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MultiWay Conventional loudspeakers with crossovers 

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9th February 2010, 10:11 PM  #1 
diyAudio Member
Join Date: Feb 2009

Zobel calculation, help needed!
Hello Guys, I need some advice here...
First, I have a pair of 2way loudspeakers, consisting of a 8" midbass driver which runs fullrange without any crossover, and a 1" softdome 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 D26TG46, 1" soft dome, Impedance 6 ohms (nominal), measured dcresistance 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(Lowpass) 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. 
9th February 2010, 10:38 PM  #2 
diyAudio Member
Join Date: Feb 2002
Location: Western Sydney

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 
9th February 2010, 11:36 PM  #3 
diyAudio Member
Join Date: Feb 2002
Location: Western Sydney

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 
23rd February 2011, 05:45 PM  #4 
diyAudio Member
Join Date: Oct 2009
Location: Helsinki, Finland

Do you have a idea of the calculating zobel correlation when I have two drivers in series? Just dcresistanse 3.3ohm + 3.3ohm = 6.6ohm, 0.2mH + 0.2mH = 0.4mH?

23rd February 2011, 07:42 PM  #5  
diyAudio Member
Join Date: Nov 2009
Location: The Mountain, Framingham

Quote:
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. 

23rd February 2011, 08:42 PM  #6  
diyAudio Member
Join Date: Feb 2006
Location: Cascais

Quote:
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 D26TG46, only Vifa D26TG0506. 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.
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