First Order Crossovers: Pros and Cons

Some great points from Golix and i agree with some of the points that he's making here too. This is the reason that i love my modified Ohm F's, warts and all, and why i've said what i have about them. You've got one driver that is both phase and time coherent, covering the entire audible range with great bass weight and a phenomenally spacious radiation pattern. Other than that, and as i've mentioned before, any other attempt at loudspeaker design becomes extremely complex with multitudes of trade-off's involved. Juggling the trade-off's boils down to the personal preferences of the design engineer and the individual buying / listening to the speakers. As such, it is a no-win argument, just a discussion of various beliefs and preferences. There is only one way to achieve specific levels of performance, and at this time, even that approach has limitations. Sean
>

Golix: I have to back up Roy on this. In a first-order, both drivers are at zero phase in their PASSbands, and at 90 degrees in their STOPbands. (Close, anyway. The only places either of them truly reach 0 or 90 is at DC and at infinity, both of which are well outside the audioband.)

However, when either driver is at 90, the output amplitude is ZERO, by definition, so it contributes nothing to the sound. Its major contribution comes within its PASSband, where its phase is close to zero.

Now, in beween DC and infinity, both drivers make a contribution depending on the frequency relative to the crossover frequency. In a first-order, they are ALWAYS 90 degrees out of phase, regardless of the frequency, and they ALWAYS sum to unity and zero phase. If this isn't clear, you need to look into the math (including complex variables and vector addition).

At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this.

If you wish to prove this to yourself, it is easily proved by doing some math. If you want to avoid the math, it can still be proved by simply drawing sine waves. First, draw a single sine wave with amplitude of 1.0 and any phase you choose. Next, draw two identical sine waves, each of amplitude .707, one shifted 1/8 wavelength to the left of the original one, and one shifted 1/8 wavelength to the right. Now simply sum their values. What you will find in that the summation is an EXACT replica of the original sine wave, in both phase and amplitude.

This principle works the same way with speakers. As long as your ear is equidistant from the two drivers, you will be utterly unable to distinguish the crossover. This is because the output summation IN THE AIR is identical to the original signal (in both time and amplitude), no matter what the frequency. (Again, this is true of the first-order only!)

Now, it must be said that the real world is not so perfect, and most drivers have rolloff-related and impedance-related phase shifts that add into the equation, giving a less-than-perfect end result. For this reason, designing a good first-order crossover is harder than it sounds.

>But anyway, what I understand as phase coherent means that the entire output is in phase ideally independent of listening position. The only speakers capable of this are full-range, single driver designs.

Since that last sentence is not true in all cases, nor in the majority of cases if we want to talk about phase and time alignment, which we do want to in this thread, primarily. There are other threads to talk just about phase coherent speakers which are not time coherent.

Note that I am agnostic on whether first order crossovers and stepped baffles are always the best selection of tradeoffs or not. I've mentioned near field listening situations as one situation to consider.

"At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this."

Karls, thanks for that explanation ... now I completely understand why the first order crossover can work in amplitude and phase terms through the region where both drivers are contributing to the sound. The power output of both driver is 3dB down at this point (amplitude is reduced by 1/(square root of 2), and they are 90 degrees out of phase, but the vector addition of these two waves results in a sine wave that is in phase and 0dB down in amplitude.

Let me explain my porting question on GMA's C-3's relative to time and phase coherence. I have no idea if there is an audible issue with the C-3's design and based on Roy's published specifications there is nothing to suggest what I'm about ask actually takes place, nevertheless I thought I'd throw it out there to elicit a response regarding the porting theory behind this design.

In GMA's C-3 the bass port is firing in an upward direction, directly below and slightly behind both the midrange and tweeter, with a clearance of perhaps 4-5 inches. I'm wondering if conceptually there could be some type of Doppler effect taking place with the placement of the port relative to the midrange and tweeter that could slightly alter the phasing or timing of these drivers? Although there is no high-frequency whizzer cone riding on top the woofer; as in the Tannoy, in theory as the woofer moves backward and air is pushed out of the port, is it possible that this change in air pressure could somehow modulate the midrange and tweeter response by disturbing their wave lengths? Alternatively, when the woofer pushes forward, does the port suck in enough air to also disturb the wave length of the midrange driver and tweeter, thereby throwing off time and phase coherency?