Written by Andy Wehmeyer – President, Audiofrog, Inc.
Andy’s tech [tip] for the day. This is an explanation of why you shouldn’t use delay to adjust the phase of crossovers in a car audio system that uses delays to fix distance for an offset listener.
The phase at the crossover is important for only one reason–so that the acoustic sum doesn’t include a big null in the frequency response. We don’t hear absolute phase, we hear relative phase. A crossover is designed to separate the total band of reproduced frequencies into sub bands so that the drivers for those bands can be optimized for use in that band. The region where the two drivers interact is the only place that the relative phase of the drivers matters because AC signals sum according to magnitude AND phase.
The HUGE misunderstanding EVERYWHERE in car audio is about what matters in designing a crossover. There are two things that matter most and the rest are all small considerations. One, in a passive network is impedance. We have to keep the system impedance above the minimum limit the amp can drive. Second, we listen to speakers, not to electrical filters. The electrical filters simply change the amount of power that is delivered to each of the speakers. A high pass filter (whether passive or active) reduces the power delivered to the speaker at low frequencies. A low pass filter reduces the amount of power delivered at high frequencies. The slope of the crossover determines the rate at which power is attenuated.
Crossovers do this by changing the phase of either the current or the voltage in the AC signal by a time constant. A capacitor stores energy as voltage, so the rise in voltage available at the cap is delayed compared to the current that’s applied. When current flows to the cap, it takes a little while for the cap to charge to the same voltage that’s applied. That lag changes the phase by 45 degrees and the resulting power over the frequencies where the capacitor “works” (low frequencies) is reduced because power is voltage times current times the cosine of the phase angle of 45 degrees.
An inductor (low pass filter) is similar but opposite. When AC voltage is applied to an inductor, the current lags by 45 degrees. Same thing, but high frequencies are reduced.
So, a capacitor “resists” changes in voltage and an inductor “resists” changes in current.
Active filters do the same thing. Digital filters don’t have to be designed this way, but many are. Why? Because it works just fine.
The low frequency roll off of a speaker is a crossover that’s built into the speaker. The spider and surround are a mechanical analog of a capacitor. The high frequency roll off of a speaker is also a crossover built into the speaker. That rolloff is controlled by two things– the mass of the moving assembly (mechanical analog of an inductor) and the inductance of the voice coil at high frequencies.
So, the electrical phase of the speaker changes due to these two built-in crossovers. Anytime and anywhere the frequency response changes direction, the phase also changes direction. This applies to the acoustic output of the speaker, too. When you put a speaker in a room and measure the response, frequency response changes as a result of reflections also changes phase.
When we talk about minimum phase systems, we are talking about a system in which the phase is directly related to the frequency response. That system only exists as a single driver in a nonreflective environment. A second driver, which has a phase response of its own, combined with the first driver is NOT a minimum phase system. A single speaker in a room is not a minimum phase system because each reflection changes the measured acoustic phase independent of the response of the speaker by itself.
Despite this condition, there are regions in a non-minimum phase system that behave like a minimum phase system. What defines that is if inverting the frequency response of the electrical signal sent to the speaker by the same magnitude as the dip or peak fixes the problem. In these regions, equalization is effective. In regions that don’t act like minimum phase, equalization won’t fix the problem. An acoustic null is a region in which boosting with an EQ doesn’t affect the problem by the same magnitude as the boost. We’ve all experienced that in trying to boost a deep and narrow dip in the response. When the relative ACOUSTIC phase between two drivers is 180 degrees, boosting doesn’t help. However, changing the polarity of one of the drivers changes the relative phase by 180 degrees and now we don’t have that dip anymore.
When we design a crossover, we try to remove power at high frequencies at the same rate as we remove power at low frequencies from the other driver. reducing the voltage by 6dB cuts power in half. If we have two speakers both playing the same frequency with both having their output level cut in half, then the resulting response is flat. Two halves make a whole.
OK…Now remember that we don’t hear the electrical filters. They exist only to modify the acoustic response, which is what we hear. What we hear is result of the application of the electrical filters. It’s just like EQ. We use an EQ to modify the acoustic response. This seems obvious to everyone. Crossovers are EXACTLY THE SAME. It doesn’t matter what the electrical response (magnitude or phase) is EXCEPT that is should combine with the speaker to produce a measured ACOUSTIC response that matches the Butterworth, Linkwitz-Riley, 2nd order, third order, or what have you. In many cases, additional EQ is required to make the acoustic output match one of those classical alignments. In a passive network, we can change the Q of the filters to boost or cut at the knee. In an active system, we can do the same thing by choosing a different filter shape or Q. Or we can use an equalizer to tweak the response so it matches.
All of these classical alignments assume (and require) that the sound from one speaker arrives at the same time as the sound of the other speaker because the summation of the low pass and high pass acoustic responses depend on magnitude and phase. Phase at the listening or measuring position is ALSO determined by distance. So, we can use delay to align the arrival of the sound from the low pass and the high pass output of the two speakers.
When we design a home audio speaker, we design ONE speaker in an anechoic room so its response is correct. Then, we REPLICATE it for the other speaker in a stereo pair. Then, we sit in between. We are the same distance from the speakers and the speakers are the same. If we sit a little closer to one than the other, then we can delay the ENTIRE speaker to correct for the distance. The responses of the speakers and all of the correction filters that are contained within each one are still the same.
In a car, this is not the case because we use asymmetrical filters to correct the responses of the left and right channels independently. If we set the delays of all the speakers individually so that the sound arrives at our ear at the same time, we do two things. We align the arrivals so we can design crossovers according to the classical alignments AND we correct for the offset listener.
In order to hear a correct image of a stage, the left and right acoustic signal has to arrive at our ears at the same time, in phase and precisely matched in level at all frequencies. So, let’s say that we delay the right mid in a three way to fix the crossover, what have we done to the relative phase between that mid and the one on the other side that has to be in phase with the first one in order to provide a correct image? We’ve changed it. Now, the image will shift over those frequencies toward the speaker from which the sound arrives first.
This is why using delay to fix phase at the crossover is fine for home audio speakers, but isn’t OK for car audio systems that use delay to optimize for a single offset listener. Get the crossover right using EQ and set the delays based on measured distance. It’s the only correct way.
In systems (like those with upmixers and center speakers), the use of delay to create an image is less important because sound is steered to a real center speaker and we don’t rely on the left and right being precisely matched in frequency and phase to create that center image.
So, when you look at the phase curve in the analyzer, try adjusting the EQ or the crossover to achieve flat frequency response and flat phase and leave the delay setting alone.
The reason that i recommend 4th order slopes in cars is because the rate of attenuation is so steep that the acoustic output of the speaker is much more likely to track the electrical response. And the electrical response of a 4th order LR filter sums flat in phase and magnitude. This minimizes the need for EQ. It’s much more predictable and much more likely to just work without a bunch of futzing around.
July 22, 2015 at 8:07 AM