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High Efficiency Speaker Asylum Need speakers that can rock with just one watt? You found da place. |
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In Reply to: Re: Phase Shift posted by Art J. on March 22, 2001 at 10:28:11:
Hi Art!You wrote:
> > Im reading very careful here, it takes time to sink in.
Yeah. I did another one of those long posts, where a short one would have sufficed. So let's try again, shall we? This time, with a little less attention to the details.
If Bill were to reply to your question about phase shifts, he would likely quote a technical reference that says something like "a first order filter will exhibit a 45 degree phase shift at crossover, with 90 degrees at the asymptotes." And Bill would be absolutely right. But what I'm telling you is that - for loudspeaker crossover networks - the word "asymptotes" can be interpreted to mean "places you can't ever go."
Just to recap, the reason the asymptotes aren't relevant is because they occur at frequencies that are attenuated. Nothing is coming out of the speaker at the frequencies where this amount of phase shift occurs.
Now to give you some "concrete" formulas to use when designing crossover networks:
Remember on first order (6dB/octave) crossovers that I said the place where Xc = R is the -3dB point, and that response is down -7dB an octave away. An octave further and we're at -13dB, and the slope continues to fall by 6dB/octave.
The best way to calculate a 1st order network is by using this "octave away" method - and not by setting reactance equal to driver (advertised) impedance.
So here's our formulas: [details that you can pass over if you wish]
For low pass: Xl = 2 * PI * F * L
rewritten to find for L = Xl / (2 * PI * F)And High Pass: Xc = 1 / (2 * PI * F * C)
rewritten to find for C = 1 / (2 * PI * F * Xc)Note that Xl and Xc are reactive impedance, and the general rule is to set this equal to the impedance of the driver. Also note that L is Henries and C is Farads, so millihenries is 1/1000 Henry and microfarads is 1/1000000 Farads.
Since we actually want to find a part that is -6dB down at a specific frequency, we really want to find a frequency that's an octave higher than these formulas indicate for high pass or an octave lower for low pass. You can easily use the formulas above, or we can just rewrite them to find the exact -6dB point, which is exactly an octave from the frequency where reactive impedance equals resistance:
For low pass: L = Xl / (2 * PI * ( F/2 ))
and high pass: C = 1 / (2 * PI * ( F * 2 ) * Xc)or to simplify:
[here's where the details end - these are important but easy]
1st order (6dB/octave) network calculation:
Low pass: L = speaker impedeance / (PI * crossover frequency)
High pass: C = 1 / (4 * PI * crossover frequency * speaker impedance)Those two formulas will get you where you need to be on 1st order networks. Just choose the frequency you want, and the value of the speaker's impedance. If you have an impedance chart - or you can measure its impedance at this frequency - then do so. Your results are more accurate. If not, just use the advertised impedance.
But if you use advertised impedance, be careful. As RBP pointed out, the speaker motor is a reactive device and this makes it have a big change in impedance with respect to frequency. Most speakers have significantly higher impedance at resonance than the "advertised" (8 ohm) value, and they also have greater impedance at their upper cutoff.
So it is wise to crossover well above speaker resonance when using a 6dB/octave crossover. If you cross an octave above - you're in the midband of the driver and you can reasonably expect it to maintain advertised impedance for a few octaves. This is an acceptable design method. But just don't forget that a very high impedance at resonance can exceed the reactive impedance of your 6dB/octave crossover device and, in this case, no crossover has been performed.
For example, let's assume you have a tweeter rated from 800Hz to 16Khz and you want to use a 6dB/octave crossover. I would not recommend anything below 1.6Khz, and it would be better to go even higher - like 3Khz. So but for the sake of example, let's see what happens with a 2Khz crossover having a 6dB/octave slope. This is formed with a 5uF capacitor, assuming the tweeter has advertised impedance of 8 ohms.
At 4Khz, we'd have 8 ohms reactive impedance, and the tweeter would be at -3dB
at 2Khz, we'd have 16 ohms reactive impedance, and the tweeter would be at -7dB
at 1Khz, we'd have 32 ohms reactive impedance, and could expect the tweeter to be -13dB, and
at 500Hz, we'd have 64 ohms reactive impedance, and would expect -19dB from the tweeter.But what if the tweeter's impedance at resonance is 40 ohms at 600Hz? The reactive impedance of our 5uF crossover capacitor is only 42 ohms at this point - so the tweeter will be only -3dB attenuated at its resonant frequency. That's a long way from our expected -18dB, and we'll probably destroy this tweeter.
So be careful with 1st order networks. Check the motor's impedance at resonance when you can, and use a different network or shift the 1st order crossover frequency very far away when you can't.
Application of 12dB/octave crossovers doesn't require as much analysis. All high order networks are relatively safe. They have shunt reactances that make driver impedance a relatively trivial matter in determining slope. A 12dB/octave crossover should be built where Xc and Xl are equal to the motor's advertised impedance at the intended crossover frequency. That's pretty much all there is to these little guys.
So just use the standard reactive impedance formulas to determine values for your inductor and for your capacitor:
2nd order (12dB/octave) network calculation:
L = speaker impedance / (2 * PI * F)
and C = 1 / (2 * PI * F * speaker impedance)Nothing to 'em. Sling some solder and you're ready to rock-n-roll.
Wayne
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Follow Ups
- Makin' it easy - Wayne Parham 03/22/0120:06:31 03/22/01 (1)
- to the printer,thanks NT - Art J. 07:13:20 03/23/01 (0)
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