Numerical Solving Techniques for Optimum Crossover Design
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 Multi-Way Conventional loudspeakers with crossovers

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 20th May 2009, 09:38 PM #1 thadman   diyAudio Member   Join Date: Dec 2005 Location: west lafayette Numerical Solving Techniques for Optimum Crossover Design 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 __________________ "It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."
 20th May 2009, 10:56 PM #2 Ron E   diyAudio Member     Join Date: Jun 2002 Location: USA, MN I like your thinking. I made a big spreadsheet in Excel (yeah I know, Matlab is better but Excel was the hammer I had and I have pounded a lot of nails with it) that calculated a large circuit capable of analyzing a wide variety of xo circuits. I then measured some drivers and input their axial (only) response into the spreadsheet,. I gave the program some starting values for circuit elements and tried a number of goal functions. I ended up with a ~2nd order circuit that gave a reasonably flat on axis response and a fairly weak reverse null. I built it and it sounded initially OK, better in many ways than a lot of speakers, but there was some excess in energy in the presence region that became fatiguing after a while. Your method, using the polar response, should improve on mine. It leaves out listening, however. You may need to try a few different goal functions before attaining a true "optimum", if there is such a thing in the realm of audio. __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Armaments, universal debt, and planned obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley
 21st May 2009, 02:03 AM #3 JoshK   diyAudio Member   Join Date: May 2004 Location: Toronto, ON I am having a hard time seeing why the genetic algorithm is needed in this case. Granted my knowledge of GAs is cursory, but it seems like a simple grid search would be sufficient since there is a reasonably small finite set of options. You can go crazy to completely smooth out the FR (or in this case PR) but this would end up with a complicated crossover that would be expensive, likely sound bad and could give some amps fits. Seems like there might be an easier way to do the optimization through simple heuristics combined with some penalty functions for say excessive group delay, large phase angle, too low of a min impedance, etc.
 21st May 2009, 02:30 AM #4 pblossom   diyAudio Member   Join Date: Jan 2004 Location: Michigan You'll have a large number of variables in your error function. Every 5 degrees over 360 degrees is 72*72=5184, multiply that times a number of discrete frequencies, say 30, and you have over 150,000 variables in your error function. GA's would probably work. I used tabu search and simulated annealing in my dissertation which used over 39,000 variables. SA worked the best. You will have to calculate the response and phase of the combined crossover network and driver - cabinet combination for both drivers for some number of frequencies around the crossover frequency. My experience is that coding SA or GA is not much harder than coding a grid search, and either probably works better. YMMV. __________________ The human capacity for self delusion is nearly infinite.
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Quote:
 Originally posted by JoshK I am having a hard time seeing why the genetic algorithm is needed in this case. Granted my knowledge of GAs is cursory, but it seems like a simple grid search would be sufficient since there is a reasonably small finite set of options. You can go crazy to completely smooth out the FR (or in this case PR) but this would end up with a complicated crossover that would be expensive, likely sound bad and could give some amps fits. Seems like there might be an easier way to do the optimization through simple heuristics combined with some penalty functions for say excessive group delay, large phase angle, too low of a min impedance, etc.
A genetic algorithm allows for the optimization of both radiation profile as well as distortion/compression profile. In this regard, I believe its complexity may be justified because it optimizes several interdependent variables simultaneously.

distortion/compression vs frequency measurements could 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.
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 21st May 2009, 05:29 AM #6 planet10   frugal-phile(tm) diyAudio Moderator     Join Date: Oct 2001 Location: Victoria, BC, NA, Sol III I believe that the software Dan Wiggins wrote to his cross-over optimization of similar bent. dave __________________ community sites t-linespeakers.org, frugal-horn.com, frugal-phile.com ........ commercial site planet10-HiFi p10-hifi forum here at diyA

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