LSi 9 crossover question

[Deleted User]

Forum members,
Here's a question sent to me about the LSi 9 crossover from a customer:

This question is about the LSI series and its Cascaded Taper array.

The second woofer with lower crossover frequency has crossover phase
time delay relative to the primary mid/woofer. This really mess up the
impulse response and imaging. Kind of like ((but not exactly because the
degrees of phase shift are different)) the sound stage effect of listening
to two speakers out of phase. Has Polk solved this problem?

Here is Matthew Polk's response:

All low pass filters have some delay. So, Chris is correct in thinking that using a different low pass filter on one driver introduces some phase shift relative the other driver. However, it is not the same as having two speakers connected "out of phase" and does not necessarily cause any problems.

"Out of phase" usually means that the speakers are connected in reverse phase which puts them 180 degrees out of phase with each other at all frequencies. If two speakers in the same cabinet are connected "out of phase" they will cancel each other almost perfectly and the system will produce very little bass. If your left and right speakers are connected "out of phase" they will cancel each other somewhat at low frequencies and low bass response will be reduced. At higher frequencies they will produce a strange "phasey" sound and will not produce a center image between the speakers. This depends quite a lot on exactly where the listener stands. At some positions the two speakers will cancel one group of frequencies and reinforce others. The precise frequencies that get canceled change as the listener moves and are different for each ear.

The situation in the Lsi-9, for example, is very different. This system uses two drivers and a tweeter. The low pass filters for each driver are different by about one octave. Therefore, the lower frequency driver has slightly greater delay than the higher frequency driver. Both drivers are delayed relative to the tweeter. The best way to think about these delays is that they shift the acoustic position of the driver. Effectively, these delays make the drivers seem to be slightly further away from the listener. In the case of the Lsi-9 the effective delay between drivers is quite a bit less than one inch. The amount of phase shift this produces is greater for higher frequencies (shorter wavelengths) and less for lower frequencies (longer wavelengths). Since the low pass filter creating the delay rolls off the higher frequencies which have greater phase shift it helps reduce the problem.

However, what we are really concerned with is the phase and amplitude combined output of the two drivers. For example, at a particular frequency if one driver is shifted 10 degrees relative to the other when they are added together the net phase shift is less than 5 degrees and the amplitude will be a little less than if you just measured the output of each driver at that frequency and added them together. If you picked a frequency where they were 180 degrees out of phase they would cancel, but only at that frequency.

So, the art of crossover design is to pick the right filter characteristics so that when the output of all the drivers and tweeters is added together you get both a flat frequency response and a smooth (linear) phase response at the listening position. The reason I say smooth (linear) phase response instead of flat phase response is a little difficult to explain. Above I explained that the delay introduced by the low pass filter effectively shifts the position of the driver further away. It's just the same as if you move the driver further away by the distance that corresponds to the filter delay. That delay distance corresponds to a phase shift that is different for each frequency. For example, a delay distance of 6 inches corresponds to phase shift of approximately 90 degrees at 500Hz, 180 degrees at 1kHz, 360 degrees at 2kHz, etc.

Suppose we have a speaker with absolutely flat frequency response and flat phase response when measured right at the loudspeaker. It will also have perfect impulse response. Now let's measure at the listening location which might be 10 feet away. We still get flat frequency response but the phase response looks like a complete mess because we have introduced a delay distance of 10 feet. That corresponds to roughly 3,600 degrees at 1kHz (10 full wavelengths of phase shift). But, the impulse response will still be perfect. The point is that the absolute amount of delay or phase shift is not important. What is important is that when the output of all the drivers and tweeters is added together, the delay is roughly the same at all frequencies at the listening location.

We spend a great deal of time making sure this works as well as possible over a broad range of listening locations when we design our systems. (However, keep in mind that the impulse of even the best loudspeakers never looks very good. This is because of the bandwidth limitations of the system at both the low and high end.)

Sorry for the length. I hope this helps.

-msp

Lsi9

I am relatively new to this forum, but I must say it is good to see Polk Audio respond to a customer and to see how you guys are so careful in the development of your product line, Thank You

Tour2ma

Thanks for posting, Ken. It's nice to "hear" what Matt has to say about spoeaker design.

Please post more of his musings from time to time...

hoosier21

very interesting read, thank Ken, I agree post more stuff like this, this is the kind of info we love to read.