topology (2-way, 3-way etc)
- specific drivers chosen
- specific cabinets chosen and built
- complete measurements available

Really, what's left? Xover points and slopes, which are going go be very highly constrained by these choices anyway; even more, without further constraints on the slopes, you may well end up with brick-wall transfer functions being considered optimal.

Academically, it may be interesting to speculate on which pieces of the audio design problem might be aided by this approach. I wonder whether 'baffle design and layout' might be a more interesting application. The math used in the Baffle Diffraction Simulator for example seems reasonably solid; wrapping some form of a GA/optimization search around sizing of the baffle and placement of the drivers may actually generate some results that if not impossible to arrive at directly at least wouldn't be as obvious as xover points.

[thadman]

While I'm intrigued by the geek factor of this idea, I have to agree with the consensus that given our current level of psychoacoustic understanding, it's a pretty low-value proposition. This should be evident even from the way thadman phrased his original post. He assumes that we already have
- a system topology (2-way, 3-way etc)
- specific drivers chosen
- specific cabinets chosen and built
- complete measurements available

Really, what's left? Xover points and slopes, which are going go be very highly constrained by these choices anyway; even more, without further constraints on the slopes, you may well end up with brick-wall transfer functions being considered optimal.

What about optimizing the distribution of energy in an array so that it emulates a point source while using the least displacement? From a physics perspective, as long as the length of the line is <1/4 wavelength for all frequencies being reproduced it can be assumed to be omnidirectional.

Let's assume we have a line of finite length and we restrict our radiation analysis to one dimension (length, we will assume the distribution of energy in the width dimension is uniform).

How would you go about determining the segmentation of the line (ie a 48" line could be divided into 2 15" sections, 2 6" sections, 2 2.5" sections, and 1 1" section) and the electrical filters that dictate how the sections interact so that only a particular length of the line is reproducing a frequency of given wavelength?

Anybody got any ideas?

[thadman]

After a little bit of thinking, it appears the problem is easier than I initially expected it to be.

Intuitively, we divide our bandwidth by however many sections we determine as appropriate (ie if we're going 6 channel active, divide each line into 3 sections). We then restrict (with theoretical brickwall filters) each particular section so that the total radiating length does not exceed our criteria (ex. 1/4 wavelength) at a given frequency. We do this by progressively adding the exterior sections.

We can now focus on the crossover slope as length and position have already been dictated. By allowing sections that exceed our length criteria to operate, we are increasing the on-axis to power response energy ratio. We would seek the shallowest slope that lies within our power response goals. Slopes could be evaluated based on the integral of the power response, with higher being better (assumes we are aiming for omni).

What needs to be determined is how much of a shift is audible? We certainly wish to avoid any aberrations in the +/-30* window, but beyond that? How much energy can we lose at the sides before we start to get into trouble?