Phase and time delay

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emdubya

First post in this forum, so my apologies if it's a simplistic one.

In this hypothetical situation, let's say that we have a two-way speaker with zero acoustic alignment difference between the two drivers. It has a fourth order crossover at 1 kHz and we supply the speaker with a 1kHz pulse.

I understand that there will be a 360° phase difference and thus the pulses from each driver will be in phase. My question is whether one of the pulses will be delayed by 1 ms.

Thanks!

steveu

You can not modulate (pulse) 1khz or any other frequency without the addition of side-band frequencies. I suggest you draw your crossover with resistor loads in spice and simulate the pulse you have in mind. The reality is more complicated than a delay time.

emdubya

Thanks for your reply, steveu. In essence my question is solely about whether a 360° phase delay results in a timing delay. Everything else is hypothetical.

Let me put it another way: suppose that we mount two identical drivers on a very large baffle. We supply each driver with the same piece of music, but one driver is some multiple of 360° out of phase with the other driver. Do we hear coherent music or do we hear two slightly off-beat streams?

Soldermizer

I believe "phase" requires specification at a certain frequency. Mount two speakers any way you like. They will be a fixed distance from each other. This distance of itself will result in peaks and dips in the response. Now, if you add a delay ("out of phase" at a certain frequency), nothing has really changed. Unless you added a truly audible delay, like dozens of milliseconds, probably it would sound "ok". The human ear is substantially immune to phase delay, but can easily hear phase shift, which is another way of saying the delay of one frequency is varying relative to another frequency.

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rayma

Do we hear coherent music or do we hear two slightly off-beat streams?

Pulses won't look coherent on a scope (sines will, since you can't tell one cycle from another),
but some may not hear a problem. If an amplifier did that, there would be riots in the streets.

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rayma

The human ear is substantially immune to phase delay, but can easily hear phase shift, which is another way of saying the delay of one frequency is varying relative to another frequency.

Nonlinear phase shift. Linear phase shift is a pure time delay.

GM

I understand that there will be a 360° phase difference and thus the pulses from each driver will be in phase. My question is whether one of the pulses will be delayed by 1 ms.

Right, at its most basic, they are in acoustic phase, but one is offset [delayed] by 1 Hz/1 ms, so if you want to do it right, then you have to move the HF behind the LF 1 ms to be both time and phase coherent.

GM

emdubya

Right, at its most basic, they are in acoustic phase, but one is offset [delayed] by 1 Hz/1 ms, so if you want to do it right, then you have to move the HF behind the LF 1 ms to be both time and phase coherent.

GM

Thank you for your clear and simple explanation. "Basic" is definitely what I need.

So if we use a fourth order crossover between two drivers, this implies that the sound from the drivers will be "out of sync" by a small amount due to the phase lag.

Thus if we have a 3-way speaker with drivers whose axes are magically co-incident on the baffle and we use LR4 crossovers at, say, 333 Hz and 3,333 Hz, we should ideally add a 0.33 ms delay to the mid and a further 0.03 ms delay to the tweeter in addition to their respective acoustic delays. These delays might not be constant across each crossover range, but it would a lot better than nothing. Does this make sense or am I talking nonsense?

It might be obvious by now that I'm trying to learn about the implications of phase at crossover frequencies. I'm currently working on a 3-way design and discovered that at one particular set of delays the sound suddenly snapped into focus. The difference wasn't subtle. This was with a DSP system. I appreciate that this forum is for loudspeakers with crossovers, but the problem must surely exist with both approaches. I'm trying to figure out the best way to deal with this when choosing crossover points.

Thanks again,

emdubya

AllenB

Paid Member
Your tweeter is not going to be delayed, just because your crossover phase goes around. This doesn't mean you won't have some excess group delay but don't assume it will be one cycle at the crossover frequency, it is dependent on the slope of the change.

YSDR

Right, at its most basic, they are in acoustic phase, but one is offset [delayed] by 1 Hz/1 ms, so if you want to do it right, then you have to move the HF behind the LF 1 ms to be both time and phase coherent.

GM
But moving the HF 1ms behind the LF works only at 1kHz. Right?

emdubya

Your tweeter is not going to be delayed, just because your crossover phase goes around. This doesn't mean you won't have some excess group delay but don't assume it will be one cycle at the crossover frequency, it is dependent on the slope of the change.

Thank you...yes, you're right - I've just discovered this empirically. Trying to calculate the additional delay is going to be too difficult for my tired old brain, so I'll just continue doing it by trial and error, starting with the acoustic delays and working upwards until I optimise the nulls.

YSDR

Thank you for your clear and simple explanation. "Basic" is definitely what I need.

So if we use a fourth order crossover between two drivers, this implies that the sound from the drivers will be "out of sync" by a small amount due to the phase lag.

Thus if we have a 3-way speaker with drivers whose axes are magically co-incident on the baffle and we use LR4 crossovers at, say, 333 Hz and 3,333 Hz, we should ideally add a 0.33 ms delay to the mid and a further 0.03 ms delay to the tweeter in addition to their respective acoustic delays. These delays might not be constant across each crossover range, but it would a lot better than nothing. Does this make sense or am I talking nonsense?

It might be obvious by now that I'm trying to learn about the implications of phase at crossover frequencies. I'm currently working on a 3-way design and discovered that at one particular set of delays the sound suddenly snapped into focus. The difference wasn't subtle. This was with a DSP system. I appreciate that this forum is for loudspeakers with crossovers, but the problem must surely exist with both approaches. I'm trying to figure out the best way to deal with this when choosing crossover points.

Thanks again,

emdubya
If you use LR4 slopes with IIR (or analog) filters you only want to delay to compensate the driver's acoustical center difference (and not to the slope-caused 1 cycle delay) on the desired axis. If you do this and your driver's frequency curves follows LR4, then you have good phase match not only at the crossover point but at other frequencies as well, although 1 period behind the higher frequency driver.
Btw, LR2 causes 1/2 cycle delay, that's why you need to flip polarity on one driver if the acoustical centers are aligned.
If you want to remove that 1 cycle LR4 delay you need to use FIR filters.

KSTR

You can create sort of 1kHz pulses by applying a raised cosine envelope to it, which should span some 4...6 cycles, this gives a shaped tone burst which is rather narrowband and still has sufficiently "sharp" boundaries in the time domain. See JAES papers for an introduction.

Apply these to your crossover. If it is a Linkwitz-Riley, both the (idealized) woofer and tweeter will show a close to identical waveform, they overlay neatly. This is what is expected because a LR-XO has *identical* phase response on both channels.
But they also both have the group delay (associated to the phase). To visualize this, you need to run a set of those shaped tone burst with varying start phase of the 1kHz base signal through it and look at the total envelope of this, using the "persistent" mode of the oscilloscope. That envelope is... the raised cosine window. Compare that to the total envelope of the input signal, looking a the points where level is maximum. The time offset you see from input to output is the group delay.

emdubya

If you use LR4 slopes with IIR (or analog) filters you only want to delay to compensate the driver's acoustical center difference (and not to the slope-caused 1 cycle delay) on the desired axis. If you do this and your driver's frequency curves follows LR4, then you have good phase match not only at the crossover point but at other frequencies as well, although 1 period behind the higher frequency driver.
Btw, LR2 causes 1/2 cycle delay, that's why you need to flip polarity on one driver if the acoustical centers are aligned.
If you want to remove that 1 cycle LR4 delay you need to use FIR filters.

Just done a little reading on IRR and FIR filters...I think I have enough to learn for now, so FIR sounds like a new project sometime in the future.

So the key with IRR and analogue filters is to match the roll-off of the filter to the natural roll-off of the driver...am I reading that correctly?

emdubya

You can create sort of 1kHz pulses by...

You are a long way over my head already! Thank you, but this is beyond my abilities.

YSDR

Yes, the goal is to get an exact LR2, LR4 or whatever slope you want out of your drivers acoustically.
The easiest method is with DSP. You flatten the driver's frequency response, then apply the desired slope.

KSTR

Btw, LR2 causes 1/2 cycle delay, that's why you need to flip polarity on one driver if the acoustical centers are aligned.
If you want to remove that 1 cycle LR4 delay you need to use FIR filters.
This is *not* correct. An LR4's group delay at XO delay is *not* one period, the group delay has nothing to do with the phase being 180° at the XO (which would equal half a cycle, btw). Group delay at some point depends on the shape of the phase response at that point, not on the value just at that point (because group delay is the derivative --the slope -- of phase vs frequency). For a LR4, the group delay at XO is a time equivalent to 0.58 periods, the delay peak is a bit before the XO (at 0.9*f_xo) and raises to 0.62 periods equivalent.

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KSTR

You are a long way over my head already! Thank you, but this is beyond my abilities.
This experiment can be made in the virtual domain, for example with LTspice... I might show an example if time allows...

YSDR

This is *not* correct. An LR4's group delay at XO delay is *not* one period, the group delay has nothing to do with the phase being 180° at the XO (which would equal half a cycle, btw). Group delay at some point depends on the shape of the phase response at that point, not on the value just at that point (because group delay is the derivative of phase vs frequency). For a LR4, the group delay at XO is a time equivalent to 0.58 periods, the delay peak is a bit before the XO (at 0.9*f_xo) and raises to 0.62 periods equivalent.
I am not mentioned *group delay*. If the delay is not one cycle for LR4 slopes then the reverse polarity test doesn't show that deep notch called reverse null.

KSTR

Which delay are you speaking of?

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