# 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 capacitor 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 * pi * f * Z). The needed inductance in henries is Z/(2 *
pi * 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 an
"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.

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