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29th April 2004, 03:15 PM  #1 
diyAudio Member
Join Date: Apr 2004
Location: Milano

Zobel network, notch filters and ... a lot of confusion
Hi all,
I'm trying to start understanding something about Zobel netwoks and notch filters, and I'm reading anything I can find on the Net. My problem is that I find so many different formulas, giving so many different results, that I'm convinced that the thruth (if any) should be somewhere else. To test the formulas I'm using Speaker Worshop (it could be THE problem), and I was unable to check any of the (all different) result I've got. Is there something more "scientific" on the Net ? Thanks
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Teodoro 
29th April 2004, 07:52 PM  #2 
diyAudio Member

Here is a zobel
C = Le/(Rc2) Rc =1.25 * Re Where Rc is the resistor value and C is the cap. A notch filter is around posted by me just use the search function and you'll find it.
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29th April 2004, 07:55 PM  #3 
diyAudio Member

I assume you've actually used these equations with good results? Like him, I've found at least 5 different zobel equations, and I've never been sure whether any was more accurate than the rest.

29th April 2004, 09:06 PM  #4 
diyAudio Member
Join Date: Feb 2004
Location: Stockholm

I think the reason for the many equations is that a RC zobel network cannot give anything but an approximation to a constant load. The voice coil inductance does not behave like an ordinary inductance.
The ordinary inductor has an impedance Zl=jwL On the othe rhand, a typical voice coil inductance can be approximated by Zlvc=K*w^n * (cos (n*pi/2) + j * sin (n*pi/2)) where n= 0.6..0.8, typically. Note that if n=1, the equation becomes that of the ordinary inductor. The equation looks complicated, but the important part is w^n, ie the impedance is not proportional to the frequency, but increases slightly slower. Such a component is impossible to compensate for perfectly with a RC network, but with a bit of tweaking, a reasonably good compensation can be acheived. I suppose that this tweaking part is the reason for the slightly different "rules of thumb" that you have found. HTH 
29th April 2004, 09:37 PM  #5 
diyAudio Member

I have used the equation I posted with a driver in LSPcad it provided more then good enough results for its use. Obviously tinkering with the values a bit got better results but this was not by much.
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30th April 2004, 05:54 AM  #6 
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Join Date: Apr 2004
Location: Milano

Agree ...
I agree with Svante, the formula
Z=Re+Le*(jw)^n (it's the same as yours) was given by Leech on purely physical grounds, and I have "tested" it, using Excel and Solver (that is Mean Square Root methods), on many loudspeakers impendance curves. My problem is that even the formulas given by Leech on a different paper seem not to work, and the rest of the humanity ... gives 6 different interpretations: none working !
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Teodoro 
30th April 2004, 09:28 AM  #7 
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Join Date: Feb 2004
Location: Stockholm

Teodorom:
If you are thinking of the same article as I am, with a number of RC links, the approach should work. I have not tried it though even if I wrote a related computer program once, that filtered a signal over a wide frequency range at a constant tilt anywhere in the range +/ 6dB/octave. Could you tell us something on why you are interested in this, is it a purely theoretical interest, or are you trying to do a practical design? And why do you want to flatten the impedance curve? 
30th April 2004, 09:44 AM  #8 
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Join Date: Apr 2004
Location: Milano

Both theoretical and practical
Hi Svante,
my interests are both theoretical and practical. I have a couple of speakers I made a long time ago using Coral/Peerless drivers (and a Coral project). The sound is pretty good, but it can be improved. First I made calculations using the MJK worksheets for the vented box, and I discovered that a light stuffing could help. It was true ! Now basses are deeper and the mediums are clearer. Now I'm adressing the crossover. For sure I could use the same schema and values, using better components (now I have nonpolarized electrolic caps and inductances with core: http://www.coralelectronic.com/Home/Filtri/NT_850_C.htm). This schema seems too generic (it's used even with different woofers) so I would like to check the values too. Why: It is said that it is worthwhile to control the impendace rise in the crossover region. Thanks
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Teodoro 
30th August 2010, 05:50 AM  #9 
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Join Date: Mar 2005
Location: Taiwan

teodorom, it seems like you are determined to get things right
However, the fact is that zobels are based on the assumption of a simple driver model used to generate T/S parameters. Since the curve fitting criteria may be different, each different software will generate different parameters. So what I would just recommend is to use the equations for first estimate and adjust the values until you get what you want.
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