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Old 9th February 2010, 10:11 PM   #1
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Default Zobel calculation, help needed!

Hello Guys, I need some advice here...

First, I have a pair of 2-way loudspeakers, consisting of a 8" mid-bass driver which runs fullrange without any crossover, and a 1" soft-dome tweeter with a single cap of 4,7uF in series.

I found out that there was something wrong with the sound I got from these speakers, so recently I tried out a zobel network parallel to the tweeter, with fantastic results!
But I have a few questions about the zobel network in general.

Here are a few parametres of the drivers:
Midbass: 8", 8 ohm (nominal), fullrange
Tweeter: Vifa D26TG-46, 1" soft dome, Impedance 6 ohms (nominal), measured dc-resistance 4,6 ohm, measured voice coil inductance 0,7 mH (in fact, 0,666 mH for one, 0,764 mH for the other one, so I thought to say 0,7 mH would be just fine).

Now, on this site
Speaker Zobel / Impedance Equalization Circuit Calculator
the calculations give the values of (rounded) Cz=21uF, Rz=5,6ohm.
Same values when calculated on this page:
ZOBEL Filters for CROSSOVER Networks

But DIFFERENT value for Cz when calculated on this page:
Crossover Design Chart and Inductance vs. Frequency Calculator(Low-pass)
which says Cz=33uF, Rz=5,6ohm.

Why?

And one more question: Let's assume Cz=21uF is the correct value. What happens when I use different values for Rz (I know, the impedance curve would differ, but I mean soundwise)? Ok, not less than 5,6 ohm (because of the total impedance, which should remain above 6 ohms over the frequency range), but what about values of 10,0 ohms or 15,0 ohms? I tried it, and I found of course differences in the sound of the tweeter, but I don't know what effect is responsible for this.

These pages mention that the value for Rz is always Re of the driver multiplied with 1,25. But I saw some crossover circuits with zobels on tweeters and the values for the resistor Rz were always larger, sometimes much larger than Re x 1,25.

Why?

I would be totally happy if someone of you could bring a little bit of light into this!
Thanks!
Martin

Last edited by martinbls; 9th February 2010 at 10:14 PM.
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Old 9th February 2010, 10:38 PM   #2
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There are two methods for calculating the values, one uses the formulas in your first link or variants - to complicate matters further, some calculators use a multiplying factor for Re (In your case 1.25. others use a different factor or none)
The other method involves the Le in the formula of the driver IIRC.
The moral – when using online calculators, you need to know which method the calculator is using, and understand the implications of that.
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Impedance varies with frequency, use impedance plots of your drivers and make crossover calculations using the actual impedance of the driver at the crossover frequency
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Old 9th February 2010, 11:36 PM   #3
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googling around for the derivation of the zobel formula, I can't find a derivation where the 1.25x Re is justified - any sites that use that multiplier simply state it as gospel.
I suspect it's to make the Re closer to a 'nominal' value rather than actual impedance...???
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Impedance varies with frequency, use impedance plots of your drivers and make crossover calculations using the actual impedance of the driver at the crossover frequency
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Old 23rd February 2011, 05:45 PM   #4
kahvis is offline kahvis  Finland
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Do you have a idea of the calculating zobel correlation when I have two drivers in series? Just dc-resistanse 3.3ohm + 3.3ohm = 6.6ohm, 0.2mH + 0.2mH = 0.4mH?
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Old 23rd February 2011, 07:42 PM   #5
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Quote:
Originally Posted by kahvis View Post
Do you have a idea of the calculating zobel correlation when I have two drivers in series? Just dc-resistanse 3.3ohm + 3.3ohm = 6.6ohm, 0.2mH + 0.2mH = 0.4mH?
Yes, 2 drivers in series will have double the R and double the L.

I think the main reason why the formulas are a little approximate is that the inductance rise is never ideal. Rather than a 6dB per Octave rise as from a real inductor, it rises at a slower rate, due to the loosly coupled iron of the core pole within the voice coil. This make it impossible for a simple conjugate to exactly flatten impedance.

David S.
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Old 23rd February 2011, 08:42 PM   #6
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Quote:
Originally Posted by martinbls View Post
...
Now, on this site
Speaker Zobel / Impedance Equalization Circuit Calculator
the calculations give the values of (rounded) Cz=21uF, Rz=5,6ohm.
Same values when calculated on this page:
ZOBEL Filters for CROSSOVER Networks

But DIFFERENT value for Cz when calculated on this page:
Crossover Design Chart and Inductance vs. Frequency Calculator(Low-pass)
which says Cz=33uF, Rz=5,6ohm.

Why?
...
I'm guessing here.
First formulas have Cz=Le/Rz2 for the value of the resistor (Rz) =21.
Third formula has Cz=Le/Re2 for the value of the driver Re (Re) =33.
Wayne P. is using the second formula in his book/notes "Speaker motors and passive crossover filters" Feb, 2002 (The formula for calculating an optimal RC damper). He also advises for not using zobels on tweeters. (But if it's working for you fine.)
I could not find the tweeter you mention Vifa D26TG-46, only Vifa D26TG-05-06.
With a slight problem, if you have ressonance frequency very high e.g. 1500Hz, it might affect your xover, thus not optimized first order system, and the need (you say) of the zobel.
My guess.

Last edited by Inductor; 23rd February 2011 at 08:57 PM.
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