First Order Crossovers: Pros and Cons

A previous poster has made the statement that using a 1st order crossover causes the LF and HF drivers to be 90degrees out of phase and this confuses me. At what frequency ?

If the LF driver uses a 1st order butterworth type low pass filter, and the HF driver uses a 1st order butterworth type high pass filter, with the -3dB frequencies at the same point (to give a flat amplitude response) doesn't this automatically put the two drivers in phase at the crossover frequency ? I must admit it's a long time since I studied filter design (since I went over to the dark side of software).

That would be a phase-coherent time for me ... the two drivers in phase at the crossover frequency, with linear phase response in the low pass and high pass filters as you move away from the crossover point ensuring phase response continuity elsewhere in the frequency response.

Such a speaker should have a good step response, because linear phase filters offer the least distortion of the original waveform.

I am assuming that this is what the Green Mountain Audio designs attempt to approximate (given that everything in real life is an approximation).

The output of a crossover network is a vector sum with real and imaginary components in polar coordinates. What you have in a 1st order at the crossover freq is one vector at .707, +45, and the other at .707, -45, which adds to unity in vector space with a combined phase shift of zero. But because the vectors rotate together with frequency, they are always 90 degrees apart, and they always add to unity voltage and zero phase in vector space, no matter what the frequency.

To say it differently, the combined output of the two drivers is always unity at zero phase, even though the two vectors are always 90 degrees apart. This is difficult to conceptualize, but the math behind it is relatively simple.

For obvious reasons, this is called a constant-voltage minimum-phase transfer function, and the first-order is the only crossover type that has this characteristic. I should note that this presumes identical drivers mounted very closely together and resistive loading, which is hard to achieve in the real world. But with some effort, one can come close, and the effort is well rewarded in the listening.

The exchange between Roy and Golix above leads me to bring up something I have been thinking about for a long time – the phasing of the recorded music before it even reaches your stereo system.

I have read enough about 1st order crossovers and phasing and to convince myself that this design philosophy is valid and this approach is the only one that can achieved a time coherent design. To me the $20,000 question is – does it matter enough to outweigh all the other compromises that speaker designers must make?

Others have asked if time coherence, or lack there of, audible. Let’s assume the answer is yes. The next question, is it preferable? Obviously not to everyone. Many have auditioned Vandersteens, Theils, and Meadowlarks and still chosen other brands.

Time coherence designs with first order crossovers are the only design that can come close to preserving the original waveform, most easily seen by measuring its step response. I totally agree with this. But music is not a square wave, so tracking something that doesn’t exist in natural music doesn’t prove you can make better music. Transients can be sharp, but they are not infinite slop step functions.

Going back to my first paragraph, what about the phasing of the music recorded on that CD or LP? Even if a stereo system from source to speaker was perfectly able to preserve the original waveform, what are we trying to preserve? I know very little about the recording process, but I can bet many an album has been processed by recording engineers in ways that destroys the phasing of the instruments used to make the music. Some genre’s may be better than others. Some studios may be better than others. But how are we, the music buyer, supposed to know if the waveform we are buying is worth preserving? I would love to see some discussion on this HUGE factor. I have read Richard Vandersteen tests his speakers with his own recordings. I am sure those recording have their phasing preserved. But doesn’t this say something about the phasing of recorded music in general?

Finally I would also like to see discussions on the real world trade-offs of using 1st order crossovers. Like small sweet spots. Is that inherent to all 1st order designs or do all good imaging direct radiating speakers have that? And is the sound outside the sweet spot worse for time coherent designs? If so why? I have only listened to Vandersteens (of the 1st order designs) and the difference in sound from sitting in the time coherence zone to standing up is quite alarming. There is something special going on in the sweet spot, but the Vandersteens sound flat when I stand up – treble drops right off. I know they just lost their time coherence, but when I perform the stand/sit test with my home speakers, the difference is far less dramatic. Do 1st order designs sound extra good in the sweet spot and extra bad everywhere else? Comments please.

Other inherent trade-offs of 1st order designs? Thanks in advance.

It seems Roy is correct, as usual.

But I do want to chime in on one point: There are companies which design and advertise phase coherent speakers without making claims of time alignment, such as VMPS or Fried. There is nothing wrong with doing this, although it's understood that Roy Johnson would not pursue or endorse this design decision.

Then there are companies whose ads specifically claim time coherence, when their multi driver speakers do not have first order crossovers and the baffles are not stepped back in any way. These ads are lying consciously, or someone in the engineering or marketing department is confused. Dali is the most recent and eggregious example of this phenomenon, which unlike VMPS or Fried, amounts to snake oil.

Applejelly:

You are indeed correct that recorded phase is a serious problem, and one which is utterly ignored by many recording engineers. However, some of them do take it seriously, along with many other aspects of their craft. So, in my opinion, it is well worth having a system that preserves time and phase. It can't fix the bad recordings, but at least it doesn't screw up the good ones.

About the step response: You are correct that music is not a square wave, but I will make the argument that the square wave (or step function) is the best test signal yet devised for predicting musical fidelity in a loudspeaker. The square wave, after all, is simply the mathematical summation of an infinite number of phase-matched sine waves in a specific frequency progression. As such, any transducer that passes a clean square wave is eminently qualified to perform well on any musical signal it will ever encounter.

The reason that first-order designs change sound when going from sitting to standing has to do with lobing patterns, as discussed in previous posts. First-order designs have more overlap in output between the two drivers, so the lobing effects are more noticeable than with higher-order crossovers. However, there is an important point to keep in mind: The higher-order crossovers have non-uniform phase characteristics by definition, resulting in audible distortions of a different kind, even when listening on-axis. In other words, first-order is bad if you want to listen critically while standing up; higher-order is bad no matter where you are.

I think that many people who listen to Vandys (etc.) and end up buying something else are doing so because of issues other than time-and-phase coherence. This is not the only thing that matters, not by a long shot. The Vandys are built to a specific budget point, and in their price range, there are other speakers that give higher resolution, tighter bass, more treble extension, a more neutral tonal balance, etc. Anyone who values one of these specific things highly could easily decide to buy something else.

However, having said that, it is hard to imagine a better "real-world" compromise at a given price point than what Vandersteen has achieved. As I am fond of saying, the 2C may not be "the best" in any one area, but it is the cheapest speaker ever made that can truly lay claim to having addressed all of the important fundamentals in loudspeaker design. Its status as the best-selling high-end speaker of all time supports this conclusion.