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On Dec 25, 11:28 pm, "Chollie" wrote:
On Dec 25, 8:32 pm, wrote:
On Dec 25, 2:47 pm, "Chollie" wrote:

I am looking for a formula that was only in Volume 1 of
Vance Dickason's Loudspeaker Design Cookbook. If
anybody out there has a copy please email me so I
can get the formula from you. Thanks in advance.

As the Loudspeaker Design Cookbook is a derivative
work, and is based on the work of Thiele, Small and
others, perhaps going to the original sources will work.

What was the formula you're looking for supposed to do?

The formula was to calculate a resistance value to smooth
the roll off below Fs of a tweeter in the crossover. I drew
a 2nd order high pass circuit below to illustrate what I thin
I remember. I thought the formula stated the total dc
resistance of Lx + Rx should be the impedance of Lx at
the tweeter's Fs.

---------Cx---|------- +
|
Lx
| Tweeter
|
Rx
|
--------------|------- -

Thanks for any assistance you can provide.

The circuit you drew and your memory are both faulty.
First, the "impedance of Lx at the tweeter's Fs" is
0: at resonance, there is no capacitive or inductive
component to the impedance: it is purely resistive.

Secondly, the circuit you describe cannot "smooth
the roll off below Fs of a tweeter ." What you
describe is a simple shelving circuit, depending
upon the relative values of all the components.
Let's assume the LxRx corner frequency is reasonably
below the crossover point. The effect of the cricuit
you drew would be to convert the 2nd order rolloff
into a 1st order rolloff.

Perhaps what you are thinkg of is the standard
complex conjugate correction (often referred to
as a "Zobel") for the inductive component of the
driver's impedance ABOVE resonance (and, presumably,
the crossover frequency is selected to be above the
tweeter's resonance).

In the simplest such model, the tweeter's impedance
above the resonance behaves like a series resistor
and inductor. something like:

+---+
|
Le
|
Re
|
+---+

A shunt conjugate circuit to eliminate the
inductive component of the impedance would
consist of a series resistor and capacitor,
e.g.:

+---+
|
Cc
|
Rc
|
+---+

Assuming the driver resistance and inductance were
constant with frequency (they are not), you'd end
up with a circuit (including the tweeter model
above) which looks like:

+---+---+
| |
Cc Le
| |
Rc Re
| |
+---+---+

Now, again assuming that the values of Re and
Le were independent of frequency (and, again,
be cautined that, due to secondary effects,
they are not), then one would determine the
values of Cc and Rc as:

Cc = Le / Re^2

and

Rc = Re

The result will be that instead of a rising
impedance with frequency, the load presented
to the crossover will be, in essence, constant
with frequency and thus resistive. Especially
for a first order network, this is important
to achieve the correct response (with a rising,
partially inductive impedance, you CANNOT get
a first-order response from a passive network).

Two problems with this approach:

First, as I already mentioned, the technique assumes
incorrectly that the voice coil resistance and
inductance are independent of frequency (I don't
mean reactance, I mean inductance). Due to effects
such as eddy current losses in the magnet structure,
the resistance portion tends to rise as roughly
the square root of frequency, and the inductive
portion tends to fall as the square root of
frequency.

Second issue is that it fails to take into account
the more important and often more challenging issue
of the rise in impedance at the tweeter's mechanical
resonance, usually not far below the crossover
(like within an octave in many cases). If the tweeter
is not well mechanically damped, this rise is often
on the order of twice the DC resistance and more,
and makes a shambles of any passive crossover response.
To adequately correct for that takes much more,
essentially a series LRC tank circuit, where the
component values are determined, in essence, by the
tweeter's moving mass, suspension stiffness and
frictional losses.

Fortunately, many tweeters, especially those which
employ ferrofluid for damping and colling, are highly
damped at resonance and present a more constant load.

By the way, in later editions of the Loudspeaker
Design Cookbook, these and other formulas are found
in the chapter on crossovers.