White Paper: Phase Issues and Crossover Considerations in Loudspeakers

[CharlieLaub]

I have recently done some modeling of crossovers, looking at phase related issues. I decided to share some of my findings by writing up a white paper. The attached pdf,

"A Consideration of Phase in Loudspeaker Design:
A study of sources of phase and their influence on the on-axis and off-axis
frequency response in the crossover region of a two-way loudspeaker"

can be downloaded from my web site by clicking on the title above.

I used a point-source model of a two driver (e.g. midwoofer and tweeter) loudspeaker. The drivers are described by their vertical (y-coordinate) offset in the baffle plane, and the difference their horizontal (z-coordinate) offset, of their acoustic centers. Each driver is modeled as a second order high-pass filter, e.g. a driver in a sealed box.

The influence of the offsets, and some aspects of analog delay design are covered. The influence of the tweeter phase in the crossover region, and how to fix the response problems that this can create, are covered at the end of the paper.

This is just a limited study, but brings up some interesting issues. I hope that this is informative, and starts some discussion of the topic.

-Charlie

[Helmuth]

Originally Posted by CharlieLaub

I have recently done some modeling of crossovers, looking at phase related issues. I decided to share some of my findings by writing up a white paper. The attached pdf,

"A Consideration of Phase in Loudspeaker Design:
A study of sources of phase and their influence on the on-axis and off-axis
frequency response in the crossover region of a two-way loudspeaker"

can be downloaded from my web site by clicking on the title above.

I used a point-source model of a two driver (e.g. midwoofer and tweeter) loudspeaker. The drivers are described by their vertical (y-coordinate) offset in the baffle plane, and the difference their horizontal (z-coordinate) offset, of their acoustic centers. Each driver is modeled as a second order high-pass filter, e.g. a driver in a sealed box.

The influence of the offsets, and some aspects of analog delay design are covered. The influence of the tweeter phase in the crossover region, and how to fix the response problems that this can create, are covered at the end of the paper.

This is just a limited study, but brings up some interesting issues. I hope that this is informative, and starts some discussion of the topic.

-Charlie

Impressive work Charlie,

I just took a quick look Charlie I have to take more time to get a overview. I hoped to see a concrete conclusion about what outcome is best filter solution.

[pooge]

I haven't read the paper yet, but as further info, you may want to read this paper, and especially reference 7 in the references cited at the end of the paper.

http://users.ece.gatech.edu/~mleach/papers/LinkRyl.pdf

[CharlieLaub]

Originally Posted by pooge

I haven't read the paper yet, but as further info, you may want to read this paper, and especially reference 7 in the references cited at the end of the paper.

http://users.ece.gatech.edu/~mleach/papers/LinkRyl.pdf

Ah, it seems that one can not do work that hasn't already been done before when it comes to loudspeakers! Thanks for bringing that Leach paper to my attention. It addresses some of the same things that I do, with respect to the driver's phase response and integrating the driver response in to the crossover. I know that is not a new concept, and I wasn't trying to make that case, but I wasn't aware of Leach's work. I will look in to REF#7 as well.

-Charlie

[Alex Copeland]

Originally Posted by CharlieLaub

These effects can be mitigated by:

(1) minimizing the vertical driver spacing
(2) compensating for the time delay caused by a non-zero z-offset between the drivers by:
a. delaying the tweeter using an analog or digital delay network, or
b. choosing the crossover frequency so that the z-offset is exactly 0.5 wavelength at that frequency
(3) removing the influence of the tweeter’s own phase response by transforming it’s low frequency behavior so
that it acts as one of the second order crossover stages. This can be accomplished with a biquadratic transfer

function filter such as the Linkwitz transform.

You forgot to mention the optimum mitigation - Achieve Correct Mechanical Time-Alignment.

[CharlieLaub]

Originally Posted by Alex Copeland

You forgot to mention the optimum mitigation - Achieve Correct Mechanical Time-Alignment.

If what you mean is physically aligning the driver by tilting the baffle, setting back parts of the cabinet (e.g. for the tweeter) and so on, this often causes other even more problems (IMHO).

Perhaps the only system that I have seen where this might have been pulled off in an OK way is shown here:



-Charlie

[Alex Copeland]

It has been my experience that the improvements in overall sound character that result from correct mechanical alignment of all drivers far outweighs any minor response anomolies that might occur. The sound character that results from no alignment and use of phase-shift time-correction circuits sounds peculiar and veiled.

[phivates]

EVERY solution is a new problem. We're here to deal with that. Enjoy!

[DDF]

Originally Posted by pooge

I haven't read the paper yet, but as further info, you may want to read this paper, and especially reference 7 in the references cited at the end of the paper.

http://users.ece.gatech.edu/~mleach/papers/LinkRyl.pdf

I based my 4th year EE project on exactly this concept, back in the 80s, except I generalized it for all all-pass xover, not just LR (which is Butterworth derived). Looked at on axis, off axis, acoustic power response, impedance and group delay.

Bottom line is that including the tweeter xover phase function as a phase eq branch results in reduced rolloff of one of the orders (HP or LP). You can determine which order is lower, by how you derive LP and HP from the all pass function. ie the derived one is lower order. In my sims, found best tradeoff between off axis control and group delay was with a biquad where the poles were placed between Bessel and Butterworth.

The xfer function requires zeroes, so it has to be active. Knocked it up in LM833s back then (good stuff at the time) and it all measures/works as advertised.

IME the only potentially advantageous application of this is if you xover very close to tweeter resonance. However, the tweeter must be very robust and I don't know that this xover makes sense for any real world domes out there, unless maybe if they're heavily waveguide loaded for the extra power handling. Even then, its more a theoretical advantage than real world because there are simpler ways to get very nearly the same effect, with standard all-pole filters.

Dave

[makingmoney]

Just glancing at your paper, it reminds me of how Gedlee solves problems in the xovers he uses.
Very good.