Demystifying Phase in speaker systems

Misunderstandings
When I first began fiddling with speakers I felt like I was out sick the day phase was explained. It seemed everybody understood this mysterious effect except me. I understood that filters made phase changes and even that a speaker alone had some phase but exactly what phase is, eluded me. It wasn’t until my ego got in the way that I realized I couldn’t bluff my way past it any more. I had to at least try to understand this mysterious effect called “Phase” if I was going to be able converse with the crowd who did understand it, so I began reading. I was immediately relieved to hear how complex it really is and that I didn’t understand it because it couldn’t be understood. It’s simply too complex. More reading led me to realize the “too complex” attitude was a copout from someone who didn’t really understand phase. So I kept reading. Now I despise articles that present large squiggles of math as “proof” that “a butterworth filter has no phase” and hearing such things only confused me further. Turns out there is more misunderstanding about this innoccuous relationship than fact, even from some reputable places. Many years have passed since I began my search for understanding and in all that time only one thing remains constant. It was so close to me I missed it. In fact I missed it because it is so simple. In reality it’s the phase relationships that are complex, probably the most complex relationship in reality. But in the end it comes to this: phase is a measurement of time. It’s really that simple. It can be expressed in minutes, seconds, hours, years, even centuries, or it can be expressed in degress, radians, milliseconds or microseconds but they all represent the same thing, time. Phase is a measurement of time. More specifically, loudspeaker phase is a measurement of the arrival time of the individual harmonic components of a sound.
Time
Normally we think of time as being absolute. When it’s noon here on the West coast and 9 am on the East Coast but we normally think of it as “noon” not “three hours past 9 am NY time”, and that may be the reason it appears so difficult to understand for so many. Phase is also expressed in both normal time measurements such as microseconds or milliseconds and in degrees or radians, although in the first case it may not be called “Phase”. The measurement is the same but it’s expression is different. Phase is expressed in degrees because it’s nearly always applied to a sinusoidal wave form. A sine wave has 360 degrees of “rotation” from beginning to end. 90 deg of rising voltage, 90 deg of falling voltage (half wave) followed by another 90 deg of negative voltage and lastly 90 deg of decreasing voltage until we return to zero. When two sinusoidal waves of the same frequency are out of phase its easiest to understand and see the change on a graph if we overlap the divergent waves and assign degrees of rotation to their shapes. This allows us to accurately determine the time difference (phase change as an angle) between any two points on the sinusoidal waveform using degrees of rotation. And that is the reason it’s expressed in degrees or radians.
Absolute vs relative phase.
In the example above the time “noon” would be absolute time and “three hours past 9 am NY time” would be relative time. In measuring phase on loudspeakers we nearly always use relative phase rather than absolute phase. In a speaker system the absolute phase would be the arrival time of the entire signal from the time the electric signal was applied to the speaker to the time it arrives at the listener. The only time you’ll see anything like an absolute phase value applied to a speaker is when you read the “in flight” time on an impulse response. This does represent phase but it’s not frequency dependent phase and yes it could be expressed in degrees but you would need to choose a reference frequency and analyze only that frequeny, so it never is. Hopefully for obvious reasons.
A speaker really doesn’t have an absolute phase value so you’ll almost never see arrival time exressed as a single number. It doesn’t have an absolute phase because sound from a speaker almost never arrives at the listener at the same time it was applied to the driver over the frequencies being reproduced. The measurement of arrival time at a specific frequency is “relative” phase and that is the most useful measurement in designing and building a speaker system. A speaker, despite attempts to “correct” for cone shape, radiates different frequencies at different places on the cone and therefore in space as well. Some parts of the cone are closer to the listener and some are further away. Frequencies have different wavelengths as well so it’s nearly impossible to re-assemble the original electric wave form at the listener position from a distance using a loudspeaker. But that does not mean we can’t try or that changes in relative phase over the frequency response of a speaker make the reproduced sound un-usable or unpleasant. When it comes to phase it’s the arrival time relationships between different frequencies that color the sound the most. Changes in arrival time itself are only a fixed delay and only in extreme cases where it alters synchronization with a video is it an issue. For that reason a single cone often sounds more phase correct than a multi-driver speaker system. But single cones suffer from high distortion and narrow frequency response. A well designed multi-driver speaker system can sound just as good if the arrival time of all frequencies is kept as close as possible. For that reason we take phase measurements of the raw drivers before designing a crossover so we can do our best to align the arrival time of all frequencies at the listeners position.

Finally
Phase alignment is one of the most important aspects of a working loudspeaker. A speaker takes an electric signal from an amplifier and converts it to an acoustic singnal we call sound. When taking phase measurements using various tools for crossover design it’s best to be sure exactly how the phase data is calculated. For example, I use Omnimic to quickly get a frequency response from a speaker while I’m listening or working on a crossover. I also use ARTA for the same thing. But if I take a gated measurement in ARTA and try to use the phase data to produce a crossover it will be wrong. It must be “massaged” so it contains only relative phase. That means we only want the change in phase at various frequencies across the audio spectrum. This also assumes the in-flight time is zero. When using tools to take phase measurements it’s best to use the same tool for all drivers measured. Taking a measurement in ARTA for the woofer and another measurement in Omnimic for the tweeter will undoubtedly result in erroneous phase data and an incorrectly aligned crossover phase summation. Part of the reason is that in ARTA you need only relative phase data so when you save the Frequency response plot you first select “minimum phase”. This process removes any phase changes before or after the frequencies being measured resulting in a plot that contains only the changes beginning with the lowest frequency. Omnimic uses a “blended” impulse response that when converted to frequency data has it’s own phase characteristics that are not compatible with the minimum phase from ARTA.

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