5.13 How do I design my own passive crossovers? [JSC,JR]

A first order high pass crossover is simply a capacitor placed inline
with the driver. A first
order low pass crossover is an inductor inline with the driver. These
roles can be reversed
under certain circumstances: a capacitor in parallel with a driver will
act as a low pass
filter, while an inductor in parallel with a driver will act as a high
pass filter. However, a
parallel device should not be the first element in a set; for example,
using only a capacitor
in parallel to a driver will cause the amplifier to see a short circuit
above the cutoff
frequency. Thus, a series device should always be the first element in a
crossover. 

When like combinations are used, the order increases: a crossover in
series followed by an
inductor in parallel is a second order high pass crossover. An inductor
in series followed
by a capacitor in parallel is a second order low pass crossover. 

To calculate the correct values of capacitors and inductors to use, you
need to know the
nominal impedance (Z) of the circuit in ohms and the desired crossover
point (f) in hertz.
The needed capacitance in farads is then 1/(2 x pi x f x Z). The needed
inductance in
henries is Z/(2 x pi x f). For example, if the desired crossover point
is 200Hz for a 4 ohm
driver, you need a 198.9 x 10^-6 F (or 199uF) capacitor for a high pass
first order filter,
or a 3.18 x 10^-3 H (or 3.18mH) inductor for a low pass first order
filter. 

To build a second order passive crossover, calculate the same initial
values for the
capacitance and inductance, and then decide whether you want a
Linkwitz-Riley,
Butterworth, or Bessel filter. An L-R filter matches the attenuation
slopes so that both
-3dB points are at the same frequency, so that the system response is
flat at the crossover
frequency. A Butterworth filter matches the slopes so that there is a
peak at the crossover
frequency, and a Bessel filter is in between the two. For an L-R filter,
halve the
capacitance and double the inductance. For a Butterworth filter,
multiply the capacitance
by 1/sqrt(2) and the inductance by sqrt(2). For a Bessel filter,
multiply the capacitance by
1/sqrt(3) and the inductance by sqrt(3). 

You should realize, too, that crossovers induce a phase shift in the
signal of 90 degrees per
order. In a second order filter, then, this can be corrected by simply
reversing the polarity
of one of the drivers, since they would otherwise be 180 degrees out of
phase with
respect to each other. In any case with any crossover, though, you
should always
experiment with the polarity of the drivers to achieve the best total
system response. 

One other thing to consider when designing passive crossovers is the
fact that most
passive crossovers are designed based on the speakers' nominal
impedance. This value is
NOT constant, as it varies with frequency. Therefore, the crossover will
not work as it has
been designed. To combat this problem, a Zobel circuit (also known as
"Impedance
Stabilization Network") should be used. This consists of a capacitor and
resistor in series
with one another, in parallel with the speaker, e.g., 

                          ________                __
                 +  o----|        |----o-----o + |  | /
           INPUT         |  Xover |    R1        |  |/
                         |        |    C1        |  |\
                 -  o----|________|----o-----o - |__| \


To calculate these values, R1 = Re (in ohms) x 1.25, and C1 = (Lces {in
henries} / Re^2)
* 10^6. See 4.1 for definitions of Re and Lces. R1 will be in ohms, and
C1 will be in uF
(micro- farads). As an example, an Orion XTR10 single voice coil woofer
has Re = 3.67
ohms and Lces = 0.78 mH. So, R1 = 3.67 * 1.25 = 4.6 ohms. C1 = ( 7.8E-4
/ 3.67^2 )
* 10^6 = 57.9 uF (be careful with units -- 0.78 mH = 7.8E-4 H) 

As with the definition of crossover slopes, the above definition of the
phase shift
associated with a crossover is also an approximation. This will be
addressed in future
revisions of this document. 

5.14 How do I build my own passive crossovers? [JSC] 

This section assumes that you have a basic understanding of how to
solder, so the actual
assembly of the crossover is not discussed. Rather, tips on choosing the
proper types of
capacitors and inductors are given here. 

To obtain low insertion losses, the inductors should have very low
resistance, perhaps as
low as 0.1 to 0.2 ohms. 

Also, be sure to select capacitors with proper voltage ratings. The
maximum voltage in the
circuit will be less than the square root of the product of the maximum
power in the circuit
and the nominal impedance of the driver. For example, a 4 ohm woofer
being given 100W
peak will see a maximum voltage of sqrt(100*4) = sqrt(400) = 20V. Make
sure that the
capacitors are bipolar, too, since speaker signals are AC signals. If
you cannot find bipolar
capacitors, you can use two polar capacitors in parallel and in opposite
polarity (+ to -
and - to +). However, there are some possible problems with this
approach: the forward
voltage rating will probably not be equal to the reverse voltage rating,
and there could be a
reverse capacitance as well. Both problems could adversely affect your
circuit if you
decide to use opposite polarity capacitors in parallel.