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In Reply to: Phase Shift posted by Art J. on March 21, 2001 at 19:33:56:
Hi Art!You wrote:
> > There seems to be confusion about the amount of
> > phase shift in each order of cross-over.This one's actually pretty simple. Phase shifts in reactive electrical devices.
Here's the scoop: The three values - R esistance, ( L ) Inductance and C apacitance are each 90 degrees out of phase with each other. Capacitors provide impedance that's 90 degrees ahead of an equivalent value of resistance. And inductors have impedance that's 90 degrees behind.
This is literally the way power runs through these things. In a capacitor - voltage rises across it before current can run through it. And in an inductor, voltage cannot rise across it until after current has already begin to flow through it. With a resistor - voltage rises across it at the exact same rate that current flows through it.
So what we have here truly is a phase relationship, where things happen at different times.
This makes simple RCL circuits very easy to calculate. Everything is two dimensional. You can calculate total impedance and phase angles with the same formulas you would use to calculate a right triangle. Right triangles have 90 degree angles, and that's the exact same relationship between the three values, inductance, capacitance and resistance.
When we have a 6dB/octave crossover - we have only two of these. A cap and a resistor or an inductor and a resistor. What that means is that the phase difference can be a maximum of 90 degrees.
But wait - that's a bit misleading. I tell people that a 6dB/octave crossover can't shift the driver's output more than 45 degrees, and here's why:
Let's use the tweeter circuit, just for sake of example. The woofer acts the same, so there's no point in doing both of them. When the tweeter is fully cutoff - at very low frequencies - the phase angle is very nearly 90 degrees. That's because the capacitor's impedance approaches infinity, while the tweeter is sitting there at 8 ohms. So the phase angle is 90 degrees -
- but you can't hear anything. The tweeter is fully cutoff.
As we approach the crossover point, the capacitor approaches 8 ohms. At this point, the tweeter is 8 ohms (hopefully you've crossed it much past resonance so it isn't 25 ohms or something). Now, we use that 2D math stuff. Pythagoran's theorem tells us what the impedance is:
Z = (R^2 + Xc^2)^0.5 Our impedance is 11.3 ohms. We find power distribution by calculating a divider network using 8 ohms and 11.3 ohms. We're about 3dB down at this point. An octave lower, we're about 7dB down. That's where you'd probably want to consider your true crossover to be.
At the -3dB point, we had 8 ohms or resistance and 8 ohms of capacitive reactance. That's exactly a 45 degree difference. So at this point, we're shifted 45 degrees. Much below this point, you cannot hear the tweeter - because it's attenuated by the crossover. So that's the point. While the network is capable of presenting signals to the tweeter that have been shifted 90 degrees, it is precisely these signals that have been attenuated sufficiently that you can't hear them.
By definition, the speaker motor driven by a 6dB/octave crossover cannot possibly provide output that is shifted 90 degrees. Because at the point where phase shift is ninety dgrees - by definition - the attenuation created by the network is infinite. In practice, the motor will begin to become audible (barely) when phase shift is 60 degrees and will be only -3dB at 45 degrees. So it's gotten pretty loud by 46 degrees.
Therefore, it is reasonable to say that a speaker driver with a 6dB/octave crossover will present audible signals of 45 degrees phase shift or less. It cannot possibly provide audible output shifted much more than that.
12dB/octave crossovers aren't much more difficult to calculate, since they still have the same three "nodes." We can still use simple "Phythagoran-style" math. What you'll find is that all the same things occur, but the maximum shift is now 90 degrees. That can be a problem when two are used contiguously, because the tweeter shifts 90 degree in one direction and the woofer shifts 90 degrees in the other. That means in the crossover region - they're very nearly 180 degrees apart.
Two 12dB/octave crossovers on contiguous drivers will cause complete cancellation of the crossover frequency. In practice, it can be shown that this really does happen. There is about -20dB to -40dB, depending on placement of the two drivers on the baffle. So I'd recommend this kind of system have the two motors connected out of phase.
Some would perhaps object to running a woofer 180 degrees out of phase with a tweeter. I don't really like it either - it just "doesn't feel right." But if you're gonna run two 2nd order networks side by side, and the two drivers are mounted on the same baffle, it's the lesser of two evils. be 180 degrees out of phase in the passbands, or have a 40dB dip in the crossover frequency.
Honestly, you can't hear the 180 degree thing. The woofer's phase changes to "meet" the tweeters at the crossover frequency and the the tweeter's phase continues to rotate through to 180 degrees. That's what the phase relationship "looks" like when you run two 12dB/octave crossover slopes with "cross connected" motors.
When you consider higher order slopes, you can't use this kind of math anymore. Now the phase generated by the first "node" must be calculated against the proceeding nodes using vector math. But you can see the trend. You're right in that there's 90 degrees per node, but that's a number that you can't ever hear. The audible phase produced is exactly half that.
Wayne
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Follow Ups
- Re: Phase Shift - Wayne Parham 03/22/0107:22:06 03/22/01 (5)
- Unfortunantly... - RBP 16:03:10 03/22/01 (1)
- Re: Unfortunantly... - Wayne Parham 18:28:02 03/22/01 (0)
- Re: Phase Shift - Art J. 10:28:11 03/22/01 (2)
- Makin' it easy - Wayne Parham 20:06:31 03/22/01 (1)
- to the printer,thanks NT - Art J. 07:13:20 03/23/01 (0)
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