Zobel Calcs making me crazy!

[MtnBob]

OK, I'm already crazy, but this is making it worse.
I'm working with some online calculators and formulas to figure out Zobel values, but I'm getting numbers all over the place!
3 places say 7.99 uF, 15.5 ohms
one says 7.5 uF, 8 ohms
one says 12.46 uF, 15.5 ohms
one says 1.9895 uF, 20 ohms
and another says 3.9 uF, 10 ohms
The last two ask for Re and Freq that impedance doubles, the others for Re and Le.
The values I'm using are: Re 12.4, Le 1.92 Freq 5000 hz
So do I go with the majority, something inbetween, or what?
Thanks for your help/suggestions.

MB

[GM]

Greets!

7.99 uF/15.5 ohms is the correct textbook calcs, but better to reactance annul Re:

resistor (ohms) = 1.25*Re

cap (uF) = 10^6/(2*pi*Re*F)

where:

F = frequency at 2*Re

GM

[MtnBob]

Thanks, Gm
I get 2.567 uF and 15.5 ohms. Pretty much in the middle of the two sites which used F@2Re. I wish all these sites would post the formulas they use for their calculators - and their rational for using that particular formula, since there seems to be several "correct" ways of arriving at the values.
Pretty confusing for those of us who are lacking knowledge and testing equipment.

[MJK]

I think that the biggest problem with deriving a single pair of equations for the Zobel component values is the real life non-constant voice coil impedance properties. If you look closely at the voice coil imedance (magnitude and phase), and then try and calculate the resistance and inductance of the voice coil at several frequencies, you will find that the results are not constant.

It is easy to derive a set of expressions for the R and C of the Zobel based on an assumed constant R and L for the voice coil. Unfortunately in the real world R and L of the voice coil are functions of frequency. The expressions that GM provided are reasonable rules of thumb :

R (ohms) = 1.25*Re

C (uF) = 10^6/(2*pi*Re*F)

where:

F = frequency at 2*Re

The other thing I have found when using real impedance data and calculating the corrected impedance response with a Zobel is that the Zobel values are not very sensitive. If your R or C are not exact as calculated, it really has a minimal impact on the final combined impedance. The Zobel is a forgiving design.

[MtnBob]

Martin, thanks for the encouraging words. It seems that everything is more complicated than it seems at first, but it's nice to know that this, at least is easy enough for us beginners to get right.

MB